Merge pull request #887 from NathanFallet/rsa

RSA

CryptoSwift.xcodeproj/project.pbxproj

@@ -15,6 +15,30 @@
 		35F3E51C23BF9A6700A024A1 /* OCB.swift in Sources */ = {isa = PBXBuildFile; fileRef = 35F3E51B23BF9A6700A024A1 /* OCB.swift */; };
 		42012783267A6F1C00F82506 /* ISO10126Padding.swift in Sources */ = {isa = PBXBuildFile; fileRef = 42012782267A6F1C00F82506 /* ISO10126Padding.swift */; };
 		674A736F1BF5D85B00866C5B /* RabbitTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 674A736E1BF5D85B00866C5B /* RabbitTests.swift */; };
+		6A072FF726CAB3F900F4E94F /* RSA.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6A072FF626CAB3F900F4E94F /* RSA.swift */; };
+		6A7CDEED26CD1E4C00FFB1AF /* RSATests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6A7CDEEC26CD1E4C00FFB1AF /* RSATests.swift */; };
+		6AC893F626DB950F00F7E787 /* Addition.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E026DB950C00F7E787 /* Addition.swift */; };
+		6AC893F726DB950F00F7E787 /* Square Root.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E126DB950C00F7E787 /* Square Root.swift */; };
+		6AC893F826DB950F00F7E787 /* GCD.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E226DB950D00F7E787 /* GCD.swift */; };
+		6AC893F926DB950F00F7E787 /* Comparable.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E326DB950D00F7E787 /* Comparable.swift */; };
+		6AC893FA26DB950F00F7E787 /* Hashable.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E426DB950D00F7E787 /* Hashable.swift */; };
+		6AC893FB26DB950F00F7E787 /* Bitwise Ops.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E526DB950D00F7E787 /* Bitwise Ops.swift */; };
+		6AC893FC26DB950F00F7E787 /* Codable.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E626DB950D00F7E787 /* Codable.swift */; };
+		6AC893FD26DB950F00F7E787 /* Shifts.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E726DB950D00F7E787 /* Shifts.swift */; };
+		6AC893FE26DB950F00F7E787 /* Prime Test.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E826DB950D00F7E787 /* Prime Test.swift */; };
+		6AC893FF26DB950F00F7E787 /* Words and Bits.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893E926DB950D00F7E787 /* Words and Bits.swift */; };
+		6AC8940026DB950F00F7E787 /* Subtraction.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893EA26DB950D00F7E787 /* Subtraction.swift */; };
+		6AC8940126DB950F00F7E787 /* Data Conversion.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893EB26DB950D00F7E787 /* Data Conversion.swift */; };
+		6AC8940226DB950F00F7E787 /* Multiplication.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893EC26DB950D00F7E787 /* Multiplication.swift */; };
+		6AC8940326DB950F00F7E787 /* Integer Conversion.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893ED26DB950E00F7E787 /* Integer Conversion.swift */; };
+		6AC8940426DB950F00F7E787 /* Floating Point Conversion.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893EE26DB950E00F7E787 /* Floating Point Conversion.swift */; };
+		6AC8940526DB950F00F7E787 /* Strideable.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893EF26DB950E00F7E787 /* Strideable.swift */; };
+		6AC8940626DB950F00F7E787 /* BigInt.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893F026DB950E00F7E787 /* BigInt.swift */; };
+		6AC8940726DB950F00F7E787 /* Exponentiation.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893F126DB950E00F7E787 /* Exponentiation.swift */; };
+		6AC8940826DB950F00F7E787 /* Random.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893F226DB950E00F7E787 /* Random.swift */; };
+		6AC8940926DB950F00F7E787 /* String Conversion.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893F326DB950E00F7E787 /* String Conversion.swift */; };
+		6AC8940A26DB950F00F7E787 /* BigUInt.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893F426DB950E00F7E787 /* BigUInt.swift */; };
+		6AC8940B26DB950F00F7E787 /* Division.swift in Sources */ = {isa = PBXBuildFile; fileRef = 6AC893F526DB950E00F7E787 /* Division.swift */; };
 		750509991F6BEF2A00394A1B /* PKCS7.swift in Sources */ = {isa = PBXBuildFile; fileRef = 750509981F6BEF2A00394A1B /* PKCS7.swift */; };
 		750CC3EB1DC0CACE0096BE6E /* BlowfishTests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 750CC3EA1DC0CACE0096BE6E /* BlowfishTests.swift */; };
 		75100F8F19B0BC890005C5F5 /* Poly1305Tests.swift in Sources */ = {isa = PBXBuildFile; fileRef = 75100F8E19B0BC890005C5F5 /* Poly1305Tests.swift */; };
@@ -207,6 +231,30 @@
 		35F3E51D23BF9AD300A024A1 /* AESOCBTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = AESOCBTests.swift; sourceTree = "<group>"; };
 		42012782267A6F1C00F82506 /* ISO10126Padding.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = ISO10126Padding.swift; sourceTree = "<group>"; };
 		674A736E1BF5D85B00866C5B /* RabbitTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = RabbitTests.swift; sourceTree = "<group>"; };
+		6A072FF626CAB3F900F4E94F /* RSA.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = RSA.swift; sourceTree = "<group>"; };
+		6A7CDEEC26CD1E4C00FFB1AF /* RSATests.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = RSATests.swift; sourceTree = "<group>"; };
+		6AC893E026DB950C00F7E787 /* Addition.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Addition.swift; sourceTree = "<group>"; };
+		6AC893E126DB950C00F7E787 /* Square Root.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = "Square Root.swift"; sourceTree = "<group>"; };
+		6AC893E226DB950D00F7E787 /* GCD.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = GCD.swift; sourceTree = "<group>"; };
+		6AC893E326DB950D00F7E787 /* Comparable.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Comparable.swift; sourceTree = "<group>"; };
+		6AC893E426DB950D00F7E787 /* Hashable.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Hashable.swift; sourceTree = "<group>"; };
+		6AC893E526DB950D00F7E787 /* Bitwise Ops.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = "Bitwise Ops.swift"; sourceTree = "<group>"; };
+		6AC893E626DB950D00F7E787 /* Codable.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Codable.swift; sourceTree = "<group>"; };
+		6AC893E726DB950D00F7E787 /* Shifts.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Shifts.swift; sourceTree = "<group>"; };
+		6AC893E826DB950D00F7E787 /* Prime Test.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = "Prime Test.swift"; sourceTree = "<group>"; };
+		6AC893E926DB950D00F7E787 /* Words and Bits.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = "Words and Bits.swift"; sourceTree = "<group>"; };
+		6AC893EA26DB950D00F7E787 /* Subtraction.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Subtraction.swift; sourceTree = "<group>"; };
+		6AC893EB26DB950D00F7E787 /* Data Conversion.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = "Data Conversion.swift"; sourceTree = "<group>"; };
+		6AC893EC26DB950D00F7E787 /* Multiplication.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Multiplication.swift; sourceTree = "<group>"; };
+		6AC893ED26DB950E00F7E787 /* Integer Conversion.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = "Integer Conversion.swift"; sourceTree = "<group>"; };
+		6AC893EE26DB950E00F7E787 /* Floating Point Conversion.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = "Floating Point Conversion.swift"; sourceTree = "<group>"; };
+		6AC893EF26DB950E00F7E787 /* Strideable.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Strideable.swift; sourceTree = "<group>"; };
+		6AC893F026DB950E00F7E787 /* BigInt.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BigInt.swift; sourceTree = "<group>"; };
+		6AC893F126DB950E00F7E787 /* Exponentiation.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Exponentiation.swift; sourceTree = "<group>"; };
+		6AC893F226DB950E00F7E787 /* Random.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Random.swift; sourceTree = "<group>"; };
+		6AC893F326DB950E00F7E787 /* String Conversion.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = "String Conversion.swift"; sourceTree = "<group>"; };
+		6AC893F426DB950E00F7E787 /* BigUInt.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BigUInt.swift; sourceTree = "<group>"; };
+		6AC893F526DB950E00F7E787 /* Division.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Division.swift; sourceTree = "<group>"; };
 		750509981F6BEF2A00394A1B /* PKCS7.swift */ = {isa = PBXFileReference; lastKnownFileType = sourcecode.swift; path = PKCS7.swift; sourceTree = "<group>"; };
 		750CC3EA1DC0CACE0096BE6E /* BlowfishTests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = BlowfishTests.swift; sourceTree = "<group>"; };
 		75100F8E19B0BC890005C5F5 /* Poly1305Tests.swift */ = {isa = PBXFileReference; fileEncoding = 4; lastKnownFileType = sourcecode.swift; path = Poly1305Tests.swift; sourceTree = "<group>"; };
@@ -379,6 +427,35 @@
 			name = Frameworks;
 			sourceTree = "<group>";
 		};
+		6AC893DF26DB94F700F7E787 /* BigInt */ = {
+			isa = PBXGroup;
+			children = (
+				6AC893E026DB950C00F7E787 /* Addition.swift */,
+				6AC893F026DB950E00F7E787 /* BigInt.swift */,
+				6AC893F426DB950E00F7E787 /* BigUInt.swift */,
+				6AC893E526DB950D00F7E787 /* Bitwise Ops.swift */,
+				6AC893E626DB950D00F7E787 /* Codable.swift */,
+				6AC893E326DB950D00F7E787 /* Comparable.swift */,
+				6AC893EB26DB950D00F7E787 /* Data Conversion.swift */,
+				6AC893F526DB950E00F7E787 /* Division.swift */,
+				6AC893F126DB950E00F7E787 /* Exponentiation.swift */,
+				6AC893EE26DB950E00F7E787 /* Floating Point Conversion.swift */,
+				6AC893E226DB950D00F7E787 /* GCD.swift */,
+				6AC893E426DB950D00F7E787 /* Hashable.swift */,
+				6AC893ED26DB950E00F7E787 /* Integer Conversion.swift */,
+				6AC893EC26DB950D00F7E787 /* Multiplication.swift */,
+				6AC893E826DB950D00F7E787 /* Prime Test.swift */,
+				6AC893F226DB950E00F7E787 /* Random.swift */,
+				6AC893E726DB950D00F7E787 /* Shifts.swift */,
+				6AC893E126DB950C00F7E787 /* Square Root.swift */,
+				6AC893EF26DB950E00F7E787 /* Strideable.swift */,
+				6AC893F326DB950E00F7E787 /* String Conversion.swift */,
+				6AC893EA26DB950D00F7E787 /* Subtraction.swift */,
+				6AC893E926DB950D00F7E787 /* Words and Bits.swift */,
+			);
+			path = BigInt;
+			sourceTree = "<group>";
+		};
 		75211F93207249D8004E41F8 /* CryptoSwift-TestHostApp */ = {
 			isa = PBXGroup;
 			children = (
@@ -453,6 +530,7 @@
 				757DA2521A4ED0A4002BA3EF /* PaddingTests.swift */,
 				75482EA31CB310B7001F66A5 /* PBKDF.swift */,
 				7576F6F6207290F8006688F8 /* PBKDFPerf.swift */,
+				6A7CDEEC26CD1E4C00FFB1AF /* RSATests.swift */,
 				75C2E76C1D55F097003D2BCA /* Access.swift */,
 				756BFDCA1A82B87300B9D9A4 /* Bridging.h */,
 			);
@@ -518,6 +596,7 @@
 				75EC52391EE8B6CA0048EB3B /* Array+Extension.swift */,
 				75EC523A1EE8B6CA0048EB3B /* Authenticator.swift */,
 				75EC523B1EE8B6CA0048EB3B /* BatchedCollection.swift */,
+				6AC893DF26DB94F700F7E787 /* BigInt */,
 				75EC523C1EE8B6CA0048EB3B /* Bit.swift */,
 				75EC523D1EE8B6CA0048EB3B /* BlockCipher.swift */,
 				75EC523E1EE8B6CA0048EB3B /* BlockMode */,
@@ -561,6 +640,7 @@
 				754310432050111A003FB1DF /* CompactMap.swift */,
 				75B3ED76210F9DF7005D4ADA /* BlockDecryptor.swift */,
 				75B3ED78210FA016005D4ADA /* BlockEncryptor.swift */,
+				6A072FF626CAB3F900F4E94F /* RSA.swift */,
 				753674062175D012003E32A6 /* StreamDecryptor.swift */,
 				756A64C52111083B00BE8805 /* StreamEncryptor.swift */,
 			);
@@ -663,6 +743,8 @@
 			dependencies = (
 			);
 			name = CryptoSwift;
+			packageProductDependencies = (
+			);
 			productName = CryptoSwift;
 			productReference = 754BE45519693E190098E6F3 /* CryptoSwift.framework */;
 			productType = "com.apple.product-type.framework";
@@ -769,6 +851,8 @@
 				Base,
 			);
 			mainGroup = 754BE44B19693E190098E6F3;
+			packageReferences = (
+			);
 			productRefGroup = 754BE45619693E190098E6F3 /* Products */;
 			projectDirPath = "";
 			projectRoot = "";
@@ -835,8 +919,11 @@
 			buildActionMask = 2147483647;
 			files = (
 				42012783267A6F1C00F82506 /* ISO10126Padding.swift in Sources */,
+				6AC8940926DB950F00F7E787 /* String Conversion.swift in Sources */,
+				6AC8940226DB950F00F7E787 /* Multiplication.swift in Sources */,
 				0AF023D5230F2B0F008E4E68 /* ISO78164Padding.swift in Sources */,
 				75EC52861EE8B8170048EB3B /* CFB.swift in Sources */,
+				6AC893FF26DB950F00F7E787 /* Words and Bits.swift in Sources */,
 				75EC52901EE8B81A0048EB3B /* Collection+Extension.swift in Sources */,
 				0EE73E71204D598100110E11 /* CMAC.swift in Sources */,
 				7523742D2083C61D0016D662 /* GCM.swift in Sources */,
@@ -846,15 +933,19 @@
 				75EC529F1EE8B8230048EB3B /* HMAC.swift in Sources */,
 				75EC52B91EE8B83D0048EB3B /* ZeroPadding.swift in Sources */,
 				7529366A20683DFC00195874 /* AEADChaCha20Poly1305.swift in Sources */,
+				6AC893FA26DB950F00F7E787 /* Hashable.swift in Sources */,
 				75EC529E1EE8B8230048EB3B /* Generics.swift in Sources */,
 				75EC52AA1EE8B83D0048EB3B /* Poly1305.swift in Sources */,
 				75EC52AC1EE8B83D0048EB3B /* Cryptor.swift in Sources */,
 				75EC52821EE8B8170048EB3B /* BlockMode.swift in Sources */,
 				75EC52AE1EE8B83D0048EB3B /* SecureBytes.swift in Sources */,
+				6AC893FC26DB950F00F7E787 /* Codable.swift in Sources */,
+				6AC8940126DB950F00F7E787 /* Data Conversion.swift in Sources */,
 				75EC528F1EE8B81A0048EB3B /* Cipher.swift in Sources */,
 				75B3ED79210FA016005D4ADA /* BlockEncryptor.swift in Sources */,
 				75EC52A01EE8B8290048EB3B /* Int+Extension.swift in Sources */,
 				75EC52B01EE8B83D0048EB3B /* SHA2.swift in Sources */,
+				6AC893F626DB950F00F7E787 /* Addition.swift in Sources */,
 				752BED9D208C120D00FC4743 /* Blowfish+Foundation.swift in Sources */,
 				75EC52B71EE8B83D0048EB3B /* Updatable.swift in Sources */,
 				75EC528E1EE8B81A0048EB3B /* Checksum.swift in Sources */,
@@ -862,33 +953,45 @@
 				75EC52811EE8B8130048EB3B /* BlockCipher.swift in Sources */,
 				75EC52941EE8B81A0048EB3B /* DigestType.swift in Sources */,
 				75EC529B1EE8B8200048EB3B /* Rabbit+Foundation.swift in Sources */,
+				6AC893F926DB950F00F7E787 /* Comparable.swift in Sources */,
 				756A64C62111083B00BE8805 /* StreamEncryptor.swift in Sources */,
+				6AC8940726DB950F00F7E787 /* Exponentiation.swift in Sources */,
+				6AC8940026DB950F00F7E787 /* Subtraction.swift in Sources */,
 				75EC52A61EE8B8390048EB3B /* PBKDF1.swift in Sources */,
+				6AC893FB26DB950F00F7E787 /* Bitwise Ops.swift in Sources */,
 				75EC52B41EE8B83D0048EB3B /* UInt32+Extension.swift in Sources */,
+				6AC8940526DB950F00F7E787 /* Strideable.swift in Sources */,
 				75EC52911EE8B81A0048EB3B /* Cryptors.swift in Sources */,
+				6AC893F726DB950F00F7E787 /* Square Root.swift in Sources */,
 				75EC52881EE8B8170048EB3B /* ECB.swift in Sources */,
 				75EC52841EE8B8170048EB3B /* CipherModeWorker.swift in Sources */,
 				75EC52A41EE8B8290048EB3B /* Operators.swift in Sources */,
 				75EC529A1EE8B8200048EB3B /* HMAC+Foundation.swift in Sources */,
+				6AC8940826DB950F00F7E787 /* Random.swift in Sources */,
 				75EC52B21EE8B83D0048EB3B /* String+Extension.swift in Sources */,
 				750509991F6BEF2A00394A1B /* PKCS7.swift in Sources */,
 				75EC52B51EE8B83D0048EB3B /* UInt64+Extension.swift in Sources */,
 				75EC52AF1EE8B83D0048EB3B /* SHA1.swift in Sources */,
 				75EC52801EE8B8130048EB3B /* Bit.swift in Sources */,
+				6AC8940326DB950F00F7E787 /* Integer Conversion.swift in Sources */,
 				75EC52971EE8B8200048EB3B /* ChaCha20+Foundation.swift in Sources */,
 				75F4E434216C93EF00F09710 /* CCM.swift in Sources */,
 				75EC52871EE8B8170048EB3B /* CTR.swift in Sources */,
+				6AC893FD26DB950F00F7E787 /* Shifts.swift in Sources */,
 				75EC52A21EE8B8290048EB3B /* MD5.swift in Sources */,
 				75EC527C1EE8B8130048EB3B /* AES.swift in Sources */,
 				752BED9E208C121000FC4743 /* Blowfish.swift in Sources */,
 				75EC52A91EE8B83D0048EB3B /* PKCS7Padding.swift in Sources */,
 				75EC52A51EE8B8290048EB3B /* Padding.swift in Sources */,
+				6AC8940A26DB950F00F7E787 /* BigUInt.swift in Sources */,
 				75EC527F1EE8B8130048EB3B /* BatchedCollection.swift in Sources */,
 				75EC52991EE8B8200048EB3B /* Data+Extension.swift in Sources */,
+				6AC8940426DB950F00F7E787 /* Floating Point Conversion.swift in Sources */,
 				75EC52B61EE8B83D0048EB3B /* UInt8+Extension.swift in Sources */,
 				75EC52891EE8B8170048EB3B /* OFB.swift in Sources */,
 				75EC52831EE8B8170048EB3B /* BlockModeOptions.swift in Sources */,
 				753674072175D012003E32A6 /* StreamDecryptor.swift in Sources */,
+				6AC8940626DB950F00F7E787 /* BigInt.swift in Sources */,
 				751EE9781F93996100161FFC /* AES.Cryptors.swift in Sources */,
 				75EC527D1EE8B8130048EB3B /* Array+Extension.swift in Sources */,
 				75D7AF38208BFB1600D22BEB /* UInt128.swift in Sources */,
@@ -896,11 +999,14 @@
 				75EC52A81EE8B8390048EB3B /* PKCS5.swift in Sources */,
 				1467460F2017BB3600DF04ED /* AEAD.swift in Sources */,
 				35F3E51C23BF9A6700A024A1 /* OCB.swift in Sources */,
+				6A072FF726CAB3F900F4E94F /* RSA.swift in Sources */,
+				6AC8940B26DB950F00F7E787 /* Division.swift in Sources */,
 				75EC528A1EE8B8170048EB3B /* PCBC.swift in Sources */,
 				75EC528D1EE8B81A0048EB3B /* ChaCha20.swift in Sources */,
 				75EC52851EE8B8170048EB3B /* CBC.swift in Sources */,
 				75EC52A71EE8B8390048EB3B /* PBKDF2.swift in Sources */,
 				75EC529D1EE8B8200048EB3B /* Utils+Foundation.swift in Sources */,
+				6AC893FE26DB950F00F7E787 /* Prime Test.swift in Sources */,
 				75EC527E1EE8B8130048EB3B /* Authenticator.swift in Sources */,
 				75EC52AB1EE8B83D0048EB3B /* Rabbit.swift in Sources */,
 				75B3ED77210F9DF7005D4ADA /* BlockDecryptor.swift in Sources */,
@@ -909,6 +1015,7 @@
 				75EC52981EE8B8200048EB3B /* Array+Foundation.swift in Sources */,
 				75EC52B11EE8B83D0048EB3B /* SHA3.swift in Sources */,
 				75EC52A31EE8B8290048EB3B /* NoPadding.swift in Sources */,
+				6AC893F826DB950F00F7E787 /* GCD.swift in Sources */,
 				81F279DD2181F58300449EDA /* Scrypt.swift in Sources */,
 				75EC52931EE8B81A0048EB3B /* Digest.swift in Sources */,
 			);
@@ -931,6 +1038,7 @@
 				81F279DF2181F5A000449EDA /* ScryptTests.swift in Sources */,
 				674A736F1BF5D85B00866C5B /* RabbitTests.swift in Sources */,
 				0EE73E74204D59C200110E11 /* CMACTests.swift in Sources */,
+				6A7CDEED26CD1E4C00FFB1AF /* RSATests.swift in Sources */,
 				750CC3EB1DC0CACE0096BE6E /* BlowfishTests.swift in Sources */,
 				757DA2531A4ED0A4002BA3EF /* PaddingTests.swift in Sources */,
 				14156CE52011422400DDCFBC /* ChaCha20Poly1305Tests.swift in Sources */,

README.md

@@ -522,6 +522,33 @@ let encrypt = try AEADChaCha20Poly1305.encrypt(plaintext, key: key, iv: nonce, a
 let decrypt = try AEADChaCha20Poly1305.decrypt(ciphertext, key: key, iv: nonce, authenticationHeader: header, authenticationTag: tagArr: tag)
 ```
 
+##### RSA
+
+RSA initialization from parameters
+
+```swift
+let input: Array<UInt8> = [0,1,2,3,4,5,6,7,8,9]
+
+let n: Array<UInt8> = // RSA modulus
+let e: Array<UInt8> = // RSA public exponent
+let d: Array<UInt8> = // RSA private exponent
+
+let rsa = RSA(n: n, e: e, d: d)
+
+do {
+    let encrypted = try rsa.encrypt(input)
+    let decrypted = try rsa.decrypt(encrypted)
+} catch {
+    print(error)
+}
+```
+
+RSA key generation
+
+```swift
+let rsa = RSA(keySize: 2048) // This generates a modulus, public exponent and private exponent with the given size
+```
+
 ## Author
 
 CryptoSwift is owned and maintained by [Marcin Krzyżanowski](http://www.krzyzanowskim.com)

Sources/CryptoSwift/Array+Extension.swift

@@ -24,6 +24,11 @@ extension Array {
   var slice: ArraySlice<Element> {
     self[self.startIndex ..< self.endIndex]
   }
+  
+  @inlinable
+  subscript (safe index: Index) -> Element? {
+    return indices.contains(index) ? self[index] : nil
+  }
 }
 
 extension Array where Element == UInt8 {

Sources/CryptoSwift/BigInt/Addition.swift

@@ -0,0 +1,126 @@
+//
+//  Addition.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+    //MARK: Addition
+    
+    /// Add `word` to this integer in place.
+    /// `word` is shifted `shift` words to the left before being added.
+    ///
+    /// - Complexity: O(max(count, shift))
+    internal mutating func addWord(_ word: Word, shiftedBy shift: Int = 0) {
+        precondition(shift >= 0)
+        var carry = word
+        var i = shift
+        while carry > 0 {
+            let (d, c) = self[i].addingReportingOverflow(carry)
+            self[i] = d
+            carry = (c ? 1 : 0)
+            i += 1
+        }
+    }
+
+    /// Add the digit `d` to this integer and return the result.
+    /// `d` is shifted `shift` words to the left before being added.
+    ///
+    /// - Complexity: O(max(count, shift))
+    internal func addingWord(_ word: Word, shiftedBy shift: Int = 0) -> BigUInt {
+        var r = self
+        r.addWord(word, shiftedBy: shift)
+        return r
+    }
+
+    /// Add `b` to this integer in place.
+    /// `b` is shifted `shift` words to the left before being added.
+    ///
+    /// - Complexity: O(max(count, b.count + shift))
+    internal mutating func add(_ b: BigUInt, shiftedBy shift: Int = 0) {
+        precondition(shift >= 0)
+        var carry = false
+        var bi = 0
+        let bc = b.count
+        while bi < bc || carry {
+            let ai = shift + bi
+            let (d, c) = self[ai].addingReportingOverflow(b[bi])
+            if carry {
+                let (d2, c2) = d.addingReportingOverflow(1)
+                self[ai] = d2
+                carry = c || c2
+            }
+            else {
+                self[ai] = d
+                carry = c
+            }
+            bi += 1
+        }
+    }
+
+    /// Add `b` to this integer and return the result.
+    /// `b` is shifted `shift` words to the left before being added.
+    ///
+    /// - Complexity: O(max(count, b.count + shift))
+    internal func adding(_ b: BigUInt, shiftedBy shift: Int = 0) -> BigUInt {
+        var r = self
+        r.add(b, shiftedBy: shift)
+        return r
+    }
+
+    /// Increment this integer by one. If `shift` is non-zero, it selects
+    /// the word that is to be incremented.
+    ///
+    /// - Complexity: O(count + shift)
+    internal mutating func increment(shiftedBy shift: Int = 0) {
+        self.addWord(1, shiftedBy: shift)
+    }
+
+    /// Add `a` and `b` together and return the result.
+    ///
+    /// - Complexity: O(max(a.count, b.count))
+    public static func +(a: BigUInt, b: BigUInt) -> BigUInt {
+        return a.adding(b)
+    }
+
+    /// Add `a` and `b` together, and store the sum in `a`.
+    ///
+    /// - Complexity: O(max(a.count, b.count))
+    public static func +=(a: inout BigUInt, b: BigUInt) {
+        a.add(b, shiftedBy: 0)
+    }
+}
+
+extension BigInt {
+    /// Add `a` to `b` and return the result.
+    public static func +(a: BigInt, b: BigInt) -> BigInt {
+        switch (a.sign, b.sign) {
+        case (.plus, .plus):
+            return BigInt(sign: .plus, magnitude: a.magnitude + b.magnitude)
+        case (.minus, .minus):
+            return BigInt(sign: .minus, magnitude: a.magnitude + b.magnitude)
+        case (.plus, .minus):
+            if a.magnitude >= b.magnitude {
+                return BigInt(sign: .plus, magnitude: a.magnitude - b.magnitude)
+            }
+            else {
+                return BigInt(sign: .minus, magnitude: b.magnitude - a.magnitude)
+            }
+        case (.minus, .plus):
+            if b.magnitude >= a.magnitude {
+                return BigInt(sign: .plus, magnitude: b.magnitude - a.magnitude)
+            }
+            else {
+                return BigInt(sign: .minus, magnitude: a.magnitude - b.magnitude)
+            }
+        }
+    }
+
+    /// Add `b` to `a` in place.
+    public static func +=(a: inout BigInt, b: BigInt) {
+        a = a + b
+    }
+}
+

Sources/CryptoSwift/BigInt/BigInt.swift

@@ -0,0 +1,74 @@
+//
+//  BigInt.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2015-12-27.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+//MARK: BigInt
+
+/// An arbitary precision signed integer type, also known as a "big integer".
+///
+/// Operations on big integers never overflow, but they might take a long time to execute.
+/// The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.
+///
+/// This particular big integer type uses base-2^64 digits to represent integers.
+///
+/// `BigInt` is essentially a tiny wrapper that extends `BigUInt` with a sign bit and provides signed integer
+/// operations. Both the underlying absolute value and the negative/positive flag are available as read-write 
+/// properties.
+///
+/// Not all algorithms of `BigUInt` are available for `BigInt` values; for example, there is no square root or
+/// primality test for signed integers. When you need to call one of these, just extract the absolute value:
+///
+/// ```Swift
+/// BigInt(255).abs.isPrime()   // Returns false
+/// ```
+///
+public struct BigInt: SignedInteger {
+    public enum Sign {
+        case plus
+        case minus
+    }
+
+    public typealias Magnitude = BigUInt
+
+    /// The type representing a digit in `BigInt`'s underlying number system.
+    public typealias Word = BigUInt.Word
+    
+    public static var isSigned: Bool {
+        return true
+    }
+
+    /// The absolute value of this integer.
+    public var magnitude: BigUInt
+
+    /// True iff the value of this integer is negative.
+    public var sign: Sign
+
+    /// Initializes a new big integer with the provided absolute number and sign flag.
+    public init(sign: Sign, magnitude: BigUInt) {
+        self.sign = (magnitude.isZero ? .plus : sign)
+        self.magnitude = magnitude
+    }
+
+    /// Return true iff this integer is zero.
+    ///
+    /// - Complexity: O(1)
+    public var isZero: Bool {
+        return magnitude.isZero
+    }
+
+    /// Returns `-1` if this value is negative and `1` if it’s positive; otherwise, `0`.
+    ///
+    /// - Returns: The sign of this number, expressed as an integer of the same type.
+    public func signum() -> BigInt {
+        switch sign {
+        case .plus:
+            return isZero ? 0 : 1
+        case .minus:
+            return -1
+        }
+    }
+}

Sources/CryptoSwift/BigInt/BigUInt.swift

@@ -0,0 +1,386 @@
+//
+//  BigUInt.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2015-12-26.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+/// An arbitary precision unsigned integer type, also known as a "big integer".
+///
+/// Operations on big integers never overflow, but they may take a long time to execute.
+/// The amount of memory (and address space) available is the only constraint to the magnitude of these numbers.
+///
+/// This particular big integer type uses base-2^64 digits to represent integers; you can think of it as a wrapper
+/// around `Array<UInt64>`. (In fact, `BigUInt` only uses an array if there are more than two digits.)
+public struct BigUInt: UnsignedInteger {
+    /// The type representing a digit in `BigUInt`'s underlying number system.
+    public typealias Word = UInt
+
+    /// The storage variants of a `BigUInt`.
+    enum Kind {
+        /// Value consists of the two specified words (low and high). Either or both words may be zero.
+        case inline(Word, Word)
+        /// Words are stored in a slice of the storage array.
+        case slice(from: Int, to: Int)
+        /// Words are stored in the storage array.
+        case array
+    }
+
+    internal fileprivate (set) var kind: Kind // Internal for testing only
+    internal fileprivate (set) var storage: [Word] // Internal for testing only; stored separately to prevent COW copies
+
+    /// Initializes a new BigUInt with value 0.
+    public init() {
+        self.kind = .inline(0, 0)
+        self.storage = []
+    }
+
+    internal init(word: Word) {
+        self.kind = .inline(word, 0)
+        self.storage = []
+    }
+
+    internal init(low: Word, high: Word) {
+        self.kind = .inline(low, high)
+        self.storage = []
+    }
+
+    /// Initializes a new BigUInt with the specified digits. The digits are ordered from least to most significant.
+    public init(words: [Word]) {
+        self.kind = .array
+        self.storage = words
+        normalize()
+    }
+
+    internal init(words: [Word], from startIndex: Int, to endIndex: Int) {
+        self.kind = .slice(from: startIndex, to: endIndex)
+        self.storage = words
+        normalize()
+    }
+}
+
+extension BigUInt {
+    public static var isSigned: Bool {
+        return false
+    }
+
+    /// Return true iff this integer is zero.
+    ///
+    /// - Complexity: O(1)
+    var isZero: Bool {
+        switch kind {
+        case .inline(0, 0): return true
+        case .array: return storage.isEmpty
+        default:
+            return false
+        }
+    }
+
+    /// Returns `1` if this value is, positive; otherwise, `0`.
+    ///
+    /// - Returns: The sign of this number, expressed as an integer of the same type.
+    public func signum() -> BigUInt {
+        return isZero ? 0 : 1
+    }
+}
+
+extension BigUInt {
+    mutating func ensureArray() {
+        switch kind {
+        case let .inline(w0, w1):
+            kind = .array
+            storage = w1 != 0 ? [w0, w1]
+                : w0 != 0 ? [w0]
+                : []
+        case let .slice(from: start, to: end):
+            kind = .array
+            storage = Array(storage[start ..< end])
+        case .array:
+            break
+        }
+    }
+
+    var capacity: Int {
+        guard case .array = kind else { return 0 }
+        return storage.capacity
+    }
+
+    mutating func reserveCapacity(_ minimumCapacity: Int) {
+        switch kind {
+        case let .inline(w0, w1):
+            kind = .array
+            storage.reserveCapacity(minimumCapacity)
+            if w1 != 0 {
+                storage.append(w0)
+                storage.append(w1)
+            }
+            else if w0 != 0 {
+                storage.append(w0)
+            }
+        case let .slice(from: start, to: end):
+            kind = .array
+            var words: [Word] = []
+            words.reserveCapacity(Swift.max(end - start, minimumCapacity))
+            words.append(contentsOf: storage[start ..< end])
+            storage = words
+        case .array:
+            storage.reserveCapacity(minimumCapacity)
+        }
+    }
+
+    /// Gets rid of leading zero digits in the digit array and converts slices into inline digits when possible.
+    internal mutating func normalize() {
+        switch kind {
+        case .slice(from: let start, to: var end):
+            assert(start >= 0 && end <= storage.count && start <= end)
+            while start < end, storage[end - 1] == 0 {
+                end -= 1
+            }
+            switch end - start {
+            case 0:
+                kind = .inline(0, 0)
+                storage = []
+            case 1:
+                kind = .inline(storage[start], 0)
+                storage = []
+            case 2:
+                kind = .inline(storage[start], storage[start + 1])
+                storage = []
+            case storage.count:
+                assert(start == 0)
+                kind = .array
+            default:
+                kind = .slice(from: start, to: end)
+            }
+        case .array where storage.last == 0:
+            while storage.last == 0 {
+                storage.removeLast()
+            }
+        default:
+            break
+        }
+    }
+
+    /// Set this integer to 0 without releasing allocated storage capacity (if any).
+    mutating func clear() {
+        self.load(0)
+    }
+
+    /// Set this integer to `value` by copying its digits without releasing allocated storage capacity (if any).
+    mutating func load(_ value: BigUInt) {
+        switch kind {
+        case .inline, .slice:
+            self = value
+        case .array:
+            self.storage.removeAll(keepingCapacity: true)
+            self.storage.append(contentsOf: value.words)
+        }
+    }
+}
+
+extension BigUInt {
+    //MARK: Collection-like members
+
+    /// The number of digits in this integer, excluding leading zero digits.
+    var count: Int {
+        switch kind {
+        case let .inline(w0, w1):
+            return w1 != 0 ? 2
+                : w0 != 0 ? 1
+                : 0
+        case let .slice(from: start, to: end):
+            return end - start
+        case .array:
+            return storage.count
+        }
+    }
+
+    /// Get or set a digit at a given index.
+    ///
+    /// - Note: Unlike a normal collection, it is OK for the index to be greater than or equal to `endIndex`.
+    ///   The subscripting getter returns zero for indexes beyond the most significant digit.
+    ///   Setting these extended digits automatically appends new elements to the underlying digit array.
+    /// - Requires: index >= 0
+    /// - Complexity: The getter is O(1). The setter is O(1) if the conditions below are true; otherwise it's O(count).
+    ///    - The integer's storage is not shared with another integer
+    ///    - The integer wasn't created as a slice of another integer
+    ///    - `index < count`
+    subscript(_ index: Int) -> Word {
+        get {
+            precondition(index >= 0)
+            switch (kind, index) {
+            case (.inline(let w0, _), 0): return w0
+            case (.inline(_, let w1), 1): return w1
+            case (.slice(from: let start, to: let end), _) where index < end - start:
+                return storage[start + index]
+            case (.array, _) where index < storage.count:
+                return storage[index]
+            default:
+                return 0
+            }
+        }
+        set(word) {
+            precondition(index >= 0)
+            switch (kind, index) {
+            case let (.inline(_, w1), 0):
+                kind = .inline(word, w1)
+            case let (.inline(w0, _), 1):
+                kind = .inline(w0, word)
+            case let (.slice(from: start, to: end), _) where index < end - start:
+                replace(at: index, with: word)
+            case (.array, _) where index < storage.count:
+                replace(at: index, with: word)
+            default:
+                extend(at: index, with: word)
+            }
+        }
+    }
+
+    private mutating func replace(at index: Int, with word: Word) {
+        ensureArray()
+        precondition(index < storage.count)
+        storage[index] = word
+        if word == 0, index == storage.count - 1 {
+            normalize()
+        }
+    }
+
+    private mutating func extend(at index: Int, with word: Word) {
+        guard word != 0 else { return }
+        reserveCapacity(index + 1)
+        precondition(index >= storage.count)
+        storage.append(contentsOf: repeatElement(0, count: index - storage.count))
+        storage.append(word)
+    }
+
+    /// Returns an integer built from the digits of this integer in the given range.
+    internal func extract(_ bounds: Range<Int>) -> BigUInt {
+        switch kind {
+        case let .inline(w0, w1):
+            let bounds = bounds.clamped(to: 0 ..< 2)
+            if bounds == 0 ..< 2 {
+                return BigUInt(low: w0, high: w1)
+            }
+            else if bounds == 0 ..< 1 {
+                return BigUInt(word: w0)
+            }
+            else if bounds == 1 ..< 2 {
+                return BigUInt(word: w1)
+            }
+            else {
+                return BigUInt()
+            }
+        case let .slice(from: start, to: end):
+            let s = Swift.min(end, start + Swift.max(bounds.lowerBound, 0))
+            let e = Swift.max(s, (bounds.upperBound > end - start ? end : start + bounds.upperBound))
+            return BigUInt(words: storage, from: s, to: e)
+        case .array:
+            let b = bounds.clamped(to: storage.startIndex ..< storage.endIndex)
+            return BigUInt(words: storage, from: b.lowerBound, to: b.upperBound)
+        }
+    }
+
+    internal func extract<Bounds: RangeExpression>(_ bounds: Bounds) -> BigUInt where Bounds.Bound == Int {
+        return self.extract(bounds.relative(to: 0 ..< Int.max))
+    }
+}
+
+extension BigUInt {
+    internal mutating func shiftRight(byWords amount: Int) {
+        assert(amount >= 0)
+        guard amount > 0 else { return }
+        switch kind {
+        case let .inline(_, w1) where amount == 1:
+            kind = .inline(w1, 0)
+        case .inline(_, _):
+            kind = .inline(0, 0)
+        case let .slice(from: start, to: end):
+            let s = start + amount
+            if s >= end {
+                kind = .inline(0, 0)
+            }
+            else {
+                kind = .slice(from: s, to: end)
+                normalize()
+            }
+        case .array:
+            if amount >= storage.count {
+                storage.removeAll(keepingCapacity: true)
+            }
+            else {
+                storage.removeFirst(amount)
+            }
+        }
+    }
+
+    internal mutating func shiftLeft(byWords amount: Int) {
+        assert(amount >= 0)
+        guard amount > 0 else { return }
+        guard !isZero else { return }
+        switch kind {
+        case let .inline(w0, 0) where amount == 1:
+            kind = .inline(0, w0)
+        case let .inline(w0, w1):
+            let c = (w1 == 0 ? 1 : 2)
+            storage.reserveCapacity(amount + c)
+            storage.append(contentsOf: repeatElement(0, count: amount))
+            storage.append(w0)
+            if w1 != 0 {
+                storage.append(w1)
+            }
+            kind = .array
+        case let .slice(from: start, to: end):
+            var words: [Word] = []
+            words.reserveCapacity(amount + count)
+            words.append(contentsOf: repeatElement(0, count: amount))
+            words.append(contentsOf: storage[start ..< end])
+            storage = words
+            kind = .array
+        case .array:
+            storage.insert(contentsOf: repeatElement(0, count: amount), at: 0)
+        }
+    }
+}
+
+extension BigUInt {
+    //MARK: Low and High
+    
+    /// Split this integer into a high-order and a low-order part.
+    ///
+    /// - Requires: count > 1
+    /// - Returns: `(low, high)` such that 
+    ///   - `self == low.add(high, shiftedBy: middleIndex)`
+    ///   - `high.width <= floor(width / 2)`
+    ///   - `low.width <= ceil(width / 2)`
+    /// - Complexity: Typically O(1), but O(count) in the worst case, because high-order zero digits need to be removed after the split.
+    internal var split: (high: BigUInt, low: BigUInt) {
+        precondition(count > 1)
+        let mid = middleIndex
+        return (self.extract(mid...), self.extract(..<mid))
+    }
+
+    /// Index of the digit at the middle of this integer.
+    ///
+    /// - Returns: The index of the digit that is least significant in `self.high`.
+    internal var middleIndex: Int {
+        return (count + 1) / 2
+    }
+
+    /// The low-order half of this BigUInt.
+    ///
+    /// - Returns: `self[0 ..< middleIndex]`
+    /// - Requires: count > 1
+    internal var low: BigUInt {
+        return self.extract(0 ..< middleIndex)
+    }
+
+    /// The high-order half of this BigUInt.
+    ///
+    /// - Returns: `self[middleIndex ..< count]`
+    /// - Requires: count > 1
+    internal var high: BigUInt {
+        return self.extract(middleIndex ..< count)
+    }
+}
+

Sources/CryptoSwift/BigInt/Bitwise Ops.swift

@@ -0,0 +1,121 @@
+//
+//  Bitwise Ops.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+//MARK: Bitwise Operations
+
+extension BigUInt {
+    /// Return the ones' complement of `a`.
+    ///
+    /// - Complexity: O(a.count)
+    public static prefix func ~(a: BigUInt) -> BigUInt {
+        return BigUInt(words: a.words.map { ~$0 })
+    }
+
+    /// Calculate the bitwise OR of `a` and `b`, and store the result in `a`.
+    ///
+    /// - Complexity: O(max(a.count, b.count))
+    public static func |= (a: inout BigUInt, b: BigUInt) {
+        a.reserveCapacity(b.count)
+        for i in 0 ..< b.count {
+            a[i] |= b[i]
+        }
+    }
+
+    /// Calculate the bitwise AND of `a` and `b` and return the result.
+    ///
+    /// - Complexity: O(max(a.count, b.count))
+    public static func &= (a: inout BigUInt, b: BigUInt) {
+        for i in 0 ..< Swift.max(a.count, b.count) {
+            a[i] &= b[i]
+        }
+    }
+
+    /// Calculate the bitwise XOR of `a` and `b` and return the result.
+    ///
+    /// - Complexity: O(max(a.count, b.count))
+    public static func ^= (a: inout BigUInt, b: BigUInt) {
+        a.reserveCapacity(b.count)
+        for i in 0 ..< b.count {
+            a[i] ^= b[i]
+        }
+    }
+}
+
+extension BigInt {
+    public static prefix func ~(x: BigInt) -> BigInt {
+        switch x.sign {
+        case .plus:
+            return BigInt(sign: .minus, magnitude: x.magnitude + 1)
+        case .minus:
+            return BigInt(sign: .plus, magnitude: x.magnitude - 1)
+        }
+    }
+    
+    public static func &(lhs: inout BigInt, rhs: BigInt) -> BigInt {
+        let left = lhs.words
+        let right = rhs.words
+        // Note we aren't using left.count/right.count here; we account for the sign bit separately later.
+        let count = Swift.max(lhs.magnitude.count, rhs.magnitude.count)
+        var words: [UInt] = []
+        words.reserveCapacity(count)
+        for i in 0 ..< count {
+            words.append(left[i] & right[i])
+        }
+        if lhs.sign == .minus && rhs.sign == .minus {
+            words.twosComplement()
+            return BigInt(sign: .minus, magnitude: BigUInt(words: words))
+        }
+        return BigInt(sign: .plus, magnitude: BigUInt(words: words))
+    }
+    
+    public static func |(lhs: inout BigInt, rhs: BigInt) -> BigInt {
+        let left = lhs.words
+        let right = rhs.words
+        // Note we aren't using left.count/right.count here; we account for the sign bit separately later.
+        let count = Swift.max(lhs.magnitude.count, rhs.magnitude.count)
+        var words: [UInt] = []
+        words.reserveCapacity(count)
+        for i in 0 ..< count {
+            words.append(left[i] | right[i])
+        }
+        if lhs.sign == .minus || rhs.sign == .minus {
+            words.twosComplement()
+            return BigInt(sign: .minus, magnitude: BigUInt(words: words))
+        }
+        return BigInt(sign: .plus, magnitude: BigUInt(words: words))
+    }
+    
+    public static func ^(lhs: inout BigInt, rhs: BigInt) -> BigInt {
+        let left = lhs.words
+        let right = rhs.words
+        // Note we aren't using left.count/right.count here; we account for the sign bit separately later.
+        let count = Swift.max(lhs.magnitude.count, rhs.magnitude.count)
+        var words: [UInt] = []
+        words.reserveCapacity(count)
+        for i in 0 ..< count {
+            words.append(left[i] ^ right[i])
+        }
+        if (lhs.sign == .minus) != (rhs.sign == .minus) {
+            words.twosComplement()
+            return BigInt(sign: .minus, magnitude: BigUInt(words: words))
+        }
+        return BigInt(sign: .plus, magnitude: BigUInt(words: words))
+    }
+    
+    public static func &=(lhs: inout BigInt, rhs: BigInt) {
+        lhs = lhs & rhs
+    }
+    
+    public static func |=(lhs: inout BigInt, rhs: BigInt) {
+        lhs = lhs | rhs
+    }
+    
+    public static func ^=(lhs: inout BigInt, rhs: BigInt) {
+        lhs = lhs ^ rhs
+    }
+}

Sources/CryptoSwift/BigInt/Codable.swift

@@ -0,0 +1,155 @@
+//
+//  Codable.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2017-8-11.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+
+// Little-endian to big-endian
+struct Units<Unit: FixedWidthInteger, Words: RandomAccessCollection>: RandomAccessCollection
+where Words.Element: FixedWidthInteger, Words.Index == Int {
+    typealias Word = Words.Element
+    let words: Words
+    init(of type: Unit.Type, _ words: Words) {
+        precondition(Word.bitWidth % Unit.bitWidth == 0 || Unit.bitWidth % Word.bitWidth == 0)
+        self.words = words
+    }
+    var count: Int { return (words.count * Word.bitWidth + Unit.bitWidth - 1) / Unit.bitWidth }
+    var startIndex: Int { return 0 }
+    var endIndex: Int { return count }
+    subscript(_ index: Int) -> Unit {
+        let index = count - 1 - index
+        if Unit.bitWidth == Word.bitWidth {
+            return Unit(words[index])
+        }
+        else if Unit.bitWidth > Word.bitWidth {
+            let c = Unit.bitWidth / Word.bitWidth
+            var unit: Unit = 0
+            var j = 0
+            for i in (c * index) ..< Swift.min(c * (index + 1), words.endIndex) {
+                unit |= Unit(words[i]) << j
+                j += Word.bitWidth
+            }
+            return unit
+        }
+        // Unit.bitWidth < Word.bitWidth
+        let c = Word.bitWidth / Unit.bitWidth
+        let i = index / c
+        let j = index % c
+        return Unit(truncatingIfNeeded: words[i] >> (j * Unit.bitWidth))
+    }
+}
+
+extension Array where Element: FixedWidthInteger {
+    // Big-endian to little-endian
+    init<Unit: FixedWidthInteger>(count: Int?, generator: () throws -> Unit?) rethrows {
+        typealias Word = Element
+        precondition(Word.bitWidth % Unit.bitWidth == 0 || Unit.bitWidth % Word.bitWidth == 0)
+        self = []
+        if Unit.bitWidth == Word.bitWidth {
+            if let count = count {
+                self.reserveCapacity(count)
+            }
+            while let unit = try generator() {
+                self.append(Word(unit))
+            }
+        }
+        else if Unit.bitWidth > Word.bitWidth {
+            let wordsPerUnit = Unit.bitWidth / Word.bitWidth
+            if let count = count {
+                self.reserveCapacity(count * wordsPerUnit)
+            }
+            while let unit = try generator() {
+                var shift = Unit.bitWidth - Word.bitWidth
+                while shift >= 0 {
+                    self.append(Word(truncatingIfNeeded: unit >> shift))
+                    shift -= Word.bitWidth
+                }
+            }
+        }
+        else {
+            let unitsPerWord = Word.bitWidth / Unit.bitWidth
+            if let count = count {
+                self.reserveCapacity((count + unitsPerWord - 1) / unitsPerWord)
+            }
+            var word: Word = 0
+            var c = 0
+            while let unit = try generator() {
+                word <<= Unit.bitWidth
+                word |= Word(unit)
+                c += Unit.bitWidth
+                if c == Word.bitWidth {
+                    self.append(word)
+                    word = 0
+                    c = 0
+                }
+            }
+            if c > 0 {
+                self.append(word << c)
+                var shifted: Word = 0
+                for i in self.indices {
+                    let word = self[i]
+                    self[i] = shifted | (word >> c)
+                    shifted = word << (Word.bitWidth - c)
+                }
+            }
+        }
+        self.reverse()
+    }
+}
+
+extension BigInt: Codable {
+    public init(from decoder: Decoder) throws {
+        var container = try decoder.unkeyedContainer()
+
+        // Decode sign
+        let sign: BigInt.Sign
+        switch try container.decode(String.self) {
+        case "+":
+            sign = .plus
+        case "-":
+            sign = .minus
+        default:
+            throw DecodingError.dataCorrupted(.init(codingPath: container.codingPath,
+                                                    debugDescription: "Invalid big integer sign"))
+        }
+
+        // Decode magnitude
+        let words = try [UInt](count: container.count?.advanced(by: -1)) { () -> UInt64? in
+            guard !container.isAtEnd else { return nil }
+            return try container.decode(UInt64.self)
+        }
+        let magnitude = BigUInt(words: words)
+
+        self.init(sign: sign, magnitude: magnitude)
+    }
+
+    public func encode(to encoder: Encoder) throws {
+        var container = encoder.unkeyedContainer()
+        try container.encode(sign == .plus ? "+" : "-")
+        let units = Units(of: UInt64.self, self.magnitude.words)
+        if units.isEmpty {
+            try container.encode(0 as UInt64)
+        }
+        else {
+            try container.encode(contentsOf: units)
+        }
+    }
+}
+
+extension BigUInt: Codable {
+    public init(from decoder: Decoder) throws {
+        let value = try BigInt(from: decoder)
+        guard value.sign == .plus else {
+            throw DecodingError.dataCorrupted(.init(codingPath: decoder.codingPath,
+                                                    debugDescription: "BigUInt cannot hold a negative value"))
+        }
+        self = value.magnitude
+    }
+
+    public func encode(to encoder: Encoder) throws {
+        try BigInt(sign: .plus, magnitude: self).encode(to: encoder)
+    }
+}

Sources/CryptoSwift/BigInt/Comparable.swift

@@ -0,0 +1,63 @@
+//
+//  Comparable.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+import Foundation
+
+extension BigUInt: Comparable {
+    //MARK: Comparison
+    
+    /// Compare `a` to `b` and return an `NSComparisonResult` indicating their order.
+    ///
+    /// - Complexity: O(count)
+    public static func compare(_ a: BigUInt, _ b: BigUInt) -> ComparisonResult {
+        if a.count != b.count { return a.count > b.count ? .orderedDescending : .orderedAscending }
+        for i in (0 ..< a.count).reversed() {
+            let ad = a[i]
+            let bd = b[i]
+            if ad != bd { return ad > bd ? .orderedDescending : .orderedAscending }
+        }
+        return .orderedSame
+    }
+
+    /// Return true iff `a` is equal to `b`.
+    ///
+    /// - Complexity: O(count)
+    public static func ==(a: BigUInt, b: BigUInt) -> Bool {
+        return BigUInt.compare(a, b) == .orderedSame
+    }
+
+    /// Return true iff `a` is less than `b`.
+    ///
+    /// - Complexity: O(count)
+    public static func <(a: BigUInt, b: BigUInt) -> Bool {
+        return BigUInt.compare(a, b) == .orderedAscending
+    }
+}
+
+extension BigInt {
+    /// Return true iff `a` is equal to `b`.
+    public static func ==(a: BigInt, b: BigInt) -> Bool {
+        return a.sign == b.sign && a.magnitude == b.magnitude
+    }
+
+    /// Return true iff `a` is less than `b`.
+    public static func <(a: BigInt, b: BigInt) -> Bool {
+        switch (a.sign, b.sign) {
+        case (.plus, .plus):
+            return a.magnitude < b.magnitude
+        case (.plus, .minus):
+            return false
+        case (.minus, .plus):
+            return true
+        case (.minus, .minus):
+            return a.magnitude > b.magnitude
+        }
+    }
+}
+
+

Sources/CryptoSwift/BigInt/Data Conversion.swift

@@ -0,0 +1,179 @@
+//
+//  Data Conversion.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-04.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+import Foundation
+
+extension BigUInt {
+    //MARK: NSData Conversion
+
+    /// Initialize a BigInt from bytes accessed from an UnsafeRawBufferPointer
+    public init(_ buffer: UnsafeRawBufferPointer) {
+        // This assumes Word is binary.
+        precondition(Word.bitWidth % 8 == 0)
+
+        self.init()
+
+        let length = buffer.count
+        guard length > 0 else { return }
+        let bytesPerDigit = Word.bitWidth / 8
+        var index = length / bytesPerDigit
+        var c = bytesPerDigit - length % bytesPerDigit
+        if c == bytesPerDigit {
+            c = 0
+            index -= 1
+        }
+
+        var word: Word = 0
+        for byte in buffer {
+            word <<= 8
+            word += Word(byte)
+            c += 1
+            if c == bytesPerDigit {
+                self[index] = word
+                index -= 1
+                c = 0
+                word = 0
+            }
+        }
+        assert(c == 0 && word == 0 && index == -1)
+    }
+
+
+    /// Initializes an integer from the bits stored inside a piece of `Data`.
+    /// The data is assumed to be in network (big-endian) byte order.
+    public init(_ data: Data) {
+        // This assumes Word is binary.
+        precondition(Word.bitWidth % 8 == 0)
+
+        self.init()
+
+        let length = data.count
+        guard length > 0 else { return }
+        let bytesPerDigit = Word.bitWidth / 8
+        var index = length / bytesPerDigit
+        var c = bytesPerDigit - length % bytesPerDigit
+        if c == bytesPerDigit {
+            c = 0
+            index -= 1
+        }
+        let word: Word = data.withUnsafeBytes { buffPtr in
+            var word: Word = 0
+            let p = buffPtr.bindMemory(to: UInt8.self)
+            for byte in p {
+                word <<= 8
+                word += Word(byte)
+                c += 1
+                if c == bytesPerDigit {
+                    self[index] = word
+                    index -= 1
+                    c = 0
+                    word = 0
+                }
+            }
+            return word
+        }
+        assert(c == 0 && word == 0 && index == -1)
+    }
+
+    /// Return a `Data` value that contains the base-256 representation of this integer, in network (big-endian) byte order.
+    public func serialize() -> Data {
+        // This assumes Digit is binary.
+        precondition(Word.bitWidth % 8 == 0)
+
+        let byteCount = (self.bitWidth + 7) / 8
+
+        guard byteCount > 0 else { return Data() }
+
+        var data = Data(count: byteCount)
+        data.withUnsafeMutableBytes { buffPtr in
+            let p = buffPtr.bindMemory(to: UInt8.self)
+            var i = byteCount - 1
+            for var word in self.words {
+                for _ in 0 ..< Word.bitWidth / 8 {
+                    p[i] = UInt8(word & 0xFF)
+                    word >>= 8
+                    if i == 0 {
+                        assert(word == 0)
+                        break
+                    }
+                    i -= 1
+                }
+            }
+        }
+        return data
+    }
+}
+
+extension BigInt {
+    
+    /// Initialize a BigInt from bytes accessed from an UnsafeRawBufferPointer,
+    /// where the first byte indicates sign (0 for positive, 1 for negative)
+    public init(_ buffer: UnsafeRawBufferPointer) {
+        // This assumes Word is binary.
+        precondition(Word.bitWidth % 8 == 0)
+        
+        self.init()
+        
+        let length = buffer.count
+        
+        // Serialized data for a BigInt should contain at least 2 bytes: one representing
+        // the sign, and another for the non-zero magnitude. Zero is represented by an
+        // empty Data struct, and negative zero is not supported.
+        guard length > 1, let firstByte = buffer.first else { return }
+
+        // The first byte gives the sign
+        // This byte is compared to a bitmask to allow additional functionality to be added
+        // to this byte in the future.
+        self.sign = firstByte & 0b1 == 0 ? .plus : .minus
+
+        self.magnitude = BigUInt(UnsafeRawBufferPointer(rebasing: buffer.dropFirst(1)))
+    }
+    
+    /// Initializes an integer from the bits stored inside a piece of `Data`.
+    /// The data is assumed to be in network (big-endian) byte order with a first
+    /// byte to represent the sign (0 for positive, 1 for negative)
+    public init(_ data: Data) {
+        // This assumes Word is binary.
+        // This is the same assumption made when initializing BigUInt from Data
+        precondition(Word.bitWidth % 8 == 0)
+
+        self.init()
+        
+        // Serialized data for a BigInt should contain at least 2 bytes: one representing
+        // the sign, and another for the non-zero magnitude. Zero is represented by an
+        // empty Data struct, and negative zero is not supported.
+        guard data.count > 1, let firstByte = data.first else { return }
+        
+        // The first byte gives the sign
+        // This byte is compared to a bitmask to allow additional functionality to be added
+        // to this byte in the future.
+        self.sign = firstByte & 0b1 == 0 ? .plus : .minus
+        
+        // The remaining bytes are read and stored as the magnitude
+        self.magnitude = BigUInt(data.dropFirst(1))
+    }
+    
+    /// Return a `Data` value that contains the base-256 representation of this integer, in network (big-endian) byte order and a prepended byte to indicate the sign (0 for positive, 1 for negative)
+    public func serialize() -> Data {
+        // Create a data object for the magnitude portion of the BigInt
+        let magnitudeData = self.magnitude.serialize()
+        
+        // Similar to BigUInt, a value of 0 should return an initialized, empty Data struct
+        guard magnitudeData.count > 0 else { return magnitudeData }
+        
+        // Create a new Data struct for the signed BigInt value
+        var data = Data(capacity: magnitudeData.count + 1)
+        
+        // The first byte should be 0 for a positive value, or 1 for a negative value
+        // i.e., the sign bit is the LSB
+        data.append(self.sign == .plus ? 0 : 1)
+        
+        data.append(magnitudeData)
+        return data
+    }
+}

Sources/CryptoSwift/BigInt/Division.swift

@@ -0,0 +1,375 @@
+//
+//  Division.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+//MARK: Full-width multiplication and division
+
+// TODO: Return to `where Magnitude == Self` when SR-13491 is resolved
+extension FixedWidthInteger {
+    private var halfShift: Self {
+        return Self(Self.bitWidth / 2)
+
+    }
+    private var high: Self {
+        return self &>> halfShift
+    }
+
+    private var low: Self {
+        let mask: Self = 1 &<< halfShift - 1
+        return self & mask
+    }
+
+    private var upshifted: Self {
+        return self &<< halfShift
+    }
+
+    private var split: (high: Self, low: Self) {
+        return (self.high, self.low)
+    }
+
+    private init(_ value: (high: Self, low: Self)) {
+        self = value.high.upshifted + value.low
+    }
+
+    /// Divide the double-width integer `dividend` by `self` and return the quotient and remainder.
+    ///
+    /// - Requires: `dividend.high < self`, so that the result will fit in a single digit.
+    /// - Complexity: O(1) with 2 divisions, 6 multiplications and ~12 or so additions/subtractions.
+    internal func fastDividingFullWidth(_ dividend: (high: Self, low: Self.Magnitude)) -> (quotient: Self, remainder: Self) {
+        // Division is complicated; doing it with single-digit operations is maddeningly complicated.
+        // This is a Swift adaptation for "divlu2" in Hacker's Delight,
+        // which is in turn a C adaptation of Knuth's Algorithm D (TAOCP vol 2, 4.3.1).
+        precondition(dividend.high < self)
+
+        // This replaces the implementation in stdlib, which is much slower.
+        // FIXME: Speed up stdlib. It should use full-width idiv on Intel processors, and
+        // fall back to a reasonably fast algorithm elsewhere.
+
+        // The trick here is that we're actually implementing a 4/2 long division using half-words,
+        // with the long division loop unrolled into two 3/2 half-word divisions.
+        // Luckily, 3/2 half-word division can be approximated by a single full-word division operation
+        // that, when the divisor is normalized, differs from the correct result by at most 2.
+
+        /// Find the half-word quotient in `u / vn`, which must be normalized.
+        /// `u` contains three half-words in the two halves of `u.high` and the lower half of
+        /// `u.low`. (The weird distribution makes for a slightly better fit with the input.)
+        /// `vn` contains the normalized divisor, consisting of two half-words.
+        ///
+        /// - Requires: u.high < vn && u.low.high == 0 && vn.leadingZeroBitCount == 0
+        func quotient(dividing u: (high: Self, low: Self), by vn: Self) -> Self {
+            let (vn1, vn0) = vn.split
+            // Get approximate quotient.
+            let (q, r) = u.high.quotientAndRemainder(dividingBy: vn1)
+            let p = q * vn0
+            // q is often already correct, but sometimes the approximation overshoots by at most 2.
+            // The code that follows checks for this while being careful to only perform single-digit operations.
+            if q.high == 0 && p <= r.upshifted + u.low { return q }
+            let r2 = r + vn1
+            if r2.high != 0 { return q - 1 }
+            if (q - 1).high == 0 && p - vn0 <= r2.upshifted + u.low { return q - 1 }
+            //assert((r + 2 * vn1).high != 0 || p - 2 * vn0 <= (r + 2 * vn1).upshifted + u.low)
+            return q - 2
+        }
+        /// Divide 3 half-digits by 2 half-digits to get a half-digit quotient and a full-digit remainder.
+        ///
+        /// - Requires: u.high < v && u.low.high == 0 && vn.width = width(Digit)
+        func quotientAndRemainder(dividing u: (high: Self, low: Self), by v: Self) -> (quotient: Self, remainder: Self) {
+            let q = quotient(dividing: u, by: v)
+            // Note that `uh.low` masks off a couple of bits, and `q * v` and the
+            // subtraction are likely to overflow. Despite this, the end result (remainder) will
+            // still be correct and it will fit inside a single (full) Digit.
+            let r = Self(u) &- q &* v
+            assert(r < v)
+            return (q, r)
+        }
+
+        // Normalize the dividend and the divisor (self) such that the divisor has no leading zeroes.
+        let z = Self(self.leadingZeroBitCount)
+        let w = Self(Self.bitWidth) - z
+        let vn = self << z
+
+        let un32 = (z == 0 ? dividend.high : (dividend.high &<< z) | ((dividend.low as! Self) &>> w)) // No bits are lost
+        let un10 = dividend.low &<< z
+        let (un1, un0) = un10.split
+
+        // Divide `(un32,un10)` by `vn`, splitting the full 4/2 division into two 3/2 ones.
+        let (q1, un21) = quotientAndRemainder(dividing: (un32, (un1 as! Self)), by: vn)
+        let (q0, rn) = quotientAndRemainder(dividing: (un21, (un0 as! Self)), by: vn)
+
+        // Undo normalization of the remainder and combine the two halves of the quotient.
+        let mod = rn >> z
+        let div = Self((q1, q0))
+        return (div, mod)
+    }
+
+    /// Return the quotient of the 3/2-word division `x/y` as a single word.
+    ///
+    /// - Requires: (x.0, x.1) <= y && y.0.high != 0
+    /// - Returns: The exact value when it fits in a single word, otherwise `Self`.
+    static func approximateQuotient(dividing x: (Self, Self, Self), by y: (Self, Self)) -> Self {
+        // Start with q = (x.0, x.1) / y.0, (or Word.max on overflow)
+        var q: Self
+        var r: Self
+        if x.0 == y.0 {
+            q = Self.max
+            let (s, o) = x.0.addingReportingOverflow(x.1)
+            if o { return q }
+            r = s
+        }
+        else {
+            (q, r) = y.0.fastDividingFullWidth((x.0, (x.1 as! Magnitude)))
+        }
+        // Now refine q by considering x.2 and y.1.
+        // Note that since y is normalized, q * y - x is between 0 and 2.
+        let (ph, pl) = q.multipliedFullWidth(by: y.1)
+        if ph < r || (ph == r && pl <= x.2) { return q }
+
+        let (r1, ro) = r.addingReportingOverflow(y.0)
+        if ro { return q - 1 }
+
+        let (pl1, so) = pl.subtractingReportingOverflow((y.1 as! Magnitude))
+        let ph1 = (so ? ph - 1 : ph)
+
+        if ph1 < r1 || (ph1 == r1 && pl1 <= x.2) { return q - 1 }
+        return q - 2
+    }
+}
+
+extension BigUInt {
+    //MARK: Division
+
+    /// Divide this integer by the word `y`, leaving the quotient in its place and returning the remainder.
+    ///
+    /// - Requires: y > 0
+    /// - Complexity: O(count)
+    internal mutating func divide(byWord y: Word) -> Word {
+        precondition(y > 0)
+        if y == 1 { return 0 }
+        
+        var remainder: Word = 0
+        for i in (0 ..< count).reversed() {
+            let u = self[i]
+            (self[i], remainder) = y.fastDividingFullWidth((remainder, u))
+        }
+        return remainder
+    }
+
+    /// Divide this integer by the word `y` and return the resulting quotient and remainder.
+    ///
+    /// - Requires: y > 0
+    /// - Returns: (quotient, remainder) where quotient = floor(x/y), remainder = x - quotient * y
+    /// - Complexity: O(x.count)
+    internal func quotientAndRemainder(dividingByWord y: Word) -> (quotient: BigUInt, remainder: Word) {
+        var div = self
+        let mod = div.divide(byWord: y)
+        return (div, mod)
+    }
+
+    /// Divide `x` by `y`, putting the quotient in `x` and the remainder in `y`.
+    /// Reusing integers like this reduces the number of allocations during the calculation.
+    static func divide(_ x: inout BigUInt, by y: inout BigUInt) {
+        // This is a Swift adaptation of "divmnu" from Hacker's Delight, which is in
+        // turn a C adaptation of Knuth's Algorithm D (TAOCP vol 2, 4.3.1).
+
+        precondition(!y.isZero)
+
+        // First, let's take care of the easy cases.
+        if x < y {
+            (x, y) = (0, x)
+            return
+        }
+        if y.count == 1 {
+            // The single-word case reduces to a simpler loop.
+            y = BigUInt(x.divide(byWord: y[0]))
+            return
+        }
+
+        // In the hard cases, we will perform the long division algorithm we learned in school.
+        // It works by successively calculating the single-word quotient of the top y.count + 1
+        // words of x divided by y, replacing the top of x with the remainder, and repeating
+        // the process one word lower.
+        //
+        // The tricky part is that the algorithm needs to be able to do n+1/n word divisions,
+        // but we only have a primitive for dividing two words by a single
+        // word. (Remember that this step is also tricky when we do it on paper!)
+        //
+        // The solution is that the long division can be approximated by a single full division
+        // using just the most significant words. We can then use multiplications and
+        // subtractions to refine the approximation until we get the correct quotient word.
+        //
+        // We could do this by doing a simple 2/1 full division, but Knuth goes one step further,
+        // and implements a 3/2 division. This results in an exact approximation in the
+        // vast majority of cases, eliminating an extra subtraction over big integers.
+        //
+        // The function `approximateQuotient` above implements Knuth's 3/2 division algorithm.
+        // It requires that the divisor's most significant word is larger than
+        // Word.max / 2. This ensures that the approximation has tiny error bounds,
+        // which is what makes this entire approach viable.
+        // To satisfy this requirement, we will normalize the division by multiplying
+        // both the divisor and the dividend by the same (small) factor.
+        let z = y.leadingZeroBitCount
+        y <<= z
+        x <<= z // We'll calculate the remainder in the normalized dividend.
+        var quotient = BigUInt()
+        assert(y.leadingZeroBitCount == 0)
+
+        // We're ready to start the long division!
+        let dc = y.count
+        let d1 = y[dc - 1]
+        let d0 = y[dc - 2]
+        var product: BigUInt = 0
+        for j in (dc ... x.count).reversed() {
+            // Approximate dividing the top dc+1 words of `remainder` using the topmost 3/2 words.
+            let r2 = x[j]
+            let r1 = x[j - 1]
+            let r0 = x[j - 2]
+            let q = Word.approximateQuotient(dividing: (r2, r1, r0), by: (d1, d0))
+
+            // Multiply the entire divisor with `q` and subtract the result from remainder.
+            // Normalization ensures the 3/2 quotient will either be exact for the full division, or
+            // it may overshoot by at most 1, in which case the product will be greater
+            // than the remainder.
+            product.load(y)
+            product.multiply(byWord: q)
+            if product <= x.extract(j - dc ..< j + 1) {
+                x.subtract(product, shiftedBy: j - dc)
+                quotient[j - dc] = q
+            }
+            else {
+                // This case is extremely rare -- it has a probability of 1/2^(Word.bitWidth - 1).
+                x.add(y, shiftedBy: j - dc)
+                x.subtract(product, shiftedBy: j - dc)
+                quotient[j - dc] = q - 1
+            }
+        }
+        // The remainder's normalization needs to be undone, but otherwise we're done.
+        x >>= z
+        y = x
+        x = quotient
+    }
+
+    /// Divide `x` by `y`, putting the remainder in `x`.
+    mutating func formRemainder(dividingBy y: BigUInt, normalizedBy shift: Int) {
+        precondition(!y.isZero)
+        assert(y.leadingZeroBitCount == 0)
+        if y.count == 1 {
+            let remainder = self.divide(byWord: y[0] >> shift)
+            self.load(BigUInt(remainder))
+            return
+        }
+        self <<= shift
+        if self >= y {
+            let dc = y.count
+            let d1 = y[dc - 1]
+            let d0 = y[dc - 2]
+            var product: BigUInt = 0
+            for j in (dc ... self.count).reversed() {
+                let r2 = self[j]
+                let r1 = self[j - 1]
+                let r0 = self[j - 2]
+                let q = Word.approximateQuotient(dividing: (r2, r1, r0), by: (d1, d0))
+                product.load(y)
+                product.multiply(byWord: q)
+                if product <= self.extract(j - dc ..< j + 1) {
+                    self.subtract(product, shiftedBy: j - dc)
+                }
+                else {
+                    self.add(y, shiftedBy: j - dc)
+                    self.subtract(product, shiftedBy: j - dc)
+                }
+            }
+        }
+        self >>= shift
+    }
+
+
+    /// Divide this integer by `y` and return the resulting quotient and remainder.
+    ///
+    /// - Requires: `y > 0`
+    /// - Returns: `(quotient, remainder)` where `quotient = floor(self/y)`, `remainder = self - quotient * y`
+    /// - Complexity: O(count^2)
+    public func quotientAndRemainder(dividingBy y: BigUInt) -> (quotient: BigUInt, remainder: BigUInt) {
+        var x = self
+        var y = y
+        BigUInt.divide(&x, by: &y)
+        return (x, y)
+    }
+
+    /// Divide `x` by `y` and return the quotient.
+    ///
+    /// - Note: Use `divided(by:)` if you also need the remainder.
+    public static func /(x: BigUInt, y: BigUInt) -> BigUInt {
+        return x.quotientAndRemainder(dividingBy: y).quotient
+    }
+
+    /// Divide `x` by `y` and return the remainder.
+    ///
+    /// - Note: Use `divided(by:)` if you also need the remainder.
+    public static func %(x: BigUInt, y: BigUInt) -> BigUInt {
+        var x = x
+        let shift = y.leadingZeroBitCount
+        x.formRemainder(dividingBy: y << shift, normalizedBy: shift)
+        return x
+    }
+
+    /// Divide `x` by `y` and store the quotient in `x`.
+    ///
+    /// - Note: Use `divided(by:)` if you also need the remainder.
+    public static func /=(x: inout BigUInt, y: BigUInt) {
+        var y = y
+        BigUInt.divide(&x, by: &y)
+    }
+
+    /// Divide `x` by `y` and store the remainder in `x`.
+    ///
+    /// - Note: Use `divided(by:)` if you also need the remainder.
+    public static func %=(x: inout BigUInt, y: BigUInt) {
+        let shift = y.leadingZeroBitCount
+        x.formRemainder(dividingBy: y << shift, normalizedBy: shift)
+    }
+}
+
+extension BigInt {
+    /// Divide this integer by `y` and return the resulting quotient and remainder.
+    ///
+    /// - Requires: `y > 0`
+    /// - Returns: `(quotient, remainder)` where `quotient = floor(self/y)`, `remainder = self - quotient * y`
+    /// - Complexity: O(count^2)
+    public func quotientAndRemainder(dividingBy y: BigInt) -> (quotient: BigInt, remainder: BigInt) {
+        var a = self.magnitude
+        var b = y.magnitude
+        BigUInt.divide(&a, by: &b)
+        return (BigInt(sign: self.sign == y.sign ? .plus : .minus, magnitude: a),
+                BigInt(sign: self.sign, magnitude: b))
+    }
+
+    /// Divide `a` by `b` and return the quotient. Traps if `b` is zero.
+    public static func /(a: BigInt, b: BigInt) -> BigInt {
+        return BigInt(sign: a.sign == b.sign ? .plus : .minus, magnitude: a.magnitude / b.magnitude)
+    }
+
+    /// Divide `a` by `b` and return the remainder. The result has the same sign as `a`.
+    public static func %(a: BigInt, b: BigInt) -> BigInt {
+        return BigInt(sign: a.sign, magnitude: a.magnitude % b.magnitude)
+    }
+
+    /// Return the result of `a` mod `b`. The result is always a nonnegative integer that is less than the absolute value of `b`.
+    public func modulus(_ mod: BigInt) -> BigInt {
+        let remainder = self.magnitude % mod.magnitude
+        return BigInt(
+            self.sign == .minus && !remainder.isZero
+                ? mod.magnitude - remainder
+                : remainder)
+    }
+}
+
+extension BigInt {
+    /// Divide `a` by `b` storing the quotient in `a`.
+    public static func /=(a: inout BigInt, b: BigInt) { a = a / b }
+    /// Divide `a` by `b` storing the remainder in `a`.
+    public static func %=(a: inout BigInt, b: BigInt) { a = a % b }
+}

Sources/CryptoSwift/BigInt/Exponentiation.swift

@@ -0,0 +1,119 @@
+//
+//  Exponentiation.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+    //MARK: Exponentiation
+
+    /// Returns this integer raised to the power `exponent`.
+    ///
+    /// This function calculates the result by [successively squaring the base while halving the exponent][expsqr].
+    ///
+    /// [expsqr]: https://en.wikipedia.org/wiki/Exponentiation_by_squaring
+    ///
+    /// - Note: This function can be unreasonably expensive for large exponents, which is why `exponent` is
+    ///         a simple integer value. If you want to calculate big exponents, you'll probably need to use
+    ///         the modulo arithmetic variant.
+    /// - Returns: 1 if `exponent == 0`, otherwise `self` raised to `exponent`. (This implies that `0.power(0) == 1`.)
+    /// - SeeAlso: `BigUInt.power(_:, modulus:)`
+    /// - Complexity: O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too.
+    public func power(_ exponent: Int) -> BigUInt {
+        if exponent == 0 { return 1 }
+        if exponent == 1 { return self }
+        if exponent < 0 {
+            precondition(!self.isZero)
+            return self == 1 ? 1 : 0
+        }
+        if self <= 1 { return self }
+        var result = BigUInt(1)
+        var b = self
+        var e = exponent
+        while e > 0 {
+            if e & 1 == 1 {
+                result *= b
+            }
+            e >>= 1
+            b *= b
+        }
+        return result
+    }
+
+    /// Returns the remainder of this integer raised to the power `exponent` in modulo arithmetic under `modulus`.
+    ///
+    /// Uses the [right-to-left binary method][rtlb].
+    ///
+    /// [rtlb]: https://en.wikipedia.org/wiki/Modular_exponentiation#Right-to-left_binary_method
+    ///
+    /// - Complexity: O(exponent.count * modulus.count^log2(3)) or somesuch
+    public func power(_ exponent: BigUInt, modulus: BigUInt) -> BigUInt {
+        precondition(!modulus.isZero)
+        if modulus == (1 as BigUInt) { return 0 }
+        let shift = modulus.leadingZeroBitCount
+        let normalizedModulus = modulus << shift
+        var result = BigUInt(1)
+        var b = self
+        b.formRemainder(dividingBy: normalizedModulus, normalizedBy: shift)
+        for var e in exponent.words {
+            for _ in 0 ..< Word.bitWidth {
+                if e & 1 == 1 {
+                    result *= b
+                    result.formRemainder(dividingBy: normalizedModulus, normalizedBy: shift)
+                }
+                e >>= 1
+                b *= b
+                b.formRemainder(dividingBy: normalizedModulus, normalizedBy: shift)
+            }
+        }
+        return result
+    }
+}
+
+extension BigInt {
+    /// Returns this integer raised to the power `exponent`.
+    ///
+    /// This function calculates the result by [successively squaring the base while halving the exponent][expsqr].
+    ///
+    /// [expsqr]: https://en.wikipedia.org/wiki/Exponentiation_by_squaring
+    ///
+    /// - Note: This function can be unreasonably expensive for large exponents, which is why `exponent` is
+    ///         a simple integer value. If you want to calculate big exponents, you'll probably need to use
+    ///         the modulo arithmetic variant.
+    /// - Returns: 1 if `exponent == 0`, otherwise `self` raised to `exponent`. (This implies that `0.power(0) == 1`.)
+    /// - SeeAlso: `BigUInt.power(_:, modulus:)`
+    /// - Complexity: O((exponent * self.count)^log2(3)) or somesuch. The result may require a large amount of memory, too.
+    public func power(_ exponent: Int) -> BigInt {
+        return BigInt(sign: self.sign == .minus && exponent & 1 != 0 ? .minus : .plus,
+                      magnitude: self.magnitude.power(exponent))
+    }
+
+    /// Returns the remainder of this integer raised to the power `exponent` in modulo arithmetic under `modulus`.
+    ///
+    /// Uses the [right-to-left binary method][rtlb].
+    ///
+    /// [rtlb]: https://en.wikipedia.org/wiki/Modular_exponentiation#Right-to-left_binary_method
+    ///
+    /// - Complexity: O(exponent.count * modulus.count^log2(3)) or somesuch
+    public func power(_ exponent: BigInt, modulus: BigInt) -> BigInt {
+        precondition(!modulus.isZero)
+        if modulus.magnitude == 1 { return 0 }
+        if exponent.isZero { return 1 }
+        if exponent == 1 { return self.modulus(modulus) }
+        if exponent < 0 {
+            precondition(!self.isZero)
+            guard magnitude == 1 else { return 0 }
+            guard sign == .minus else { return 1 }
+            guard exponent.magnitude[0] & 1 != 0 else { return 1 }
+            return BigInt(modulus.magnitude - 1)
+        }
+        let power = self.magnitude.power(exponent.magnitude,
+                                         modulus: modulus.magnitude)
+        if self.sign == .plus || exponent.magnitude[0] & 1 == 0 || power.isZero {
+            return BigInt(power)
+        }
+        return BigInt(modulus.magnitude - power)
+    }
+}

Sources/CryptoSwift/BigInt/Floating Point Conversion.swift

@@ -0,0 +1,73 @@
+//
+//  Floating Point Conversion.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2017-08-11.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+    public init?<T: BinaryFloatingPoint>(exactly source: T) {
+        guard source.isFinite else { return nil }
+        guard !source.isZero else { self = 0; return }
+        guard source.sign == .plus else { return nil }
+        let value = source.rounded(.towardZero)
+        guard value == source else { return nil }
+        assert(value.floatingPointClass == .positiveNormal)
+        assert(value.exponent >= 0)
+        let significand = value.significandBitPattern
+        self = (BigUInt(1) << value.exponent) + BigUInt(significand) >> (T.significandBitCount - Int(value.exponent))
+    }
+
+    public init<T: BinaryFloatingPoint>(_ source: T) {
+        self.init(exactly: source.rounded(.towardZero))!
+    }
+}
+
+extension BigInt {
+    public init?<T: BinaryFloatingPoint>(exactly source: T) {
+        switch source.sign{
+        case .plus:
+            guard let magnitude = BigUInt(exactly: source) else { return nil }
+            self = BigInt(sign: .plus, magnitude: magnitude)
+        case .minus:
+            guard let magnitude = BigUInt(exactly: -source) else { return nil }
+            self = BigInt(sign: .minus, magnitude: magnitude)
+        }
+    }
+
+    public init<T: BinaryFloatingPoint>(_ source: T) {
+        self.init(exactly: source.rounded(.towardZero))!
+    }
+}
+
+extension BinaryFloatingPoint where RawExponent: FixedWidthInteger, RawSignificand: FixedWidthInteger {
+    public init(_ value: BigInt) {
+        guard !value.isZero else { self = 0; return }
+        let v = value.magnitude
+        let bitWidth = v.bitWidth
+        var exponent = bitWidth - 1
+        let shift = bitWidth - Self.significandBitCount - 1
+        var significand = value.magnitude >> (shift - 1)
+        if significand[0] & 3 == 3 { // Handle rounding
+            significand >>= 1
+            significand += 1
+            if significand.trailingZeroBitCount >= Self.significandBitCount {
+                exponent += 1
+            }
+        }
+        else {
+            significand >>= 1
+        }
+        let bias = 1 << (Self.exponentBitCount - 1) - 1
+        guard exponent <= bias else { self = Self.infinity; return }
+        significand &= 1 << Self.significandBitCount - 1
+        self = Self.init(sign: value.sign == .plus ? .plus : .minus,
+                         exponentBitPattern: RawExponent(bias + exponent),
+                         significandBitPattern: RawSignificand(significand))
+    }
+
+    public init(_ value: BigUInt) {
+        self.init(BigInt(sign: .plus, magnitude: value))
+    }
+}

Sources/CryptoSwift/BigInt/GCD.swift

@@ -0,0 +1,80 @@
+//
+//  GCD.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+    //MARK: Greatest Common Divisor
+    
+    /// Returns the greatest common divisor of `self` and `b`.
+    ///
+    /// - Complexity: O(count^2) where count = max(self.count, b.count)
+    public func greatestCommonDivisor(with b: BigUInt) -> BigUInt {
+        // This is Stein's algorithm: https://en.wikipedia.org/wiki/Binary_GCD_algorithm
+        if self.isZero { return b }
+        if b.isZero { return self }
+
+        let az = self.trailingZeroBitCount
+        let bz = b.trailingZeroBitCount
+        let twos = Swift.min(az, bz)
+
+        var (x, y) = (self >> az, b >> bz)
+        if x < y { swap(&x, &y) }
+
+        while !x.isZero {
+            x >>= x.trailingZeroBitCount
+            if x < y { swap(&x, &y) }
+            x -= y
+        }
+        return y << twos
+    }
+    
+    /// Returns the [multiplicative inverse of this integer in modulo `modulus` arithmetic][inverse],
+    /// or `nil` if there is no such number.
+    /// 
+    /// [inverse]: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Modular_integers
+    ///
+    /// - Returns: If `gcd(self, modulus) == 1`, the value returned is an integer `a < modulus` such that `(a * self) % modulus == 1`. If `self` and `modulus` aren't coprime, the return value is `nil`.
+    /// - Requires: modulus > 1
+    /// - Complexity: O(count^3)
+    public func inverse(_ modulus: BigUInt) -> BigUInt? {
+        precondition(modulus > 1)
+        var t1 = BigInt(0)
+        var t2 = BigInt(1)
+        var r1 = modulus
+        var r2 = self
+        while !r2.isZero {
+            let quotient = r1 / r2
+            (t1, t2) = (t2, t1 - BigInt(quotient) * t2)
+            (r1, r2) = (r2, r1 - quotient * r2)
+        }
+        if r1 > 1 { return nil }
+        if t1.sign == .minus { return modulus - t1.magnitude }
+        return t1.magnitude
+    }
+}
+
+extension BigInt {
+    /// Returns the greatest common divisor of `a` and `b`.
+    ///
+    /// - Complexity: O(count^2) where count = max(a.count, b.count)
+    public func greatestCommonDivisor(with b: BigInt) -> BigInt {
+        return BigInt(self.magnitude.greatestCommonDivisor(with: b.magnitude))
+    }
+
+    /// Returns the [multiplicative inverse of this integer in modulo `modulus` arithmetic][inverse],
+    /// or `nil` if there is no such number.
+    ///
+    /// [inverse]: https://en.wikipedia.org/wiki/Extended_Euclidean_algorithm#Modular_integers
+    ///
+    /// - Returns: If `gcd(self, modulus) == 1`, the value returned is an integer `a < modulus` such that `(a * self) % modulus == 1`. If `self` and `modulus` aren't coprime, the return value is `nil`.
+    /// - Requires: modulus.magnitude > 1
+    /// - Complexity: O(count^3)
+    public func inverse(_ modulus: BigInt) -> BigInt? {
+        guard let inv = self.magnitude.inverse(modulus.magnitude) else { return nil }
+        return BigInt(self.sign == .plus || inv.isZero ? inv : modulus.magnitude - inv)
+    }
+}

Sources/CryptoSwift/BigInt/Hashable.swift

@@ -0,0 +1,26 @@
+//
+//  Hashable.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt: Hashable {
+    //MARK: Hashing
+
+    /// Append this `BigUInt` to the specified hasher.
+    public func hash(into hasher: inout Hasher) {
+        for word in self.words {
+            hasher.combine(word)
+        }
+    }
+}
+
+extension BigInt: Hashable {
+    /// Append this `BigInt` to the specified hasher.
+    public func hash(into hasher: inout Hasher) {
+        hasher.combine(sign)
+        hasher.combine(magnitude)
+    }
+}

Sources/CryptoSwift/BigInt/Integer Conversion.swift

@@ -0,0 +1,89 @@
+//
+//  Integer Conversion.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2017-08-11.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+    public init?<T: BinaryInteger>(exactly source: T) {
+        guard source >= (0 as T) else { return nil }
+        if source.bitWidth <= 2 * Word.bitWidth {
+            var it = source.words.makeIterator()
+            self.init(low: it.next() ?? 0, high: it.next() ?? 0)
+            precondition(it.next() == nil, "Length of BinaryInteger.words is greater than its bitWidth")
+        }
+        else {
+            self.init(words: source.words)
+        }
+    }
+
+    public init<T: BinaryInteger>(_ source: T) {
+        precondition(source >= (0 as T), "BigUInt cannot represent negative values")
+        self.init(exactly: source)!
+    }
+
+    public init<T: BinaryInteger>(truncatingIfNeeded source: T) {
+        self.init(words: source.words)
+    }
+
+    public init<T: BinaryInteger>(clamping source: T) {
+        if source <= (0 as T) {
+            self.init()
+        }
+        else {
+            self.init(words: source.words)
+        }
+    }
+}
+
+extension BigInt {
+    public init() {
+        self.init(sign: .plus, magnitude: 0)
+    }
+
+    /// Initializes a new signed big integer with the same value as the specified unsigned big integer.
+    public init(_ integer: BigUInt) {
+        self.magnitude = integer
+        self.sign = .plus
+    }
+
+    public init<T>(_ source: T) where T : BinaryInteger {
+        if source >= (0 as T) {
+            self.init(sign: .plus, magnitude: BigUInt(source))
+        }
+        else {
+            var words = Array(source.words)
+            words.twosComplement()
+            self.init(sign: .minus, magnitude: BigUInt(words: words))
+        }
+    }
+
+    public init?<T>(exactly source: T) where T : BinaryInteger {
+        self.init(source)
+    }
+
+    public init<T>(clamping source: T) where T : BinaryInteger {
+        self.init(source)
+    }
+
+    public init<T>(truncatingIfNeeded source: T) where T : BinaryInteger {
+        self.init(source)
+    }
+}
+
+extension BigUInt: ExpressibleByIntegerLiteral {
+    /// Initialize a new big integer from an integer literal.
+    public init(integerLiteral value: UInt64) {
+        self.init(value)
+    }
+}
+
+extension BigInt: ExpressibleByIntegerLiteral {
+    /// Initialize a new big integer from an integer literal.
+    public init(integerLiteral value: Int64) {
+        self.init(value)
+    }
+}
+

Sources/CryptoSwift/BigInt/Multiplication.swift

@@ -0,0 +1,165 @@
+//
+//  Multiplication.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+
+    //MARK: Multiplication
+
+    /// Multiply this big integer by a single word, and store the result in place of the original big integer.
+    ///
+    /// - Complexity: O(count)
+    public mutating func multiply(byWord y: Word) {
+        guard y != 0 else { self = 0; return }
+        guard y != 1 else { return }
+        var carry: Word = 0
+        let c = self.count
+        for i in 0 ..< c {
+            let (h, l) = self[i].multipliedFullWidth(by: y)
+            let (low, o) = l.addingReportingOverflow(carry)
+            self[i] = low
+            carry = (o ? h + 1 : h)
+        }
+        self[c] = carry
+    }
+
+    /// Multiply this big integer by a single Word, and return the result.
+    ///
+    /// - Complexity: O(count)
+    public func multiplied(byWord y: Word) -> BigUInt {
+        var r = self
+        r.multiply(byWord: y)
+        return r
+    }
+
+    /// Multiply `x` by `y`, and add the result to this integer, optionally shifted `shift` words to the left.
+    ///
+    /// - Note: This is the fused multiply/shift/add operation; it is more efficient than doing the components
+    ///   individually. (The fused operation doesn't need to allocate space for temporary big integers.)
+    /// - Returns: `self` is set to `self + (x * y) << (shift * 2^Word.bitWidth)`
+    /// - Complexity: O(count)
+    public mutating func multiplyAndAdd(_ x: BigUInt, _ y: Word, shiftedBy shift: Int = 0) {
+        precondition(shift >= 0)
+        guard y != 0 && x.count > 0 else { return }
+        guard y != 1 else { self.add(x, shiftedBy: shift); return }
+        var mulCarry: Word = 0
+        var addCarry = false
+        let xc = x.count
+        var xi = 0
+        while xi < xc || addCarry || mulCarry > 0 {
+            let (h, l) = x[xi].multipliedFullWidth(by: y)
+            let (low, o) = l.addingReportingOverflow(mulCarry)
+            mulCarry = (o ? h + 1 : h)
+
+            let ai = shift + xi
+            let (sum1, so1) = self[ai].addingReportingOverflow(low)
+            if addCarry {
+                let (sum2, so2) = sum1.addingReportingOverflow(1)
+                self[ai] = sum2
+                addCarry = so1 || so2
+            }
+            else {
+                self[ai] = sum1
+                addCarry = so1
+            }
+            xi += 1
+        }
+    }
+
+    /// Multiply this integer by `y` and return the result.
+    ///
+    /// - Note: This uses the naive O(n^2) multiplication algorithm unless both arguments have more than
+    ///   `BigUInt.directMultiplicationLimit` words.
+    /// - Complexity: O(n^log2(3))
+    public func multiplied(by y: BigUInt) -> BigUInt {
+        // This method is mostly defined for symmetry with the rest of the arithmetic operations.
+        return self * y
+    }
+
+    /// Multiplication switches to an asymptotically better recursive algorithm when arguments have more words than this limit.
+    public static var directMultiplicationLimit: Int = 1024
+
+    /// Multiply `a` by `b` and return the result.
+    ///
+    /// - Note: This uses the naive O(n^2) multiplication algorithm unless both arguments have more than
+    ///   `BigUInt.directMultiplicationLimit` words.
+    /// - Complexity: O(n^log2(3))
+    public static func *(x: BigUInt, y: BigUInt) -> BigUInt {
+        let xc = x.count
+        let yc = y.count
+        if xc == 0 { return BigUInt() }
+        if yc == 0 { return BigUInt() }
+        if yc == 1 { return x.multiplied(byWord: y[0]) }
+        if xc == 1 { return y.multiplied(byWord: x[0]) }
+
+        if Swift.min(xc, yc) <= BigUInt.directMultiplicationLimit {
+            // Long multiplication.
+            let left = (xc < yc ? y : x)
+            let right = (xc < yc ? x : y)
+            var result = BigUInt()
+            for i in (0 ..< right.count).reversed() {
+                result.multiplyAndAdd(left, right[i], shiftedBy: i)
+            }
+            return result
+        }
+
+        if yc < xc {
+            let (xh, xl) = x.split
+            var r = xl * y
+            r.add(xh * y, shiftedBy: x.middleIndex)
+            return r
+        }
+        else if xc < yc {
+            let (yh, yl) = y.split
+            var r = yl * x
+            r.add(yh * x, shiftedBy: y.middleIndex)
+            return r
+        }
+
+        let shift = x.middleIndex
+
+        // Karatsuba multiplication:
+        // x * y = <a,b> * <c,d> = <ac, ac + bd - (a-b)(c-d), bd> (ignoring carry)
+        let (a, b) = x.split
+        let (c, d) = y.split
+
+        let high = a * c
+        let low = b * d
+        let xp = a >= b
+        let yp = c >= d
+        let xm = (xp ? a - b : b - a)
+        let ym = (yp ? c - d : d - c)
+        let m = xm * ym
+
+        var r = low
+        r.add(high, shiftedBy: 2 * shift)
+        r.add(low, shiftedBy: shift)
+        r.add(high, shiftedBy: shift)
+        if xp == yp {
+            r.subtract(m, shiftedBy: shift)
+        }
+        else {
+            r.add(m, shiftedBy: shift)
+        }
+        return r
+    }
+
+    /// Multiply `a` by `b` and store the result in `a`.
+    public static func *=(a: inout BigUInt, b: BigUInt) {
+        a = a * b
+    }
+}
+
+extension BigInt {
+    /// Multiply `a` with `b` and return the result.
+    public static func *(a: BigInt, b: BigInt) -> BigInt {
+        return BigInt(sign: a.sign == b.sign ? .plus : .minus, magnitude: a.magnitude * b.magnitude)
+    }
+
+    /// Multiply `a` with `b` in place.
+    public static func *=(a: inout BigInt, b: BigInt) { a = a * b }
+}

Sources/CryptoSwift/BigInt/Prime Test.swift

@@ -0,0 +1,153 @@
+//
+//  Prime Test.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-04.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+/// The first several [prime numbers][primes]. 
+///
+/// [primes]: https://oeis.org/A000040
+let primes: [BigUInt.Word] = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41]
+
+/// The ith element in this sequence is the smallest composite number that passes the strong probable prime test
+/// for all of the first (i+1) primes.
+///
+/// This is sequence [A014233](http://oeis.org/A014233) on the [Online Encyclopaedia of Integer Sequences](http://oeis.org).
+let pseudoPrimes: [BigUInt] = [
+    /*  2 */ 2_047,
+    /*  3 */ 1_373_653,
+    /*  5 */ 25_326_001,
+    /*  7 */ 3_215_031_751,
+    /* 11 */ 2_152_302_898_747,
+    /* 13 */ 3_474_749_660_383,
+    /* 17 */ 341_550_071_728_321,
+    /* 19 */ 341_550_071_728_321,
+    /* 23 */ 3_825_123_056_546_413_051,
+    /* 29 */ 3_825_123_056_546_413_051,
+    /* 31 */ 3_825_123_056_546_413_051,
+    /* 37 */ "318665857834031151167461",
+    /* 41 */ "3317044064679887385961981",
+]
+
+extension BigUInt {
+    //MARK: Primality Testing
+
+    /// Returns true iff this integer passes the [strong probable prime test][sppt] for the specified base.
+    ///
+    /// [sppt]: https://en.wikipedia.org/wiki/Probable_prime
+    public func isStrongProbablePrime(_ base: BigUInt) -> Bool {
+        precondition(base > (1 as BigUInt))
+        precondition(self > (0 as BigUInt))
+        let dec = self - 1
+
+        let r = dec.trailingZeroBitCount
+        let d = dec >> r
+
+        var test = base.power(d, modulus: self)
+        if test == 1 || test == dec { return true }
+
+        if r > 0 {
+            let shift = self.leadingZeroBitCount
+            let normalized = self << shift
+            for _ in 1 ..< r {
+                test *= test
+                test.formRemainder(dividingBy: normalized, normalizedBy: shift)
+                if test == 1 {
+                    return false
+                }
+                if test == dec { return true }
+            }
+        }
+        return false
+    }
+
+    /// Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.
+    ///
+    /// This function performs a probabilistic [Miller-Rabin Primality Test][mrpt], consisting of `rounds` iterations, 
+    /// each calculating the strong probable prime test for a random base. The number of rounds is 10 by default,
+    /// but you may specify your own choice.
+    ///
+    /// To speed things up, the function checks if `self` is divisible by the first few prime numbers before
+    /// diving into (slower) Miller-Rabin testing.
+    ///
+    /// Also, when `self` is less than 82 bits wide, `isPrime` does a deterministic test that is guaranteed to 
+    /// return a correct result.
+    ///
+    /// [mrpt]: https://en.wikipedia.org/wiki/Miller–Rabin_primality_test
+    public func isPrime(rounds: Int = 10) -> Bool {
+        if count <= 1 && self[0] < 2 { return false }
+        if count == 1 && self[0] < 4 { return true }
+
+        // Even numbers above 2 aren't prime.
+        if self[0] & 1 == 0 { return false }
+
+        // Quickly check for small primes.
+        for i in 1 ..< primes.count {
+            let p = primes[i]
+            if self.count == 1 && self[0] == p {
+                return true
+            }
+            if self.quotientAndRemainder(dividingByWord: p).remainder == 0 {
+                return false
+            }
+        }
+
+        /// Give an exact answer when we can.
+        if self < pseudoPrimes.last! {
+            for i in 0 ..< pseudoPrimes.count {
+                guard isStrongProbablePrime(BigUInt(primes[i])) else {
+                    break
+                }
+                if self < pseudoPrimes[i] {
+                    // `self` is below the lowest pseudoprime corresponding to the prime bases we tested. It's a prime!
+                    return true
+                }
+            }
+            return false
+        }
+
+        /// Otherwise do as many rounds of random SPPT as required.
+        for _ in 0 ..< rounds {
+            let random = BigUInt.randomInteger(lessThan: self - 2) + 2
+            guard isStrongProbablePrime(random) else {
+                return false
+            }
+        }
+
+        // Well, it smells primey to me.
+        return true
+    }
+}
+
+extension BigInt {
+    //MARK: Primality Testing
+
+    /// Returns true iff this integer passes the [strong probable prime test][sppt] for the specified base.
+    ///
+    /// [sppt]: https://en.wikipedia.org/wiki/Probable_prime
+    public func isStrongProbablePrime(_ base: BigInt) -> Bool {
+        precondition(base.sign == .plus)
+        if self.sign == .minus { return false }
+        return self.magnitude.isStrongProbablePrime(base.magnitude)
+    }
+
+    /// Returns true if this integer is probably prime. Returns false if this integer is definitely not prime.
+    ///
+    /// This function performs a probabilistic [Miller-Rabin Primality Test][mrpt], consisting of `rounds` iterations,
+    /// each calculating the strong probable prime test for a random base. The number of rounds is 10 by default,
+    /// but you may specify your own choice.
+    ///
+    /// To speed things up, the function checks if `self` is divisible by the first few prime numbers before
+    /// diving into (slower) Miller-Rabin testing.
+    ///
+    /// Also, when `self` is less than 82 bits wide, `isPrime` does a deterministic test that is guaranteed to
+    /// return a correct result.
+    ///
+    /// [mrpt]: https://en.wikipedia.org/wiki/Miller–Rabin_primality_test
+    public func isPrime(rounds: Int = 10) -> Bool {
+        if self.sign == .minus { return false }
+        return self.magnitude.isPrime(rounds: rounds)
+    }
+}

Sources/CryptoSwift/BigInt/Random.swift

@@ -0,0 +1,101 @@
+//
+//  Random.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-04.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+    /// Create a big unsigned integer consisting of `width` uniformly distributed random bits.
+    ///
+    /// - Parameter width: The maximum number of one bits in the result.
+    /// - Parameter generator: The source of randomness.
+    /// - Returns: A big unsigned integer less than `1 << width`.
+    public static func randomInteger<RNG: RandomNumberGenerator>(withMaximumWidth width: Int, using generator: inout RNG) -> BigUInt {
+        var result = BigUInt.zero
+        var bitsLeft = width
+        var i = 0
+        let wordsNeeded = (width + Word.bitWidth - 1) / Word.bitWidth
+        if wordsNeeded > 2 {
+            result.reserveCapacity(wordsNeeded)
+        }
+        while bitsLeft >= Word.bitWidth {
+            result[i] = generator.next()
+            i += 1
+            bitsLeft -= Word.bitWidth
+        }
+        if bitsLeft > 0 {
+            let mask: Word = (1 << bitsLeft) - 1
+            result[i] = (generator.next() as Word) & mask
+        }
+        return result
+    }
+
+    /// Create a big unsigned integer consisting of `width` uniformly distributed random bits.
+    ///
+    /// - Note: I use a `SystemRandomGeneratorGenerator` as the source of randomness.
+    ///
+    /// - Parameter width: The maximum number of one bits in the result.
+    /// - Returns: A big unsigned integer less than `1 << width`.
+    public static func randomInteger(withMaximumWidth width: Int) -> BigUInt {
+        var rng = SystemRandomNumberGenerator()
+        return randomInteger(withMaximumWidth: width, using: &rng)
+    }
+
+    /// Create a big unsigned integer consisting of `width-1` uniformly distributed random bits followed by a one bit.
+    ///
+    /// - Note: If `width` is zero, the result is zero.
+    ///
+    /// - Parameter width: The number of bits required to represent the answer.
+    /// - Parameter generator: The source of randomness.
+    /// - Returns: A random big unsigned integer whose width is `width`.
+    public static func randomInteger<RNG: RandomNumberGenerator>(withExactWidth width: Int, using generator: inout RNG) -> BigUInt {
+        // width == 0 -> return 0 because there is no room for a one bit.
+        // width == 1 -> return 1 because there is no room for any random bits.
+        guard width > 1 else { return BigUInt(width) }
+        var result = randomInteger(withMaximumWidth: width - 1, using: &generator)
+        result[(width - 1) / Word.bitWidth] |= 1 << Word((width - 1) % Word.bitWidth)
+        return result
+    }
+
+    /// Create a big unsigned integer consisting of `width-1` uniformly distributed random bits followed by a one bit.
+    ///
+    /// - Note: If `width` is zero, the result is zero.
+    /// - Note: I use a `SystemRandomGeneratorGenerator` as the source of randomness.
+    ///
+    /// - Returns: A random big unsigned integer whose width is `width`.
+    public static func randomInteger(withExactWidth width: Int) -> BigUInt {
+        var rng = SystemRandomNumberGenerator()
+        return randomInteger(withExactWidth: width, using: &rng)
+    }
+
+    /// Create a uniformly distributed random unsigned integer that's less than the specified limit.
+    ///
+    /// - Precondition: `limit > 0`.
+    ///
+    /// - Parameter limit: The upper bound on the result.
+    /// - Parameter generator: The source of randomness.
+    /// - Returns: A random big unsigned integer that is less than `limit`.
+    public static func randomInteger<RNG: RandomNumberGenerator>(lessThan limit: BigUInt, using generator: inout RNG) -> BigUInt {
+        precondition(limit > 0, "\(#function): 0 is not a valid limit")
+        let width = limit.bitWidth
+        var random = randomInteger(withMaximumWidth: width, using: &generator)
+        while random >= limit {
+            random = randomInteger(withMaximumWidth: width, using: &generator)
+        }
+        return random
+    }
+
+    /// Create a uniformly distributed random unsigned integer that's less than the specified limit.
+    ///
+    /// - Precondition: `limit > 0`.
+    /// - Note: I use a `SystemRandomGeneratorGenerator` as the source of randomness.
+    ///
+    /// - Parameter limit: The upper bound on the result.
+    /// - Returns: A random big unsigned integer that is less than `limit`.
+    public static func randomInteger(lessThan limit: BigUInt) -> BigUInt {
+        var rng = SystemRandomNumberGenerator()
+        return randomInteger(lessThan: limit, using: &rng)
+    }
+}

Sources/CryptoSwift/BigInt/Shifts.swift

@@ -0,0 +1,211 @@
+//
+//  Shifts.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+
+    //MARK: Shift Operators
+    
+    internal func shiftedLeft(by amount: Word) -> BigUInt {
+        guard amount > 0 else { return self }
+        
+        let ext = Int(amount / Word(Word.bitWidth)) // External shift amount (new words)
+        let up = Word(amount % Word(Word.bitWidth)) // Internal shift amount (subword shift)
+        let down = Word(Word.bitWidth) - up
+        
+        var result = BigUInt()
+        if up > 0 {
+            var i = 0
+            var lowbits: Word = 0
+            while i < self.count || lowbits > 0 {
+                let word = self[i]
+                result[i + ext] = word << up | lowbits
+                lowbits = word >> down
+                i += 1
+            }
+        }
+        else {
+            for i in 0 ..< self.count {
+                result[i + ext] = self[i]
+            }
+        }
+        return result
+    }
+    
+    internal mutating func shiftLeft(by amount: Word) {
+        guard amount > 0 else { return }
+        
+        let ext = Int(amount / Word(Word.bitWidth)) // External shift amount (new words)
+        let up = Word(amount % Word(Word.bitWidth)) // Internal shift amount (subword shift)
+        let down = Word(Word.bitWidth) - up
+        
+        if up > 0 {
+            var i = 0
+            var lowbits: Word = 0
+            while i < self.count || lowbits > 0 {
+                let word = self[i]
+                self[i] = word << up | lowbits
+                lowbits = word >> down
+                i += 1
+            }
+        }
+        if ext > 0 && self.count > 0 {
+            self.shiftLeft(byWords: ext)
+        }
+    }
+    
+    internal func shiftedRight(by amount: Word) -> BigUInt {
+        guard amount > 0 else { return self }
+        guard amount < self.bitWidth else { return 0 }
+        
+        let ext = Int(amount / Word(Word.bitWidth)) // External shift amount (new words)
+        let down = Word(amount % Word(Word.bitWidth)) // Internal shift amount (subword shift)
+        let up = Word(Word.bitWidth) - down
+        
+        var result = BigUInt()
+        if down > 0 {
+            var highbits: Word = 0
+            for i in (ext ..< self.count).reversed() {
+                let word = self[i]
+                result[i - ext] = highbits | word >> down
+                highbits = word << up
+            }
+        }
+        else {
+            for i in (ext ..< self.count).reversed() {
+                result[i - ext] = self[i]
+            }
+        }
+        return result
+    }
+
+    internal mutating func shiftRight(by amount: Word) {
+        guard amount > 0 else { return }
+        guard amount < self.bitWidth else { self.clear(); return }
+        
+        let ext = Int(amount / Word(Word.bitWidth)) // External shift amount (new words)
+        let down = Word(amount % Word(Word.bitWidth)) // Internal shift amount (subword shift)
+        let up = Word(Word.bitWidth) - down
+        
+        if ext > 0 {
+            self.shiftRight(byWords: ext)
+        }
+        if down > 0 {
+            var i = self.count - 1
+            var highbits: Word = 0
+            while i >= 0 {
+                let word = self[i]
+                self[i] = highbits | word >> down
+                highbits = word << up
+                i -= 1
+            }
+        }
+    }
+    
+    public static func >>=<Other: BinaryInteger>(lhs: inout BigUInt, rhs: Other) {
+        if rhs < (0 as Other) {
+            lhs <<= (0 - rhs)
+        }
+        else if rhs >= lhs.bitWidth {
+            lhs.clear()
+        }
+        else {
+            lhs.shiftRight(by: UInt(rhs))
+        }
+    }
+    
+    public static func <<=<Other: BinaryInteger>(lhs: inout BigUInt, rhs: Other) {
+        if rhs < (0 as Other) {
+            lhs >>= (0 - rhs)
+            return
+        }
+        lhs.shiftLeft(by: Word(exactly: rhs)!)
+    }
+
+    public static func >><Other: BinaryInteger>(lhs: BigUInt, rhs: Other) -> BigUInt {
+        if rhs < (0 as Other) {
+            return lhs << (0 - rhs)
+        }
+        if rhs > Word.max {
+            return 0
+        }
+        return lhs.shiftedRight(by: UInt(rhs))
+    }
+
+    public static func <<<Other: BinaryInteger>(lhs: BigUInt, rhs: Other) -> BigUInt {
+        if rhs < (0 as Other) {
+            return lhs >> (0 - rhs)
+        }
+        return lhs.shiftedLeft(by: Word(exactly: rhs)!)
+    }
+}
+
+extension BigInt {
+    func shiftedLeft(by amount: Word) -> BigInt {
+        return BigInt(sign: self.sign, magnitude: self.magnitude.shiftedLeft(by: amount))
+    }
+    
+    mutating func shiftLeft(by amount: Word) {
+        self.magnitude.shiftLeft(by: amount)
+    }
+    
+    func shiftedRight(by amount: Word) -> BigInt {
+        let m = self.magnitude.shiftedRight(by: amount)
+        return BigInt(sign: self.sign, magnitude: self.sign == .minus && m.isZero ? 1 : m)
+    }
+    
+    mutating func shiftRight(by amount: Word) {
+        magnitude.shiftRight(by: amount)
+        if sign == .minus, magnitude.isZero {
+            magnitude.load(1)
+        }
+    }
+    
+    public static func &<<(left: BigInt, right: BigInt) -> BigInt {
+        return left.shiftedLeft(by: right.words[0])
+    }
+    
+    public static func &<<=(left: inout BigInt, right: BigInt) {
+        left.shiftLeft(by: right.words[0])
+    }
+    
+    public static func &>>(left: BigInt, right: BigInt) -> BigInt {
+        return left.shiftedRight(by: right.words[0])
+    }
+    
+    public static func &>>=(left: inout BigInt, right: BigInt) {
+        left.shiftRight(by: right.words[0])
+    }
+    
+    public static func <<<Other: BinaryInteger>(lhs: BigInt, rhs: Other) -> BigInt {
+        guard rhs >= (0 as Other) else { return lhs >> (0 - rhs) }
+        return lhs.shiftedLeft(by: Word(rhs))
+    }
+    
+    public static func <<=<Other: BinaryInteger>(lhs: inout BigInt, rhs: Other) {
+        if rhs < (0 as Other) {
+            lhs >>= (0 - rhs)
+        }
+        else {
+            lhs.shiftLeft(by: Word(rhs))
+        }
+    }
+    
+    public static func >><Other: BinaryInteger>(lhs: BigInt, rhs: Other) -> BigInt {
+        guard rhs >= (0 as Other) else { return lhs << (0 - rhs) }
+        return lhs.shiftedRight(by: Word(rhs))
+    }
+    
+    public static func >>=<Other: BinaryInteger>(lhs: inout BigInt, rhs: Other) {
+        if rhs < (0 as Other) {
+            lhs <<= (0 - rhs)
+        }
+        else {
+            lhs.shiftRight(by: Word(rhs))
+        }
+    }
+}

Sources/CryptoSwift/BigInt/Square Root.swift

@@ -0,0 +1,41 @@
+//
+//  Square Root.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+//MARK: Square Root
+
+extension BigUInt {
+    /// Returns the integer square root of a big integer; i.e., the largest integer whose square isn't greater than `value`.
+    ///
+    /// - Returns: floor(sqrt(self))
+    public func squareRoot() -> BigUInt {
+        // This implementation uses Newton's method.
+        guard !self.isZero else { return BigUInt() }
+        var x = BigUInt(1) << ((self.bitWidth + 1) / 2)
+        var y: BigUInt = 0
+        while true {
+            y.load(self)
+            y /= x
+            y += x
+            y >>= 1
+            if x == y || x == y - 1 { break }
+            x = y
+        }
+        return x
+    }
+}
+
+extension BigInt {
+    /// Returns the integer square root of a big integer; i.e., the largest integer whose square isn't greater than `value`.
+    ///
+    /// - Requires: self >= 0
+    /// - Returns: floor(sqrt(self))
+    public func squareRoot() -> BigInt {
+        precondition(self.sign == .plus)
+        return BigInt(sign: .plus, magnitude: self.magnitude.squareRoot())
+    }
+}

Sources/CryptoSwift/BigInt/Strideable.swift

@@ -0,0 +1,38 @@
+//
+//  Strideable.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2017-08-11.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt: Strideable {
+    /// A type that can represent the distance between two values ofa `BigUInt`.
+    public typealias Stride = BigInt
+
+    /// Adds `n` to `self` and returns the result. Traps if the result would be less than zero.
+    public func advanced(by n: BigInt) -> BigUInt {
+        return n.sign == .minus ? self - n.magnitude : self + n.magnitude
+    }
+
+    /// Returns the (potentially negative) difference between `self` and `other` as a `BigInt`. Never traps.
+    public func distance(to other: BigUInt) -> BigInt {
+        return BigInt(other) - BigInt(self)
+    }
+}
+
+extension BigInt: Strideable {
+    public typealias Stride = BigInt
+
+    /// Returns `self + n`.
+    public func advanced(by n: Stride) -> BigInt {
+        return self + n
+    }
+
+    /// Returns `other - self`.
+    public func distance(to other: BigInt) -> Stride {
+        return other - self
+    }
+}
+
+

Sources/CryptoSwift/BigInt/String Conversion.swift

@@ -0,0 +1,236 @@
+//
+//  String Conversion.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+
+    //MARK: String Conversion
+
+    /// Calculates the number of numerals in a given radix that fit inside a single `Word`.
+    ///
+    /// - Returns: (chars, power) where `chars` is highest that satisfy `radix^chars <= 2^Word.bitWidth`. `power` is zero
+    ///   if radix is a power of two; otherwise `power == radix^chars`.
+    fileprivate static func charsPerWord(forRadix radix: Int) -> (chars: Int, power: Word) {
+        var power: Word = 1
+        var overflow = false
+        var count = 0
+        while !overflow {
+            let (p, o) = power.multipliedReportingOverflow(by: Word(radix))
+            overflow = o
+            if !o || p == 0 {
+                count += 1
+                power = p
+            }
+        }
+        return (count, power)
+    }
+
+    /// Initialize a big integer from an ASCII representation in a given radix. Numerals above `9` are represented by
+    /// letters from the English alphabet.
+    ///
+    /// - Requires: `radix > 1 && radix < 36`
+    /// - Parameter `text`: A string consisting of characters corresponding to numerals in the given radix. (0-9, a-z, A-Z)
+    /// - Parameter `radix`: The base of the number system to use, or 10 if unspecified.
+    /// - Returns: The integer represented by `text`, or nil if `text` contains a character that does not represent a numeral in `radix`.
+    public init?<S: StringProtocol>(_ text: S, radix: Int = 10) {
+        precondition(radix > 1)
+        let (charsPerWord, power) = BigUInt.charsPerWord(forRadix: radix)
+
+        var words: [Word] = []
+        var end = text.endIndex
+        var start = end
+        var count = 0
+        while start != text.startIndex {
+            start = text.index(before: start)
+            count += 1
+            if count == charsPerWord {
+                guard let d = Word.init(text[start ..< end], radix: radix) else { return nil }
+                words.append(d)
+                end = start
+                count = 0
+            }
+        }
+        if start != end {
+            guard let d = Word.init(text[start ..< end], radix: radix) else { return nil }
+            words.append(d)
+        }
+
+        if power == 0 {
+            self.init(words: words)
+        }
+        else {
+            self.init()
+            for d in words.reversed() {
+                self.multiply(byWord: power)
+                self.addWord(d)
+            }
+        }
+    }
+}
+
+extension BigInt {
+    /// Initialize a big integer from an ASCII representation in a given radix. Numerals above `9` are represented by
+    /// letters from the English alphabet.
+    ///
+    /// - Requires: `radix > 1 && radix < 36`
+    /// - Parameter `text`: A string optionally starting with "-" or "+" followed by characters corresponding to numerals in the given radix. (0-9, a-z, A-Z)
+    /// - Parameter `radix`: The base of the number system to use, or 10 if unspecified.
+    /// - Returns: The integer represented by `text`, or nil if `text` contains a character that does not represent a numeral in `radix`.
+    public init?<S: StringProtocol>(_ text: S, radix: Int = 10) {
+        var magnitude: BigUInt?
+        var sign: Sign = .plus
+        if text.first == "-" {
+            sign = .minus
+            let text = text.dropFirst()
+            magnitude = BigUInt(text, radix: radix)
+        }
+        else if text.first == "+" {
+            let text = text.dropFirst()
+            magnitude = BigUInt(text, radix: radix)
+        }
+        else {
+            magnitude = BigUInt(text, radix: radix)
+        }
+        guard let m = magnitude else { return nil }
+        self.magnitude = m
+        self.sign = sign
+    }
+}
+
+extension String {
+    /// Initialize a new string with the base-10 representation of an unsigned big integer.
+    ///
+    /// - Complexity: O(v.count^2)
+    public init(_ v: BigUInt) { self.init(v, radix: 10, uppercase: false) }
+
+    /// Initialize a new string representing an unsigned big integer in the given radix (base).
+    ///
+    /// Numerals greater than 9 are represented as letters from the English alphabet,
+    /// starting with `a` if `uppercase` is false or `A` otherwise.
+    ///
+    /// - Requires: radix > 1 && radix <= 36
+    /// - Complexity: O(count) when radix is a power of two; otherwise O(count^2).
+    public init(_ v: BigUInt, radix: Int, uppercase: Bool = false) {
+        precondition(radix > 1)
+        let (charsPerWord, power) = BigUInt.charsPerWord(forRadix: radix)
+
+        guard !v.isZero else { self = "0"; return }
+
+        var parts: [String]
+        if power == 0 {
+            parts = v.words.map { String($0, radix: radix, uppercase: uppercase) }
+        }
+        else {
+            parts = []
+            var rest = v
+            while !rest.isZero {
+                let mod = rest.divide(byWord: power)
+                parts.append(String(mod, radix: radix, uppercase: uppercase))
+            }
+        }
+        assert(!parts.isEmpty)
+
+        self = ""
+        var first = true
+        for part in parts.reversed() {
+            let zeroes = charsPerWord - part.count
+            assert(zeroes >= 0)
+            if !first && zeroes > 0 {
+                // Insert leading zeroes for mid-Words
+                self += String(repeating: "0", count: zeroes)
+            }
+            first = false
+            self += part
+        }
+    }
+
+    /// Initialize a new string representing a signed big integer in the given radix (base).
+    ///
+    /// Numerals greater than 9 are represented as letters from the English alphabet,
+    /// starting with `a` if `uppercase` is false or `A` otherwise.
+    ///
+    /// - Requires: radix > 1 && radix <= 36
+    /// - Complexity: O(count) when radix is a power of two; otherwise O(count^2).
+    public init(_ value: BigInt, radix: Int = 10, uppercase: Bool = false) {
+        self = String(value.magnitude, radix: radix, uppercase: uppercase)
+        if value.sign == .minus {
+            self = "-" + self
+        }
+    }
+}
+
+extension BigUInt: ExpressibleByStringLiteral {
+    /// Initialize a new big integer from a Unicode scalar.
+    /// The scalar must represent a decimal digit.
+    public init(unicodeScalarLiteral value: UnicodeScalar) {
+        self = BigUInt(String(value), radix: 10)!
+    }
+
+    /// Initialize a new big integer from an extended grapheme cluster.
+    /// The cluster must consist of a decimal digit.
+    public init(extendedGraphemeClusterLiteral value: String) {
+        self = BigUInt(value, radix: 10)!
+    }
+
+    /// Initialize a new big integer from a decimal number represented by a string literal of arbitrary length.
+    /// The string must contain only decimal digits.
+    public init(stringLiteral value: StringLiteralType) {
+        self = BigUInt(value, radix: 10)!
+    }
+}
+
+extension BigInt: ExpressibleByStringLiteral {
+    /// Initialize a new big integer from a Unicode scalar.
+    /// The scalar must represent a decimal digit.
+    public init(unicodeScalarLiteral value: UnicodeScalar) {
+        self = BigInt(String(value), radix: 10)!
+    }
+
+    /// Initialize a new big integer from an extended grapheme cluster.
+    /// The cluster must consist of a decimal digit.
+    public init(extendedGraphemeClusterLiteral value: String) {
+        self = BigInt(value, radix: 10)!
+    }
+
+    /// Initialize a new big integer from a decimal number represented by a string literal of arbitrary length.
+    /// The string must contain only decimal digits.
+    public init(stringLiteral value: StringLiteralType) {
+        self = BigInt(value, radix: 10)!
+    }
+}
+
+extension BigUInt: CustomStringConvertible {
+    /// Return the decimal representation of this integer.
+    public var description: String {
+        return String(self, radix: 10)
+    }
+}
+
+extension BigInt: CustomStringConvertible {
+    /// Return the decimal representation of this integer.
+    public var description: String {
+        return String(self, radix: 10)
+    }
+}
+
+extension BigUInt: CustomPlaygroundDisplayConvertible {
+
+    /// Return the playground quick look representation of this integer.
+    public var playgroundDescription: Any {
+        let text = String(self)
+        return text + " (\(self.bitWidth) bits)"
+    }
+}
+
+extension BigInt: CustomPlaygroundDisplayConvertible {
+
+    /// Return the playground quick look representation of this integer.
+    public var playgroundDescription: Any {
+        let text = String(self)
+        return text + " (\(self.magnitude.bitWidth) bits)"
+    }
+}

Sources/CryptoSwift/BigInt/Subtraction.swift

@@ -0,0 +1,169 @@
+//
+//  Subtraction.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2016-01-03.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension BigUInt {
+    //MARK: Subtraction
+
+    /// Subtract `word` from this integer in place, returning a flag indicating if the operation
+    /// caused an arithmetic overflow. `word` is shifted `shift` words to the left before being subtracted.
+    ///
+    /// - Note: If the result indicates an overflow, then `self` becomes the two's complement of the absolute difference.
+    /// - Complexity: O(count)
+    internal mutating func subtractWordReportingOverflow(_ word: Word, shiftedBy shift: Int = 0) -> Bool {
+        precondition(shift >= 0)
+        var carry: Word = word
+        var i = shift
+        let count = self.count
+        while carry > 0 && i < count {
+            let (d, c) = self[i].subtractingReportingOverflow(carry)
+            self[i] = d
+            carry = (c ? 1 : 0)
+            i += 1
+        }
+        return carry > 0
+    }
+
+    /// Subtract `word` from this integer, returning the difference and a flag that is true if the operation
+    /// caused an arithmetic overflow. `word` is shifted `shift` words to the left before being subtracted.
+    ///
+    /// - Note: If `overflow` is true, then the returned value is the two's complement of the absolute difference.
+    /// - Complexity: O(count)
+    internal func subtractingWordReportingOverflow(_ word: Word, shiftedBy shift: Int = 0) -> (partialValue: BigUInt, overflow: Bool) {
+        var result = self
+        let overflow = result.subtractWordReportingOverflow(word, shiftedBy: shift)
+        return (result, overflow)
+    }
+
+    /// Subtract a digit `d` from this integer in place.
+    /// `d` is shifted `shift` digits to the left before being subtracted.
+    ///
+    /// - Requires: self >= d * 2^shift
+    /// - Complexity: O(count)
+    internal mutating func subtractWord(_ word: Word, shiftedBy shift: Int = 0) {
+        let overflow = subtractWordReportingOverflow(word, shiftedBy: shift)
+        precondition(!overflow)
+    }
+
+    /// Subtract a digit `d` from this integer and return the result.
+    /// `d` is shifted `shift` digits to the left before being subtracted.
+    ///
+    /// - Requires: self >= d * 2^shift
+    /// - Complexity: O(count)
+    internal func subtractingWord(_ word: Word, shiftedBy shift: Int = 0) -> BigUInt {
+        var result = self
+        result.subtractWord(word, shiftedBy: shift)
+        return result
+    }
+
+    /// Subtract `other` from this integer in place, and return a flag indicating if the operation caused an
+    /// arithmetic overflow. `other` is shifted `shift` digits to the left before being subtracted.
+    ///
+    /// - Note: If the result indicates an overflow, then `self` becomes the twos' complement of the absolute difference.
+    /// - Complexity: O(count)
+    public mutating func subtractReportingOverflow(_ b: BigUInt, shiftedBy shift: Int = 0) -> Bool {
+        precondition(shift >= 0)
+        var carry = false
+        var bi = 0
+        let bc = b.count
+        let count = self.count
+        while bi < bc || (shift + bi < count && carry) {
+            let ai = shift + bi
+            let (d, c) = self[ai].subtractingReportingOverflow(b[bi])
+            if carry {
+                let (d2, c2) = d.subtractingReportingOverflow(1)
+                self[ai] = d2
+                carry = c || c2
+            }
+            else {
+                self[ai] = d
+                carry = c
+            }
+            bi += 1
+        }
+        return carry
+    }
+
+    /// Subtract `other` from this integer, returning the difference and a flag indicating arithmetic overflow.
+    /// `other` is shifted `shift` digits to the left before being subtracted.
+    ///
+    /// - Note: If `overflow` is true, then the result value is the twos' complement of the absolute value of the difference.
+    /// - Complexity: O(count)
+    public func subtractingReportingOverflow(_ other: BigUInt, shiftedBy shift: Int) -> (partialValue: BigUInt, overflow: Bool) {
+        var result = self
+        let overflow = result.subtractReportingOverflow(other, shiftedBy: shift)
+        return (result, overflow)
+    }
+    
+    /// Subtracts `other` from `self`, returning the result and a flag indicating arithmetic overflow.
+    ///
+    /// - Note: When the operation overflows, then `partialValue` is the twos' complement of the absolute value of the difference.
+    /// - Complexity: O(count)
+    public func subtractingReportingOverflow(_ other: BigUInt) -> (partialValue: BigUInt, overflow: Bool) {
+        return self.subtractingReportingOverflow(other, shiftedBy: 0)
+    }
+    
+    /// Subtract `other` from this integer in place.
+    /// `other` is shifted `shift` digits to the left before being subtracted.
+    ///
+    /// - Requires: self >= other * 2^shift
+    /// - Complexity: O(count)
+    public mutating func subtract(_ other: BigUInt, shiftedBy shift: Int = 0) {
+        let overflow = subtractReportingOverflow(other, shiftedBy: shift)
+        precondition(!overflow)
+    }
+
+    /// Subtract `b` from this integer, and return the difference.
+    /// `b` is shifted `shift` digits to the left before being subtracted.
+    ///
+    /// - Requires: self >= b * 2^shift
+    /// - Complexity: O(count)
+    public func subtracting(_ other: BigUInt, shiftedBy shift: Int = 0) -> BigUInt {
+        var result = self
+        result.subtract(other, shiftedBy: shift)
+        return result
+    }
+
+    /// Decrement this integer by one.
+    ///
+    /// - Requires: !isZero
+    /// - Complexity: O(count)
+    public mutating func decrement(shiftedBy shift: Int = 0) {
+        self.subtract(1, shiftedBy: shift)
+    }
+
+    /// Subtract `b` from `a` and return the result.
+    ///
+    /// - Requires: a >= b
+    /// - Complexity: O(a.count)
+    public static func -(a: BigUInt, b: BigUInt) -> BigUInt {
+        return a.subtracting(b)
+    }
+
+    /// Subtract `b` from `a` and store the result in `a`.
+    ///
+    /// - Requires: a >= b
+    /// - Complexity: O(a.count)
+    public static func -=(a: inout BigUInt, b: BigUInt) {
+        a.subtract(b)
+    }
+}
+
+extension BigInt {
+    public mutating func negate() {
+        guard !magnitude.isZero else { return }
+        self.sign = self.sign == .plus ? .minus : .plus
+    }
+
+    /// Subtract `b` from `a` and return the result.
+    public static func -(a: BigInt, b: BigInt) -> BigInt {
+        return a + -b
+    }
+
+    /// Subtract `b` from `a` in place.
+    public static func -=(a: inout BigInt, b: BigInt) { a = a - b }
+}

Sources/CryptoSwift/BigInt/Words and Bits.swift

@@ -0,0 +1,202 @@
+//
+//  Words and Bits.swift
+//  BigInt
+//
+//  Created by Károly Lőrentey on 2017-08-11.
+//  Copyright © 2016-2017 Károly Lőrentey.
+//
+
+extension Array where Element == UInt {
+    mutating func twosComplement() {
+        var increment = true
+        for i in 0 ..< self.count {
+            if increment {
+                (self[i], increment) = (~self[i]).addingReportingOverflow(1)
+            }
+            else {
+                self[i] = ~self[i]
+            }
+        }
+    }
+}
+
+extension BigUInt {
+    public subscript(bitAt index: Int) -> Bool {
+        get {
+            precondition(index >= 0)
+            let (i, j) = index.quotientAndRemainder(dividingBy: Word.bitWidth)
+            return self[i] & (1 << j) != 0
+        }
+        set {
+            precondition(index >= 0)
+            let (i, j) = index.quotientAndRemainder(dividingBy: Word.bitWidth)
+            if newValue {
+                self[i] |= 1 << j
+            }
+            else {
+                self[i] &= ~(1 << j)
+            }
+        }
+    }
+}
+
+extension BigUInt {
+    /// The minimum number of bits required to represent this integer in binary.
+    ///
+    /// - Returns: floor(log2(2 * self + 1))
+    /// - Complexity: O(1)
+    public var bitWidth: Int {
+        guard count > 0 else { return 0 }
+        return count * Word.bitWidth - self[count - 1].leadingZeroBitCount
+    }
+
+    /// The number of leading zero bits in the binary representation of this integer in base `2^(Word.bitWidth)`.
+    /// This is useful when you need to normalize a `BigUInt` such that the top bit of its most significant word is 1.
+    ///
+    /// - Note: 0 is considered to have zero leading zero bits.
+    /// - Returns: A value in `0...(Word.bitWidth - 1)`.
+    /// - SeeAlso: width
+    /// - Complexity: O(1)
+    public var leadingZeroBitCount: Int {
+        guard count > 0 else { return 0 }
+        return self[count - 1].leadingZeroBitCount
+    }
+
+    /// The number of trailing zero bits in the binary representation of this integer.
+    ///
+    /// - Note: 0 is considered to have zero trailing zero bits.
+    /// - Returns: A value in `0...width`.
+    /// - Complexity: O(count)
+    public var trailingZeroBitCount: Int {
+        guard count > 0 else { return 0 }
+        let i = self.words.firstIndex { $0 != 0 }!
+        return i * Word.bitWidth + self[i].trailingZeroBitCount
+    }
+}
+
+extension BigInt {
+    public var bitWidth: Int {
+        guard !magnitude.isZero else { return 0 }
+        return magnitude.bitWidth + 1
+    }
+
+    public var trailingZeroBitCount: Int {
+        // Amazingly, this works fine for negative numbers
+        return magnitude.trailingZeroBitCount
+    }
+}
+
+extension BigUInt {
+    public struct Words: RandomAccessCollection {
+        private let value: BigUInt
+
+        fileprivate init(_ value: BigUInt) { self.value = value }
+
+        public var startIndex: Int { return 0 }
+        public var endIndex: Int { return value.count }
+
+        public subscript(_ index: Int) -> Word {
+            return value[index]
+        }
+    }
+
+    public var words: Words { return Words(self) }
+
+    public init<Words: Sequence>(words: Words) where Words.Element == Word {
+        let uc = words.underestimatedCount
+        if uc > 2 {
+            self.init(words: Array(words))
+        }
+        else {
+            var it = words.makeIterator()
+            guard let w0 = it.next() else {
+                self.init()
+                return
+            }
+            guard let w1 = it.next() else {
+                self.init(word: w0)
+                return
+            }
+            if let w2 = it.next() {
+                var words: [UInt] = []
+                words.reserveCapacity(Swift.max(3, uc))
+                words.append(w0)
+                words.append(w1)
+                words.append(w2)
+                while let word = it.next() {
+                    words.append(word)
+                }
+                self.init(words: words)
+            }
+            else {
+                self.init(low: w0, high: w1)
+            }
+        }
+    }
+}
+
+extension BigInt {
+    public struct Words: RandomAccessCollection {
+        public typealias Indices = CountableRange<Int>
+
+        private let value: BigInt
+        private let decrementLimit: Int
+
+        fileprivate init(_ value: BigInt) {
+            self.value = value
+            switch value.sign {
+            case .plus:
+                self.decrementLimit = 0
+            case .minus:
+                assert(!value.magnitude.isZero)
+                self.decrementLimit = value.magnitude.words.firstIndex(where: { $0 != 0 })!
+            }
+        }
+
+        public var count: Int {
+            switch value.sign {
+            case .plus:
+                if let high = value.magnitude.words.last, high >> (Word.bitWidth - 1) != 0 {
+                    return value.magnitude.count + 1
+                }
+                return value.magnitude.count
+            case .minus:
+                let high = value.magnitude.words.last!
+                if high >> (Word.bitWidth - 1) != 0 {
+                    return value.magnitude.count + 1
+                }
+                return value.magnitude.count
+            }
+        }
+
+        public var indices: Indices { return 0 ..< count }
+        public var startIndex: Int { return 0 }
+        public var endIndex: Int { return count }
+
+        public subscript(_ index: Int) -> UInt {
+            // Note that indices above `endIndex` are accepted.
+            if value.sign == .plus {
+                return value.magnitude[index]
+            }
+            if index <= decrementLimit {
+                return ~(value.magnitude[index] &- 1)
+            }
+            return ~value.magnitude[index]
+        }
+    }
+
+    public var words: Words {
+        return Words(self)
+    }
+
+    public init<S: Sequence>(words: S) where S.Element == Word {
+        var words = Array(words)
+        if (words.last ?? 0) >> (Word.bitWidth - 1) == 0 {
+            self.init(sign: .plus, magnitude: BigUInt(words: words))
+        }
+        else {
+            words.twosComplement()
+            self.init(sign: .minus, magnitude: BigUInt(words: words))
+        }
+    }
+}

Sources/CryptoSwift/RSA.swift

@@ -0,0 +1,131 @@
+//
+//  CryptoSwift
+//
+//  Copyright (C) 2014-2021 Marcin Krzyżanowski <marcin@krzyzanowskim.com>
+//  This software is provided 'as-is', without any express or implied warranty.
+//
+//  In no event will the authors be held liable for any damages arising from the use of this software.
+//
+//  Permission is granted to anyone to use this software for any purpose,including commercial applications, and to alter it and redistribute it freely, subject to the following restrictions:
+//
+//  - The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation is required.
+//  - Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
+//  - This notice may not be removed or altered from any source or binary distribution.
+//
+
+// Foundation is required for `Data` to be found
+import Foundation
+
+// Note: The `BigUInt` struct was copied from:
+// https://github.com/attaswift/BigInt
+// It allows fast calculation for RSA big numbers
+
+public final class RSA {
+  
+  public enum Error: Swift.Error {
+    /// No private key specified
+    case noPrivateKey
+  }
+  
+  /// RSA Modulus
+  public let n: BigUInt
+  
+  /// RSA Public Exponent
+  public let e: BigUInt
+  
+  /// RSA Private Exponent
+  public let d: BigUInt?
+  
+  /// The size of the modulus, in bits
+  public let keySize: Int
+  
+  /// Initialize with RSA parameters
+  /// - Parameters:
+  ///   - n: The RSA Modulus
+  ///   - e: The RSA Public Exponent
+  ///   - d: The RSA Private Exponent (or nil if unknown, e.g. if only public key is known)
+  public init(n: BigUInt, e: BigUInt, d: BigUInt? = nil) {
+    self.n = n
+    self.e = e
+    self.d = d
+    
+    self.keySize = n.bitWidth
+  }
+  
+  /// Initialize with RSA parameters
+  /// - Parameters:
+  ///   - n: The RSA Modulus
+  ///   - e: The RSA Public Exponent
+  ///   - d: The RSA Private Exponent (or nil if unknown, e.g. if only public key is known)
+  public convenience init(n: Array<UInt8>, e: Array<UInt8>, d: Array<UInt8>? = nil) {
+    if let d = d {
+      self.init(n: BigUInt(Data(n)), e: BigUInt(Data(e)), d: BigUInt(Data(d)))
+    } else {
+      self.init(n: BigUInt(Data(n)), e: BigUInt(Data(e)))
+    }
+  }
+  
+  /// Initialize with a generated key pair
+  /// - Parameter keySize: The size of the modulus
+  public convenience init(keySize: Int) {
+    // Generate prime numbers
+    let p = BigUInt.generatePrime(keySize / 2)
+    let q = BigUInt.generatePrime(keySize / 2)
+    
+    // Calculate modulus
+    let n = p * q
+    
+    // Calculate public and private exponent
+    let e: BigUInt = 65537
+    let phi = (p - 1) * (q - 1)
+    let d = e.inverse(phi)
+    
+    // Initialize
+    self.init(n: n, e: e, d: d)
+  }
+  
+  // TODO: Add initializer from PEM (ASN.1 with DER header) (See #892)
+  
+  // TODO: Add export to PEM (ASN.1 with DER header) (See #892)
+  
+}
+
+// MARK: Cipher
+
+extension RSA: Cipher {
+  
+  @inlinable
+  public func encrypt(_ bytes: ArraySlice<UInt8>) throws -> Array<UInt8> {
+    // Calculate encrypted data
+    return BigUInt(Data(bytes)).power(e, modulus: n).serialize().bytes
+  }
+
+  @inlinable
+  public func decrypt(_ bytes: ArraySlice<UInt8>) throws -> Array<UInt8> {
+    // Check for Private Exponent presence
+    guard let d = d else {
+      throw RSA.Error.noPrivateKey
+    }
+    
+    // Calculate decrypted data
+    return BigUInt(Data(bytes)).power(d, modulus: n).serialize().bytes
+  }
+  
+}
+
+// MARK: BigUInt extension
+
+extension BigUInt {
+  
+  public static func generatePrime(_ width: Int) -> BigUInt {
+    // Note: Need to find a better way to generate prime numbers
+    while true {
+      var random = BigUInt.randomInteger(withExactWidth: width)
+      random |= BigUInt(1)
+      if random.isPrime() {
+        return random
+      }
+    }
+  }
+  
+}

Tests/CryptoSwiftTests/RSATests.swift

@@ -0,0 +1,206 @@
+//
+//  CryptoSwift
+//
+//  Copyright (C) 2014-2021 Marcin Krzyżanowski <marcin@krzyzanowskim.com>
+//  This software is provided 'as-is', without any express or implied warranty.
+//
+//  In no event will the authors be held liable for any damages arising from the use of this software.
+//
+//  Permission is granted to anyone to use this software for any purpose,including commercial applications, and to alter it and redistribute it freely, subject to the following restrictions:
+//
+//  - The origin of this software must not be misrepresented; you must not claim that you wrote the original software. If you use this software in a product, an acknowledgment in the product documentation is required.
+//  - Altered source versions must be plainly marked as such, and must not be misrepresented as being the original software.
+//  - This notice may not be removed or altered from any source or binary distribution.
+//
+
+import Foundation
+import XCTest
+@testable import CryptoSwift
+
+final class RSATests: XCTestCase {
+  
+  func testSmallRSA() {
+    /*
+     * Example taken from the book "Understanding Cryptography"
+     *
+     * p = 3; q = 11; n = pq = 33; e = 3; d = 7
+     */
+    
+    let n: Array<UInt8> = [33]
+    let e: Array<UInt8> = [3]
+    let d: Array<UInt8> = [7]
+    let message: Array<UInt8> = [4]
+    let expected: Array<UInt8> = [31]
+    
+    let rsa = RSA(n: n, e: e, d: d)
+    XCTAssertEqual(rsa.keySize, 6, "key size is not correct")
+    
+    let encrypted = try! rsa.encrypt(message)
+    XCTAssertEqual(encrypted, expected, "small encrypt failed")
+    
+    let decrypted = try! rsa.decrypt(encrypted)
+    XCTAssertEqual(decrypted, message, "small decrypt failed")
+  }
+
+  func testRSA1() {
+    /*
+     * Taken from http://cryptomanager.com/tv.html
+     *
+     * 1. 1024-bit RSA bare exponentiation
+     */
+    
+    let n: Array<UInt8> = [
+      0xF0, 0xC4, 0x2D, 0xB8, 0x48, 0x6F, 0xEB, 0x95, 0x95, 0xD8, 0xC7, 0x8F, 0x90, 0x8D, 0x04, 0xA9,
+      0xB6, 0xC8, 0xC7, 0x7A, 0x36, 0x10, 0x5B, 0x1B, 0xF2, 0x75, 0x53, 0x77, 0xA6, 0x89, 0x3D, 0xC4,
+      0x38, 0x3C, 0x54, 0xEC, 0x6B, 0x52, 0x62, 0xE5, 0x68, 0x8E, 0x5F, 0x9D, 0x9D, 0xD1, 0x64, 0x97,
+      0xD0, 0xE3, 0xEA, 0x83, 0x3D, 0xEE, 0x2C, 0x8E, 0xBC, 0xD1, 0x43, 0x83, 0x89, 0xFC, 0xCA, 0x8F,
+      0xED, 0xE7, 0xA8, 0x8A, 0x81, 0x25, 0x7E, 0x8B, 0x27, 0x09, 0xC4, 0x94, 0xD4, 0x2F, 0x72, 0x3D,
+      0xEC, 0x2E, 0x0B, 0x5C, 0x09, 0x73, 0x1C, 0x55, 0x0D, 0xCC, 0x9D, 0x7E, 0x75, 0x25, 0x89, 0x89,
+      0x1C, 0xBB, 0xC3, 0x02, 0x13, 0x07, 0xDD, 0x91, 0x8E, 0x10, 0x0B, 0x34, 0xC0, 0x14, 0xA5, 0x59,
+      0xE0, 0xE1, 0x82, 0xAF, 0xB2, 0x1A, 0x72, 0xB3, 0x07, 0xCC, 0x39, 0x5D, 0xEC, 0x99, 0x57, 0x47
+    ]
+    let e: Array<UInt8> = [
+      0x01, 0x00, 0x01
+    ]
+    let d: Array<UInt8> = [
+      0x24, 0x89, 0x10, 0x8B, 0x0B, 0x6A, 0xF8, 0x6B, 0xED, 0x9E, 0x44, 0xC2, 0x33, 0x64, 0x42, 0xD5,
+      0xE2, 0x27, 0xDB, 0xA5, 0x5E, 0xF8, 0xE2, 0x6A, 0x7E, 0x43, 0x71, 0x94, 0x11, 0x90, 0x77, 0xF0,
+      0x03, 0xBC, 0x9C, 0x02, 0x78, 0x52, 0xBB, 0x31, 0x26, 0xC9, 0x9C, 0x16, 0xD5, 0xF1, 0x05, 0x7B,
+      0xC8, 0x36, 0x1D, 0xCB, 0x26, 0xA5, 0xB2, 0xDB, 0x42, 0x29, 0xDB, 0x3D, 0xE5, 0xBD, 0x97, 0x9B,
+      0x2E, 0x59, 0x7D, 0x19, 0x16, 0xD7, 0xBB, 0xC9, 0x27, 0x46, 0xFC, 0x07, 0x59, 0x5C, 0x76, 0xB4,
+      0x4B, 0x39, 0xA4, 0x76, 0xA6, 0x5C, 0x86, 0xF0, 0x86, 0xDC, 0x92, 0x83, 0xCA, 0x6D, 0x1E, 0xEF,
+      0xC1, 0x49, 0x15, 0x98, 0x2F, 0x9C, 0x4C, 0xED, 0x5F, 0x62, 0xA9, 0xFF, 0x3B, 0xE2, 0x42, 0x18,
+      0xA9, 0x93, 0x57, 0xB5, 0xB6, 0x5C, 0x3B, 0x10, 0xAE, 0xB3, 0x67, 0xE9, 0x11, 0xEB, 0x9E, 0x21
+    ]
+    let message: Array<UInt8> = [
+      0x11, 0x22, 0x33, 0x44
+    ]
+    let expected: Array<UInt8> = [
+      0x50, 0x5B, 0x09, 0xBD, 0x5D, 0x0E, 0x66, 0xD7, 0xC8, 0x82, 0x9F, 0x5B, 0x47, 0x3E, 0xD3, 0x4D,
+      0xB5, 0xCF, 0xDB, 0xB5, 0xD5, 0x8C, 0xE7, 0x83, 0x29, 0xC8, 0xBF, 0x85, 0x20, 0xE4, 0x86, 0xD3,
+      0xC4, 0xCF, 0x9B, 0x70, 0xC6, 0x34, 0x65, 0x94, 0x35, 0x80, 0x80, 0xF4, 0x3F, 0x47, 0xEE, 0x86,
+      0x3C, 0xFA, 0xF2, 0xA2, 0xE5, 0xF0, 0x3D, 0x1E, 0x13, 0xD6, 0xFE, 0xC5, 0x7D, 0xFB, 0x1D, 0x55,
+      0x22, 0x24, 0xC4, 0x61, 0xDA, 0x41, 0x1C, 0xFE, 0x5D, 0x0B, 0x05, 0xBA, 0x87, 0x7E, 0x3A, 0x42,
+      0xF6, 0xDE, 0x4D, 0xA4, 0x6A, 0x96, 0x5C, 0x9B, 0x69, 0x5E, 0xE2, 0xD5, 0x0E, 0x40, 0x08, 0x94,
+      0x06, 0x1C, 0xB0, 0xA2, 0x1C, 0xA3, 0xA5, 0x24, 0xB4, 0x07, 0xE9, 0xFF, 0xBA, 0x87, 0xFC, 0x96,
+      0x6B, 0x3B, 0xA9, 0x45, 0x90, 0x84, 0x9A, 0xEB, 0x90, 0x8A, 0xAF, 0xF4, 0xC7, 0x19, 0xC2, 0xE4
+    ]
+    
+    let rsa = RSA(n: n, e: e, d: d)
+    XCTAssertEqual(rsa.keySize, 1024, "key size is not correct")
+    
+    let encrypted = try! rsa.encrypt(message)
+    XCTAssertEqual(encrypted, expected, "encrypt failed")
+    
+    let decrypted = try! rsa.decrypt(encrypted)
+    XCTAssertEqual(decrypted, message, "decrypt failed")
+  }
+  
+  func testRSA2() {
+    /*
+     * Taken from http://cryptomanager.com/tv.html
+     *
+     * 2. 2048-bit PKCS V. 1.5 enciphering.
+     */
+    
+    let n: Array<UInt8> = [
+      0xF7, 0x48, 0xD8, 0xD9, 0x8E, 0xD0, 0x57, 0xCF, 0x39, 0x8C, 0x43, 0x7F, 0xEF, 0xC6, 0x15, 0xD7,
+      0x57, 0xD3, 0xF8, 0xEC, 0xE6, 0xF2, 0xC5, 0x80, 0xAE, 0x07, 0x80, 0x76, 0x8F, 0x9E, 0xC8, 0x3A,
+      0xAA, 0x08, 0x1F, 0xF0, 0x9E, 0x53, 0x17, 0xED, 0x60, 0x99, 0xC6, 0x3F, 0xD1, 0x5C, 0xFE, 0x11,
+      0x17, 0x2F, 0x78, 0x90, 0x8C, 0xD5, 0x8C, 0x03, 0xAE, 0xC9, 0x3A, 0x48, 0x1F, 0xF5, 0x0E, 0x17,
+      0x22, 0x04, 0xAF, 0xED, 0xFC, 0x1F, 0x16, 0xAF, 0xDB, 0x99, 0x0A, 0xAB, 0x45, 0xBE, 0x19, 0x0B,
+      0xC1, 0x92, 0x59, 0xBD, 0x4A, 0x1B, 0xFC, 0xDF, 0xBE, 0x2A, 0x29, 0x8B, 0x3C, 0x0E, 0x31, 0x8F,
+      0x78, 0xA3, 0x39, 0x19, 0x88, 0x23, 0x28, 0xDA, 0xCA, 0xC8, 0x5C, 0xB3, 0x5A, 0x0D, 0xE5, 0x37,
+      0xB1, 0x63, 0x76, 0x97, 0x52, 0x17, 0xE5, 0xA5, 0xEA, 0xAF, 0x98, 0x26, 0x6B, 0x58, 0x8C, 0x2D,
+      0xBA, 0xFD, 0x0B, 0xE3, 0x71, 0xC3, 0x49, 0x89, 0xCB, 0x36, 0xE6, 0x23, 0xD7, 0x5E, 0xFF, 0xED,
+      0xBE, 0x4A, 0x95, 0x1A, 0x68, 0x40, 0x98, 0x2B, 0xC2, 0x79, 0xB3, 0x0F, 0xCD, 0x41, 0xDA, 0xC8,
+      0x7C, 0x00, 0x74, 0xD4, 0x62, 0xF1, 0x01, 0x29, 0x00, 0xB8, 0x97, 0x3B, 0x46, 0xAD, 0xC7, 0xEA,
+      0xC0, 0x17, 0x70, 0xDF, 0xC6, 0x32, 0xEA, 0x96, 0x7F, 0x94, 0x71, 0xE9, 0x78, 0x98, 0x31, 0xF3,
+      0xA4, 0x10, 0x73, 0x0F, 0xF9, 0x14, 0x34, 0x8B, 0xE1, 0x11, 0x86, 0x3C, 0x13, 0x37, 0x63, 0x01,
+      0x07, 0x97, 0x56, 0xA1, 0x47, 0xD8, 0x01, 0x03, 0xCE, 0x9F, 0xA6, 0x88, 0xA3, 0x38, 0xE2, 0x2B,
+      0x2D, 0x91, 0x6C, 0xAD, 0x42, 0xD6, 0x73, 0xC9, 0xD0, 0x0F, 0x08, 0x21, 0x4D, 0xE5, 0x44, 0xF5,
+      0xDE, 0x81, 0x2A, 0x9A, 0x94, 0x91, 0x89, 0x07, 0x8B, 0x2B, 0xDA, 0x14, 0xB2, 0x8C, 0xA6, 0x2F
+    ]
+    let e: Array<UInt8> = [
+      0x01, 0x00, 0x01
+    ]
+    let d: Array<UInt8> = [
+      0x1C, 0xBC, 0x9A, 0x76, 0xAD, 0xE2, 0x08, 0x52, 0x4C, 0x9D, 0xC0, 0x3A, 0x5D, 0xE2, 0xE7, 0x26,
+      0xDF, 0x4E, 0x02, 0xDF, 0x84, 0xF7, 0x31, 0x7C, 0x82, 0xBC, 0xDC, 0x70, 0xEA, 0xBF, 0xC9, 0x05,
+      0x08, 0x3D, 0x69, 0x78, 0xCC, 0xED, 0x5B, 0x1A, 0x7A, 0xDF, 0x63, 0xEA, 0x86, 0xAA, 0x07, 0xDC,
+      0x74, 0x95, 0x4F, 0xAD, 0x7C, 0xB0, 0x54, 0x55, 0x19, 0x3A, 0xC9, 0x4B, 0x18, 0x6B, 0xA1, 0xF7,
+      0x8E, 0x3C, 0x7D, 0x35, 0x6A, 0xD7, 0x32, 0x0B, 0xBD, 0xB9, 0x4B, 0x44, 0x1C, 0x16, 0xBB, 0x52,
+      0x62, 0x6C, 0x5F, 0x81, 0x5F, 0xDB, 0x60, 0xC7, 0x9F, 0x91, 0xC6, 0xC2, 0x27, 0x78, 0x7E, 0xC9,
+      0xED, 0x7B, 0x0A, 0x67, 0xAD, 0x2A, 0x68, 0xD5, 0x04, 0x3B, 0xC4, 0x8A, 0x13, 0x2D, 0x0A, 0x36,
+      0x2E, 0xA7, 0x20, 0x60, 0xF5, 0x69, 0x51, 0x86, 0xB6, 0x7F, 0x31, 0x6F, 0x45, 0x8A, 0x44, 0xBF,
+      0xD1, 0x40, 0x3D, 0x93, 0xA9, 0xB9, 0x12, 0xCB, 0xB5, 0x98, 0x15, 0x91, 0x6A, 0x14, 0xA2, 0xBA,
+      0xD4, 0xF9, 0xA1, 0xED, 0x57, 0x8E, 0xBD, 0x2B, 0x5D, 0x47, 0x2F, 0x62, 0x3B, 0x4B, 0xB5, 0xF9,
+      0xB8, 0x0B, 0x93, 0x57, 0x2B, 0xEA, 0x61, 0xBD, 0x10, 0x68, 0x09, 0x4E, 0x41, 0xE8, 0x39, 0x0E,
+      0x2E, 0x28, 0xA3, 0x51, 0x43, 0x3E, 0xDD, 0x1A, 0x09, 0x9A, 0x8C, 0x6E, 0x68, 0x92, 0x60, 0x4A,
+      0xEF, 0x16, 0x3A, 0x43, 0x9B, 0x1C, 0xAE, 0x6A, 0x09, 0x5E, 0x68, 0x94, 0x3C, 0xA6, 0x7B, 0x18,
+      0xC8, 0xDC, 0x7F, 0x98, 0xCC, 0x5F, 0x8E, 0xFA, 0x22, 0xBB, 0xC8, 0x7D, 0x2E, 0x73, 0x57, 0x83,
+      0xD2, 0xBA, 0xA3, 0x8F, 0x4C, 0x17, 0xD5, 0xED, 0x0C, 0x58, 0x36, 0x6D, 0xCE, 0xF5, 0xE8, 0x52,
+      0xDD, 0x3D, 0x6E, 0x0F, 0x63, 0x72, 0x95, 0x43, 0xE2, 0x63, 0x8B, 0x29, 0x14, 0xD7, 0x2A, 0x01
+    ]
+    let message: Array<UInt8> = [
+      0x11, 0x22, 0x33, 0x44
+    ]
+    let expected: Array<UInt8> = [
+      0xEE, 0x69, 0x09, 0x9A, 0xFD, 0x9F, 0x99, 0xD6, 0x06, 0x5D, 0x65, 0xE1, 0x5F, 0x90, 0xB9, 0x23,
+      0x7C, 0x16, 0x98, 0x7D, 0x48, 0x72, 0xE2, 0xB9, 0x94, 0xED, 0x2B, 0x9E, 0x56, 0x85, 0xF9, 0xBA,
+      0x48, 0x9A, 0xB9, 0x36, 0xCC, 0x1E, 0x3D, 0xFD, 0x15, 0xB3, 0x5F, 0xEE, 0x21, 0x53, 0x6F, 0x8C,
+      0x22, 0x20, 0xAE, 0x43, 0x21, 0x7D, 0x91, 0xD8, 0x1C, 0x9E, 0xD0, 0x1D, 0xE5, 0xBA, 0xEE, 0xF4,
+      0xEF, 0xC7, 0x21, 0xD7, 0x0D, 0x67, 0xB5, 0x16, 0x6E, 0x43, 0xD8, 0x27, 0x24, 0xF3, 0x9B, 0xF0,
+      0xBD, 0x19, 0x7C, 0x31, 0xE7, 0x48, 0x51, 0x8D, 0xEE, 0x63, 0xEC, 0x10, 0x98, 0x7A, 0x08, 0x39,
+      0x0B, 0x15, 0xCC, 0x41, 0x57, 0x67, 0x7C, 0x54, 0x22, 0x6A, 0x8B, 0x04, 0xB4, 0x76, 0x84, 0xAE,
+      0xDD, 0x02, 0xB4, 0x8C, 0x8E, 0xD4, 0x8A, 0x44, 0xBD, 0x13, 0x53, 0x97, 0xAC, 0x28, 0x69, 0x76,
+      0x9B, 0x68, 0xC7, 0xD3, 0xBF, 0xAC, 0xDB, 0x72, 0xAF, 0xCD, 0x74, 0x42, 0xC2, 0x25, 0x17, 0xE0,
+      0x44, 0x99, 0x6C, 0xB6, 0x8E, 0x0A, 0x31, 0x1D, 0xF5, 0xD6, 0xD2, 0xD2, 0x86, 0x37, 0x25, 0x56,
+      0xF0, 0x19, 0x31, 0x66, 0xCC, 0x36, 0x4E, 0x65, 0x4E, 0xF4, 0x05, 0xDD, 0x22, 0xFB, 0xE5, 0x84,
+      0xDB, 0xF6, 0x0F, 0x05, 0x52, 0x96, 0x06, 0x68, 0xFB, 0x69, 0x52, 0x2C, 0x1B, 0x52, 0x64, 0xF1,
+      0x94, 0xFA, 0xC9, 0xF3, 0x56, 0x22, 0xE9, 0x82, 0x27, 0x63, 0x8F, 0xF2, 0x8B, 0x91, 0x0D, 0x8C,
+      0xC9, 0x0E, 0x50, 0x11, 0x02, 0x12, 0x12, 0xC9, 0x6C, 0x64, 0xC8, 0x58, 0x20, 0x87, 0x7A, 0x7D,
+      0x15, 0x59, 0x23, 0x5E, 0x99, 0xC3, 0x2A, 0xBE, 0xF3, 0x3D, 0x95, 0xE2, 0x8E, 0x18, 0xCC, 0xA3,
+      0x44, 0x2E, 0x6E, 0x3A, 0x43, 0x2F, 0xFF, 0xEA, 0x10, 0x10, 0x4A, 0x8E, 0xEE, 0x94, 0xC3, 0x62
+    ]
+    
+    let rsa = RSA(n: n, e: e, d: d)
+    XCTAssertEqual(rsa.keySize, 2048, "key size is not correct")
+    
+    let encrypted = try! rsa.encrypt(message)
+    XCTAssertEqual(encrypted, expected, "encrypt failed")
+    
+    let decrypted = try! rsa.decrypt(encrypted)
+    XCTAssertEqual(decrypted, message, "decrypt failed")
+  }
+  
+  func testGenerateKeyPair() {
+    /*
+     * To test key generation and its validity
+     */
+    let message: Array<UInt8> = [
+      0x11, 0x22, 0x33, 0x44
+    ]
+    
+    let rsa = RSA(keySize: 2048)
+    // Sometimes the modulus size is 2047 bits, but it's okay (with two 1024 bits primes)
+    //XCTAssertEqual(rsa.keySize, 2048, "key size is not correct")
+    
+    let decrypted = try! rsa.decrypt(try! rsa.encrypt(message))
+    XCTAssertEqual(decrypted, message, "encrypt+decrypt failed")
+  }
+
+}
+
+extension RSATests {
+  static func allTests() -> [(String, (RSATests) -> () -> Void)] {
+    let tests = [
+      ("testSmallRSA", testSmallRSA),
+      ("testRSA1", testRSA1),
+      ("testRSA2", testRSA2),
+      ("testGenerateKeyPair", testGenerateKeyPair)
+    ]
+
+    return tests
+  }
+}