【加解密专辑】对接触到的PGP、RSA、AES加解密算法整理
先贴代码，有空再整理思路
PGP加密
using System;
using System.IO;
using Org.BouncyCastle.Bcpg;
using Org.BouncyCastle.Bcpg.OpenPgp;
using Org.BouncyCastle.Security;
using Org.BouncyCastle.Utilities.IO;
using System.Linq; namespace Server5.V2.Common
{
public static class PGPEncryptDecrypt
{ static void test()
{
var inputFileName = "";
var outputFileName = "";
var recipientKeyFileName = "";
var shouldArmor = false;
var shouldCheckIntegrity = false; //Encrypt a file:
PGPEncryptDecrypt.EncryptFile(inputFileName,
outputFileName,
recipientKeyFileName,
shouldArmor,
shouldCheckIntegrity); var privateKeyFileName = "";
var passPhrase = ""; //Decrypt a file:
PGPEncryptDecrypt.Decrypt(inputFileName,
privateKeyFileName,
passPhrase,
outputFileName);
} private const int BufferSize = 0x10000; // should always be power of 2 #region Encrypt /*
* Encrypt the file.
*/ public static void EncryptFile(string inputFile, string outputFile, string publicKeyFile, bool armor, bool withIntegrityCheck)
{
try
{
using (Stream publicKeyStream = File.OpenRead(publicKeyFile))
{
PgpPublicKey encKey = ReadPublicKey(publicKeyStream); using (MemoryStream bOut = new MemoryStream())
{
PgpCompressedDataGenerator comData = new PgpCompressedDataGenerator(CompressionAlgorithmTag.Zip);
PgpUtilities.WriteFileToLiteralData(comData.Open(bOut), PgpLiteralData.Binary, new FileInfo(inputFile)); comData.Close();
PgpEncryptedDataGenerator cPk = new PgpEncryptedDataGenerator(SymmetricKeyAlgorithmTag.Cast5, withIntegrityCheck, new SecureRandom()); cPk.AddMethod(encKey);
byte[] bytes = bOut.ToArray(); using (Stream outputStream = File.Create(outputFile))
{
if (armor)
{
using (ArmoredOutputStream armoredStream = new ArmoredOutputStream(outputStream))
{
using (Stream cOut = cPk.Open(armoredStream, bytes.Length))
{
cOut.Write(bytes, , bytes.Length);
}
}
}
else
{
using (Stream cOut = cPk.Open(outputStream, bytes.Length))
{
cOut.Write(bytes, , bytes.Length);
}
}
}
}
}
}
catch (PgpException e)
{
throw;
}
} #endregion Encrypt #region Encrypt and Sign /*
* Encrypt and sign the file pointed to by unencryptedFileInfo and
*/ public static void EncryptAndSign(string inputFile, string outputFile, string publicKeyFile, string privateKeyFile, string passPhrase, bool armor)
{
PgpEncryptionKeys encryptionKeys = new PgpEncryptionKeys(publicKeyFile, privateKeyFile, passPhrase); if (!File.Exists(inputFile))
throw new FileNotFoundException(String.Format("Input file [{0}] does not exist.", inputFile)); if (!File.Exists(publicKeyFile))
throw new FileNotFoundException(String.Format("Public Key file [{0}] does not exist.", publicKeyFile)); if (!File.Exists(privateKeyFile))
throw new FileNotFoundException(String.Format("Private Key file [{0}] does not exist.", privateKeyFile)); if (String.IsNullOrEmpty(passPhrase))
throw new ArgumentNullException("Invalid Pass Phrase."); if (encryptionKeys == null)
throw new ArgumentNullException("Encryption Key not found."); using (Stream outputStream = File.Create(outputFile))
{
if (armor)
using (ArmoredOutputStream armoredOutputStream = new ArmoredOutputStream(outputStream))
{
OutputEncrypted(inputFile, armoredOutputStream, encryptionKeys);
}
else
OutputEncrypted(inputFile, outputStream, encryptionKeys);
}
} private static void OutputEncrypted(string inputFile, Stream outputStream, PgpEncryptionKeys encryptionKeys)
{
using (Stream encryptedOut = ChainEncryptedOut(outputStream, encryptionKeys))
{
FileInfo unencryptedFileInfo = new FileInfo(inputFile);
using (Stream compressedOut = ChainCompressedOut(encryptedOut))
{
PgpSignatureGenerator signatureGenerator = InitSignatureGenerator(compressedOut, encryptionKeys);
using (Stream literalOut = ChainLiteralOut(compressedOut, unencryptedFileInfo))
{
using (FileStream inputFileStream = unencryptedFileInfo.OpenRead())
{
WriteOutputAndSign(compressedOut, literalOut, inputFileStream, signatureGenerator);
inputFileStream.Close();
}
}
}
}
} private static void WriteOutputAndSign(Stream compressedOut, Stream literalOut, FileStream inputFile, PgpSignatureGenerator signatureGenerator)
{
int length = ;
byte[] buf = new byte[BufferSize];
while ((length = inputFile.Read(buf, , buf.Length)) > )
{
literalOut.Write(buf, , length);
signatureGenerator.Update(buf, , length);
}
signatureGenerator.Generate().Encode(compressedOut);
} private static Stream ChainEncryptedOut(Stream outputStream, PgpEncryptionKeys m_encryptionKeys)
{
PgpEncryptedDataGenerator encryptedDataGenerator;
encryptedDataGenerator = new PgpEncryptedDataGenerator(SymmetricKeyAlgorithmTag.TripleDes, new SecureRandom());
encryptedDataGenerator.AddMethod(m_encryptionKeys.PublicKey);
return encryptedDataGenerator.Open(outputStream, new byte[BufferSize]);
} private static Stream ChainCompressedOut(Stream encryptedOut)
{
PgpCompressedDataGenerator compressedDataGenerator = new PgpCompressedDataGenerator(CompressionAlgorithmTag.Zip);
return compressedDataGenerator.Open(encryptedOut);
} private static Stream ChainLiteralOut(Stream compressedOut, FileInfo file)
{
PgpLiteralDataGenerator pgpLiteralDataGenerator = new PgpLiteralDataGenerator();
return pgpLiteralDataGenerator.Open(compressedOut, PgpLiteralData.Binary, file);
} private static PgpSignatureGenerator InitSignatureGenerator(Stream compressedOut, PgpEncryptionKeys m_encryptionKeys)
{
const bool IsCritical = false;
const bool IsNested = false;
PublicKeyAlgorithmTag tag = m_encryptionKeys.SecretKey.PublicKey.Algorithm;
PgpSignatureGenerator pgpSignatureGenerator = new PgpSignatureGenerator(tag, HashAlgorithmTag.Sha1);
pgpSignatureGenerator.InitSign(PgpSignature.BinaryDocument, m_encryptionKeys.PrivateKey);
foreach (string userId in m_encryptionKeys.SecretKey.PublicKey.GetUserIds())
{
PgpSignatureSubpacketGenerator subPacketGenerator = new PgpSignatureSubpacketGenerator();
subPacketGenerator.SetSignerUserId(IsCritical, userId);
pgpSignatureGenerator.SetHashedSubpackets(subPacketGenerator.Generate());
// Just the first one!
break;
}
pgpSignatureGenerator.GenerateOnePassVersion(IsNested).Encode(compressedOut);
return pgpSignatureGenerator;
} #endregion Encrypt and Sign #region Decrypt /*
* decrypt a given stream.
*/ public static void Decrypt(string inputfile, string privateKeyFile, string passPhrase, string outputFile)
{
if (!File.Exists(inputfile))
throw new FileNotFoundException(String.Format("Encrypted File [{0}] not found.", inputfile)); if (!File.Exists(privateKeyFile))
throw new FileNotFoundException(String.Format("Private Key File [{0}] not found.", privateKeyFile)); if (String.IsNullOrEmpty(outputFile))
throw new ArgumentNullException("Invalid Output file path."); using (Stream inputStream = File.OpenRead(inputfile))
{
using (Stream keyIn = File.OpenRead(privateKeyFile))
{
Decrypt(inputStream, keyIn, passPhrase, outputFile);
}
}
} /*
* decrypt a given stream.
*/ public static void Decrypt(Stream inputStream, Stream privateKeyStream, string passPhrase, string outputFile)
{
try
{
PgpObjectFactory pgpF = null;
PgpEncryptedDataList enc = null;
PgpObject o = null;
PgpPrivateKey sKey = null;
PgpPublicKeyEncryptedData pbe = null;
PgpSecretKeyRingBundle pgpSec = null; pgpF = new PgpObjectFactory(PgpUtilities.GetDecoderStream(inputStream));
// find secret key
pgpSec = new PgpSecretKeyRingBundle(PgpUtilities.GetDecoderStream(privateKeyStream)); if (pgpF != null)
o = pgpF.NextPgpObject(); // the first object might be a PGP marker packet.
if (o is PgpEncryptedDataList)
enc = (PgpEncryptedDataList)o;
else
enc = (PgpEncryptedDataList)pgpF.NextPgpObject(); // decrypt
foreach (PgpPublicKeyEncryptedData pked in enc.GetEncryptedDataObjects())
{
sKey = FindSecretKey(pgpSec, pked.KeyId, passPhrase.ToCharArray()); if (sKey != null)
{
pbe = pked;
break;
}
} if (sKey == null)
throw new ArgumentException("Secret key for message not found."); PgpObjectFactory plainFact = null; using (Stream clear = pbe.GetDataStream(sKey))
{
plainFact = new PgpObjectFactory(clear);
} PgpObject message = plainFact.NextPgpObject(); if (message is PgpCompressedData)
{
PgpCompressedData cData = (PgpCompressedData)message;
PgpObjectFactory of = null; using (Stream compDataIn = cData.GetDataStream())
{
of = new PgpObjectFactory(compDataIn);
} message = of.NextPgpObject();
if (message is PgpOnePassSignatureList)
{
message = of.NextPgpObject();
PgpLiteralData Ld = null;
Ld = (PgpLiteralData)message;
using (Stream output = File.Create(outputFile))
{
Stream unc = Ld.GetInputStream();
Streams.PipeAll(unc, output);
}
}
else
{
PgpLiteralData Ld = null;
Ld = (PgpLiteralData)message;
using (Stream output = File.Create(outputFile))
{
Stream unc = Ld.GetInputStream();
Streams.PipeAll(unc, output);
}
}
}
else if (message is PgpLiteralData)
{
PgpLiteralData ld = (PgpLiteralData)message;
string outFileName = ld.FileName; using (Stream fOut = File.Create(outputFile))
{
Stream unc = ld.GetInputStream();
Streams.PipeAll(unc, fOut);
}
}
else if (message is PgpOnePassSignatureList)
throw new PgpException("Encrypted message contains a signed message - not literal data.");
else
throw new PgpException("Message is not a simple encrypted file - type unknown."); #region commented code //if (pbe.IsIntegrityProtected())
//{
// if (!pbe.Verify())
// msg = "message failed integrity check.";
// //Console.Error.WriteLine("message failed integrity check");
// else
// msg = "message integrity check passed.";
// //Console.Error.WriteLine("message integrity check passed");
//}
//else
//{
// msg = "no message integrity check.";
// //Console.Error.WriteLine("no message integrity check");
//} #endregion commented code
}
catch (PgpException ex)
{
throw;
}
} #endregion Decrypt #region Private helpers /*
* A simple routine that opens a key ring file and loads the first available key suitable for encryption.
*/ private static PgpPublicKey ReadPublicKey(Stream inputStream)
{
inputStream = PgpUtilities.GetDecoderStream(inputStream); PgpPublicKeyRingBundle pgpPub = new PgpPublicKeyRingBundle(inputStream); // we just loop through the collection till we find a key suitable for encryption, in the real
// world you would probably want to be a bit smarter about this.
// iterate through the key rings.
foreach (PgpPublicKeyRing kRing in pgpPub.GetKeyRings())
{
foreach (PgpPublicKey k in kRing.GetPublicKeys())
{
if (k.IsEncryptionKey)
return k;
}
} throw new ArgumentException("Can't find encryption key in key ring.");
} /*
* Search a secret key ring collection for a secret key corresponding to keyId if it exists.
*/ private static PgpPrivateKey FindSecretKey(PgpSecretKeyRingBundle pgpSec, long keyId, char[] pass)
{
PgpSecretKey pgpSecKey = pgpSec.GetSecretKey(keyId); if (pgpSecKey == null)
return null; return pgpSecKey.ExtractPrivateKey(pass);
} #endregion Private helpers
} public class PgpEncryptionKeys
{
public PgpPublicKey PublicKey { get; private set; } public PgpPrivateKey PrivateKey { get; private set; } public PgpSecretKey SecretKey { get; private set; } /// <summary>
/// Initializes a new instance of the EncryptionKeys class.
/// Two keys are required to encrypt and sign data. Your private key and the recipients public key.
/// The data is encrypted with the recipients public key and signed with your private key.
/// </summary>
/// <param name="publicKeyPath">The key used to encrypt the data</param>
/// <param name="privateKeyPath">The key used to sign the data.</param>
/// <param name="passPhrase">The (your) password required to access the private key</param>
/// <exception cref="ArgumentException">Public key not found. Private key not found. Missing password</exception>
public PgpEncryptionKeys(string publicKeyPath, string privateKeyPath, string passPhrase)
{
if (!File.Exists(publicKeyPath))
throw new ArgumentException("Public key file not found", "publicKeyPath");
if (!File.Exists(privateKeyPath))
throw new ArgumentException("Private key file not found", "privateKeyPath");
if (String.IsNullOrEmpty(passPhrase))
throw new ArgumentException("passPhrase is null or empty.", "passPhrase");
PublicKey = ReadPublicKey(publicKeyPath);
SecretKey = ReadSecretKey(privateKeyPath);
PrivateKey = ReadPrivateKey(passPhrase);
} #region Secret Key private PgpSecretKey ReadSecretKey(string privateKeyPath)
{
using (Stream keyIn = File.OpenRead(privateKeyPath))
{
using (Stream inputStream = PgpUtilities.GetDecoderStream(keyIn))
{
PgpSecretKeyRingBundle secretKeyRingBundle = new PgpSecretKeyRingBundle(inputStream);
PgpSecretKey foundKey = GetFirstSecretKey(secretKeyRingBundle);
if (foundKey != null)
return foundKey;
}
}
throw new ArgumentException("Can't find signing key in key ring.");
} /// <summary>
/// Return the first key we can use to encrypt.
/// Note: A file can contain multiple keys (stored in "key rings")
/// </summary>
private PgpSecretKey GetFirstSecretKey(PgpSecretKeyRingBundle secretKeyRingBundle)
{
foreach (PgpSecretKeyRing kRing in secretKeyRingBundle.GetKeyRings())
{
PgpSecretKey key = kRing.GetSecretKeys()
.Cast<PgpSecretKey>()
.Where(k => k.IsSigningKey)
.FirstOrDefault();
if (key != null)
return key;
}
return null;
} #endregion Secret Key #region Public Key private PgpPublicKey ReadPublicKey(string publicKeyPath)
{
using (Stream keyIn = File.OpenRead(publicKeyPath))
{
using (Stream inputStream = PgpUtilities.GetDecoderStream(keyIn))
{
PgpPublicKeyRingBundle publicKeyRingBundle = new PgpPublicKeyRingBundle(inputStream);
PgpPublicKey foundKey = GetFirstPublicKey(publicKeyRingBundle);
if (foundKey != null)
return foundKey;
}
}
throw new ArgumentException("No encryption key found in public key ring.");
} private PgpPublicKey GetFirstPublicKey(PgpPublicKeyRingBundle publicKeyRingBundle)
{
foreach (PgpPublicKeyRing kRing in publicKeyRingBundle.GetKeyRings())
{
PgpPublicKey key = kRing.GetPublicKeys()
.Cast<PgpPublicKey>()
.Where(k => k.IsEncryptionKey)
.FirstOrDefault();
if (key != null)
return key;
}
return null;
} #endregion Public Key #region Private Key private PgpPrivateKey ReadPrivateKey(string passPhrase)
{
PgpPrivateKey privateKey = SecretKey.ExtractPrivateKey(passPhrase.ToCharArray());
if (privateKey != null)
return privateKey;
throw new ArgumentException("No private key found in secret key.");
} #endregion Private Key
}
}
调用方法举例
PGPEncryptDecrypt.EncryptFile(file.FullName, file.FullName + ".DAT", "D:\\test\\key\\dsfpublic.asc", false, false);
PGPEncryptDecrypt.Decrypt(file.FullName + ".DAT", "D:\\test\\key\\dsfsecret.asc", "mon123day", file.FullName + ".ZIP");
测试代码
static void test()
{
var inputFileName = "";
var outputFileName = "";
var recipientKeyFileName = "";
var shouldArmor = false;
var shouldCheckIntegrity = false; //Encrypt a file:
PGPEncryptDecrypt.EncryptFile(inputFileName,
outputFileName,
recipientKeyFileName,
shouldArmor,
shouldCheckIntegrity); var privateKeyFileName = "";
var passPhrase = ""; //Decrypt a file:
PGPEncryptDecrypt.Decrypt(inputFileName,
privateKeyFileName,
passPhrase,
outputFileName);
}
RSA加密
using System;
using System.Collections.Generic;
using System.Linq;
using System.Security.Cryptography;
using System.Text; namespace Server5.V2.Common
{
/// <summary>
/// 非对称RSA加密类 可以参考
/// http://www.cnblogs.com/hhh/archive/2011/06/03/2070692.html
/// http://blog.csdn.net/zhilunchen/article/details/2943158
/// 若是私匙加密 则需公钥解密
/// 反正公钥加密 私匙来解密
/// 需要BigInteger类来辅助
/// </summary>
public static class RSAHelper
{
static void test()
{
string str = "{\"sc\":\"his51\",\"no\":\"1\",\"na\":\"管理员\"}";
System.Diagnostics.Debug.Print("明文：\r\n" + str + "\r\n");
RSAHelper.RSAKey keyPair = RSAHelper.GetRASKey();
System.Diagnostics.Debug.Print("公钥：\r\n" + keyPair.PublicKey + "\r\n");
System.Diagnostics.Debug.Print("私钥：\r\n" + keyPair.PrivateKey + "\r\n"); string en = RSAHelper.EncryptString(str, keyPair.PrivateKey);
System.Diagnostics.Debug.Print("公钥加密后：\r\n" + en + "\r\n"); var de = RSAHelper.DecryptString(en, keyPair.PublicKey);
System.Diagnostics.Debug.Print("解密：\r\n" + de + "\r\n");
Console.ReadKey();
} /// <summary>
/// RSA的容器 可以解密的源字符串长度为 DWKEYSIZE/8-11
/// </summary>
public const int DWKEYSIZE = ; /// <summary>
/// RSA加密的密匙结构 公钥和私匙
/// </summary>
public struct RSAKey
{
public string PublicKey { get; set; }
public string PrivateKey { get; set; }
} #region 得到RSA的解谜的密匙对
/// <summary>
/// 得到RSA的解谜的密匙对
/// </summary>
/// <returns></returns>
public static RSAKey GetRASKey()
{
RSACryptoServiceProvider.UseMachineKeyStore = true;
//声明一个指定大小的RSA容器
RSACryptoServiceProvider rsaProvider = new RSACryptoServiceProvider(DWKEYSIZE);
//取得RSA容易里的各种参数
RSAParameters p = rsaProvider.ExportParameters(true); return new RSAKey()
{
PublicKey = ComponentKey(p.Exponent, p.Modulus),
PrivateKey = ComponentKey(p.D, p.Modulus)
};
}
#endregion #region 检查明文的有效性 DWKEYSIZE/8-11 长度之内为有效 中英文都算一个字符
/// <summary>
/// 检查明文的有效性 DWKEYSIZE/8-11 长度之内为有效 中英文都算一个字符
/// </summary>
/// <param name="source"></param>
/// <returns></returns>
public static bool CheckSourceValidate(string source)
{
return (DWKEYSIZE / - ) >= source.Length;
}
#endregion #region 组合解析密匙
/// <summary>
/// 组合成密匙字符串
/// </summary>
/// <param name="b1"></param>
/// <param name="b2"></param>
/// <returns></returns>
private static string ComponentKey(byte[] b1, byte[] b2)
{
List<byte> list = new List<byte>();
//在前端加上第一个数组的长度值 这样今后可以根据这个值分别取出来两个数组
list.Add((byte)b1.Length);
list.AddRange(b1);
list.AddRange(b2);
byte[] b = list.ToArray<byte>();
return Convert.ToBase64String(b);
} /// <summary>
/// 解析密匙
/// </summary>
/// <param name="key">密匙</param>
/// <param name="b1">RSA的相应参数1</param>
/// <param name="b2">RSA的相应参数2</param>
private static void ResolveKey(string key, out byte[] b1, out byte[] b2)
{
//从base64字符串 解析成原来的字节数组
byte[] b = Convert.FromBase64String(key);
//初始化参数的数组长度
b1 = new byte[b[]];
b2 = new byte[b.Length - b[] - ];
//将相应位置是值放进相应的数组
for (int n = , i = , j = ; n < b.Length; n++)
{
if (n <= b[])
{
b1[i++] = b[n];
}
else
{
b2[j++] = b[n];
}
}
}
#endregion #region 字符串加密解密 公开方法
/// <summary>
/// 字符串加密
/// </summary>
/// <param name="source">源字符串 明文</param>
/// <param name="key">密匙</param>
/// <returns>加密遇到错误将会返回原字符串</returns>
public static string EncryptString(string source, string key)
{
string encryptString = string.Empty;
byte[] d;
byte[] n;
try
{
if (!CheckSourceValidate(source))
{
throw new Exception("source string too long");
}
//解析这个密钥
ResolveKey(key, out d, out n);
BigInteger biN = new BigInteger(n);
BigInteger biD = new BigInteger(d);
encryptString = EncryptString(source, biD, biN);
}
catch
{
encryptString = source;
}
return encryptString;
} /// <summary>
/// 字符串解密
/// </summary>
/// <param name="encryptString">密文</param>
/// <param name="key">密钥</param>
/// <returns>遇到解密失败将会返回原字符串</returns>
public static string DecryptString(string encryptString, string key)
{
string source = string.Empty;
byte[] e;
byte[] n;
try
{
//解析这个密钥
ResolveKey(key, out e, out n);
BigInteger biE = new BigInteger(e);
BigInteger biN = new BigInteger(n);
source = DecryptString(encryptString, biE, biN);
}
catch
{
source = encryptString;
}
return source;
}
#endregion #region 字符串加密解密 私有 实现加解密的实现方法
/// <summary>
/// 用指定的密匙加密
/// </summary>
/// <param name="source">明文</param>
/// <param name="d">可以是RSACryptoServiceProvider生成的D</param>
/// <param name="n">可以是RSACryptoServiceProvider生成的Modulus</param>
/// <returns>返回密文</returns>
private static string EncryptString(string source, BigInteger d, BigInteger n)
{
int len = source.Length;
int len1 = ;
int blockLen = ;
if ((len % ) == )
len1 = len / ;
else
len1 = len / + ;
string block = "";
StringBuilder result = new StringBuilder();
for (int i = ; i < len1; i++)
{
if (len >= )
blockLen = ;
else
blockLen = len;
block = source.Substring(i * , blockLen);
byte[] oText = System.Text.Encoding.Default.GetBytes(block);
BigInteger biText = new BigInteger(oText);
BigInteger biEnText = biText.modPow(d, n);
string temp = biEnText.ToHexString();
result.Append(temp).Append("@");
len -= blockLen;
}
return result.ToString().TrimEnd('@');
} /// <summary>
/// 用指定的密匙加密
/// </summary>
/// <param name="source">密文</param>
/// <param name="e">可以是RSACryptoServiceProvider生成的Exponent</param>
/// <param name="n">可以是RSACryptoServiceProvider生成的Modulus</param>
/// <returns>返回明文</returns>
private static string DecryptString(string encryptString, BigInteger e, BigInteger n)
{
StringBuilder result = new StringBuilder();
string[] strarr1 = encryptString.Split(new char[] { '@' }, StringSplitOptions.RemoveEmptyEntries);
for (int i = ; i < strarr1.Length; i++)
{
string block = strarr1[i];
BigInteger biText = new BigInteger(block, );
BigInteger biEnText = biText.modPow(e, n);
string temp = System.Text.Encoding.Default.GetString(biEnText.getBytes());
result.Append(temp);
}
return result.ToString();
}
#endregion
} public class BigInteger
{
#region BigInteger // maximum length of the BigInteger in uint (4 bytes)
// change this to suit the required level of precision. private const int maxLength = ; // primes smaller than 2000 to test the generated prime number public static readonly int[] primesBelow2000 = {
, , , , , , , , , , , , , , , , , , , , , , , , ,
, , , , , , , , , , , , , , , , , , , , ,
, , , , , , , , , , , , , , , ,
, , , , , , , , , , , , , , , ,
, , , , , , , , , , , , , , , , ,
, , , , , , , , , , , , , ,
, , , , , , , , , , , , , , , ,
, , , , , , , , , , , , , ,
, , , , , , , , , , , , , , ,
, , , , , , , , , , , , , ,
, , , , , , , , , , , , , , , ,
, , , , , , , , , , , ,
, , , , , , , , , , , , , , ,
, , , , , , , , , , ,
, , , , , , , , , , , , , , , , ,
, , , , , , , , , , , ,
, , , , , , , , , , , , , , ,
, , , , , , , , , , , ,
, , , , , , , , , , , ,
, , , , , , , , , , , , }; private uint[] data = null; // stores bytes from the Big Integer
public int dataLength; // number of actual chars used //***********************************************************************
// Constructor (Default value for BigInteger is 0
//*********************************************************************** public BigInteger()
{
data = new uint[maxLength];
dataLength = ;
} //***********************************************************************
// Constructor (Default value provided by long)
//*********************************************************************** public BigInteger(long value)
{
data = new uint[maxLength];
long tempVal = value; // copy bytes from long to BigInteger without any assumption of
// the length of the long datatype dataLength = ;
while (value != && dataLength < maxLength)
{
data[dataLength] = (uint)(value & 0xFFFFFFFF);
value >>= ;
dataLength++;
} if (tempVal > ) // overflow check for +ve value
{
if (value != || (data[maxLength - ] & 0x80000000) != )
throw (new ArithmeticException("Positive overflow in constructor."));
}
else if (tempVal < ) // underflow check for -ve value
{
if (value != - || (data[dataLength - ] & 0x80000000) == )
throw (new ArithmeticException("Negative underflow in constructor."));
} if (dataLength == )
dataLength = ;
} //***********************************************************************
// Constructor (Default value provided by ulong)
//*********************************************************************** public BigInteger(ulong value)
{
data = new uint[maxLength]; // copy bytes from ulong to BigInteger without any assumption of
// the length of the ulong datatype dataLength = ;
while (value != && dataLength < maxLength)
{
data[dataLength] = (uint)(value & 0xFFFFFFFF);
value >>= ;
dataLength++;
} if (value != || (data[maxLength - ] & 0x80000000) != )
throw (new ArithmeticException("Positive overflow in constructor.")); if (dataLength == )
dataLength = ;
} //***********************************************************************
// Constructor (Default value provided by BigInteger)
//*********************************************************************** public BigInteger(BigInteger bi)
{
data = new uint[maxLength]; dataLength = bi.dataLength; for (int i = ; i < dataLength; i++)
data[i] = bi.data[i];
} //***********************************************************************
// Constructor (Default value provided by a string of digits of the
// specified base)
//
// Example (base 10)
// -----------------
// To initialize "a" with the default value of 1234 in base 10
// BigInteger a = new BigInteger("1234", 10)
//
// To initialize "a" with the default value of -1234
// BigInteger a = new BigInteger("-1234", 10)
//
// Example (base 16)
// -----------------
// To initialize "a" with the default value of 0x1D4F in base 16
// BigInteger a = new BigInteger("1D4F", 16)
//
// To initialize "a" with the default value of -0x1D4F
// BigInteger a = new BigInteger("-1D4F", 16)
//
// Note that string values are specified in the <sign><magnitude>
// format.
//
//*********************************************************************** public BigInteger(string value, int radix)
{
BigInteger multiplier = new BigInteger();
BigInteger result = new BigInteger();
value = (value.ToUpper()).Trim();
int limit = ; if (value[] == '-')
limit = ; for (int i = value.Length - ; i >= limit; i--)
{
int posVal = (int)value[i]; if (posVal >= '' && posVal <= '')
posVal -= '';
else if (posVal >= 'A' && posVal <= 'Z')
posVal = (posVal - 'A') + ;
else
posVal = ; // arbitrary large if (posVal >= radix)
throw (new ArithmeticException("Invalid string in constructor."));
else
{
if (value[] == '-')
posVal = -posVal; result = result + (multiplier * posVal); if ((i - ) >= limit)
multiplier = multiplier * radix;
}
} if (value[] == '-') // negative values
{
if ((result.data[maxLength - ] & 0x80000000) == )
throw (new ArithmeticException("Negative underflow in constructor."));
}
else // positive values
{
if ((result.data[maxLength - ] & 0x80000000) != )
throw (new ArithmeticException("Positive overflow in constructor."));
} data = new uint[maxLength];
for (int i = ; i < result.dataLength; i++)
data[i] = result.data[i]; dataLength = result.dataLength;
} //***********************************************************************
// Constructor (Default value provided by an array of bytes)
//
// The lowest index of the input byte array (i.e [0]) should contain the
// most significant byte of the number, and the highest index should
// contain the least significant byte.
//
// E.g.
// To initialize "a" with the default value of 0x1D4F in base 16
// byte[] temp = { 0x1D, 0x4F };
// BigInteger a = new BigInteger(temp)
//
// Note that this method of initialization does not allow the
// sign to be specified.
//
//*********************************************************************** public BigInteger(byte[] inData)
{
dataLength = inData.Length >> ; int leftOver = inData.Length & 0x3;
if (leftOver != ) // length not multiples of 4
dataLength++; if (dataLength > maxLength)
throw (new ArithmeticException("Byte overflow in constructor.")); data = new uint[maxLength]; for (int i = inData.Length - , j = ; i >= ; i -= , j++)
{
data[j] = (uint)((inData[i - ] << ) + (inData[i - ] << ) +
(inData[i - ] << ) + inData[i]);
} if (leftOver == )
data[dataLength - ] = (uint)inData[];
else if (leftOver == )
data[dataLength - ] = (uint)((inData[] << ) + inData[]);
else if (leftOver == )
data[dataLength - ] = (uint)((inData[] << ) + (inData[] << ) + inData[]); while (dataLength > && data[dataLength - ] == )
dataLength--; //Console.WriteLine("Len = " + dataLength);
} //***********************************************************************
// Constructor (Default value provided by an array of bytes of the
// specified length.)
//*********************************************************************** public BigInteger(byte[] inData, int inLen)
{
dataLength = inLen >> ; int leftOver = inLen & 0x3;
if (leftOver != ) // length not multiples of 4
dataLength++; if (dataLength > maxLength || inLen > inData.Length)
throw (new ArithmeticException("Byte overflow in constructor.")); data = new uint[maxLength]; for (int i = inLen - , j = ; i >= ; i -= , j++)
{
data[j] = (uint)((inData[i - ] << ) + (inData[i - ] << ) +
(inData[i - ] << ) + inData[i]);
} if (leftOver == )
data[dataLength - ] = (uint)inData[];
else if (leftOver == )
data[dataLength - ] = (uint)((inData[] << ) + inData[]);
else if (leftOver == )
data[dataLength - ] = (uint)((inData[] << ) + (inData[] << ) + inData[]); if (dataLength == )
dataLength = ; while (dataLength > && data[dataLength - ] == )
dataLength--; //Console.WriteLine("Len = " + dataLength);
} //***********************************************************************
// Constructor (Default value provided by an array of unsigned integers)
//********************************************************************* public BigInteger(uint[] inData)
{
dataLength = inData.Length; if (dataLength > maxLength)
throw (new ArithmeticException("Byte overflow in constructor.")); data = new uint[maxLength]; for (int i = dataLength - , j = ; i >= ; i--, j++)
data[j] = inData[i]; while (dataLength > && data[dataLength - ] == )
dataLength--; //Console.WriteLine("Len = " + dataLength);
} //***********************************************************************
// Overloading of the typecast operator.
// For BigInteger bi = 10;
//*********************************************************************** public static implicit operator BigInteger(long value)
{
return (new BigInteger(value));
} public static implicit operator BigInteger(ulong value)
{
return (new BigInteger(value));
} public static implicit operator BigInteger(int value)
{
return (new BigInteger((long)value));
} public static implicit operator BigInteger(uint value)
{
return (new BigInteger((ulong)value));
} //***********************************************************************
// Overloading of addition operator
//*********************************************************************** public static BigInteger operator +(BigInteger bi1, BigInteger bi2)
{
BigInteger result = new BigInteger(); result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; long carry = ;
for (int i = ; i < result.dataLength; i++)
{
long sum = (long)bi1.data[i] + (long)bi2.data[i] + carry;
carry = sum >> ;
result.data[i] = (uint)(sum & 0xFFFFFFFF);
} if (carry != && result.dataLength < maxLength)
{
result.data[result.dataLength] = (uint)(carry);
result.dataLength++;
} while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--; // overflow check
int lastPos = maxLength - ;
if ((bi1.data[lastPos] & 0x80000000) == (bi2.data[lastPos] & 0x80000000) &&
(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
{
throw (new ArithmeticException());
} return result;
} //***********************************************************************
// Overloading of the unary ++ operator
//*********************************************************************** public static BigInteger operator ++(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1); long val, carry = ;
int index = ; while (carry != && index < maxLength)
{
val = (long)(result.data[index]);
val++; result.data[index] = (uint)(val & 0xFFFFFFFF);
carry = val >> ; index++;
} if (index > result.dataLength)
result.dataLength = index;
else
{
while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--;
} // overflow check
int lastPos = maxLength - ; // overflow if initial value was +ve but ++ caused a sign
// change to negative. if ((bi1.data[lastPos] & 0x80000000) == &&
(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
{
throw (new ArithmeticException("Overflow in ++."));
}
return result;
} //***********************************************************************
// Overloading of subtraction operator
//*********************************************************************** public static BigInteger operator -(BigInteger bi1, BigInteger bi2)
{
BigInteger result = new BigInteger(); result.dataLength = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; long carryIn = ;
for (int i = ; i < result.dataLength; i++)
{
long diff; diff = (long)bi1.data[i] - (long)bi2.data[i] - carryIn;
result.data[i] = (uint)(diff & 0xFFFFFFFF); if (diff < )
carryIn = ;
else
carryIn = ;
} // roll over to negative
if (carryIn != )
{
for (int i = result.dataLength; i < maxLength; i++)
result.data[i] = 0xFFFFFFFF;
result.dataLength = maxLength;
} // fixed in v1.03 to give correct datalength for a - (-b)
while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--; // overflow check int lastPos = maxLength - ;
if ((bi1.data[lastPos] & 0x80000000) != (bi2.data[lastPos] & 0x80000000) &&
(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
{
throw (new ArithmeticException());
} return result;
} //***********************************************************************
// Overloading of the unary -- operator
//*********************************************************************** public static BigInteger operator --(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1); long val;
bool carryIn = true;
int index = ; while (carryIn && index < maxLength)
{
val = (long)(result.data[index]);
val--; result.data[index] = (uint)(val & 0xFFFFFFFF); if (val >= )
carryIn = false; index++;
} if (index > result.dataLength)
result.dataLength = index; while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--; // overflow check
int lastPos = maxLength - ; // overflow if initial value was -ve but -- caused a sign
// change to positive. if ((bi1.data[lastPos] & 0x80000000) != &&
(result.data[lastPos] & 0x80000000) != (bi1.data[lastPos] & 0x80000000))
{
throw (new ArithmeticException("Underflow in --."));
} return result;
} //***********************************************************************
// Overloading of multiplication operator
//*********************************************************************** public static BigInteger operator *(BigInteger bi1, BigInteger bi2)
{
int lastPos = maxLength - ;
bool bi1Neg = false, bi2Neg = false; // take the absolute value of the inputs
try
{
if ((bi1.data[lastPos] & 0x80000000) != ) // bi1 negative
{
bi1Neg = true; bi1 = -bi1;
}
if ((bi2.data[lastPos] & 0x80000000) != ) // bi2 negative
{
bi2Neg = true; bi2 = -bi2;
}
}
catch (Exception) { } BigInteger result = new BigInteger(); // multiply the absolute values
try
{
for (int i = ; i < bi1.dataLength; i++)
{
if (bi1.data[i] == ) continue; ulong mcarry = ;
for (int j = , k = i; j < bi2.dataLength; j++, k++)
{
// k = i + j
ulong val = ((ulong)bi1.data[i] * (ulong)bi2.data[j]) +
(ulong)result.data[k] + mcarry; result.data[k] = (uint)(val & 0xFFFFFFFF);
mcarry = (val >> );
} if (mcarry != )
result.data[i + bi2.dataLength] = (uint)mcarry;
}
}
catch (Exception)
{
throw (new ArithmeticException("Multiplication overflow."));
} result.dataLength = bi1.dataLength + bi2.dataLength;
if (result.dataLength > maxLength)
result.dataLength = maxLength; while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--; // overflow check (result is -ve)
if ((result.data[lastPos] & 0x80000000) != )
{
if (bi1Neg != bi2Neg && result.data[lastPos] == 0x80000000) // different sign
{
// handle the special case where multiplication produces
// a max negative number in 2's complement. if (result.dataLength == )
return result;
else
{
bool isMaxNeg = true;
for (int i = ; i < result.dataLength - && isMaxNeg; i++)
{
if (result.data[i] != )
isMaxNeg = false;
} if (isMaxNeg)
return result;
}
} throw (new ArithmeticException("Multiplication overflow."));
} // if input has different signs, then result is -ve
if (bi1Neg != bi2Neg)
return -result; return result;
} //***********************************************************************
// Overloading of unary << operators
//*********************************************************************** public static BigInteger operator <<(BigInteger bi1, int shiftVal)
{
BigInteger result = new BigInteger(bi1);
result.dataLength = shiftLeft(result.data, shiftVal); return result;
} // least significant bits at lower part of buffer private static int shiftLeft(uint[] buffer, int shiftVal)
{
int shiftAmount = ;
int bufLen = buffer.Length; while (bufLen > && buffer[bufLen - ] == )
bufLen--; for (int count = shiftVal; count > ;)
{
if (count < shiftAmount)
shiftAmount = count; //Console.WriteLine("shiftAmount = {0}", shiftAmount); ulong carry = ;
for (int i = ; i < bufLen; i++)
{
ulong val = ((ulong)buffer[i]) << shiftAmount;
val |= carry; buffer[i] = (uint)(val & 0xFFFFFFFF);
carry = val >> ;
} if (carry != )
{
if (bufLen + <= buffer.Length)
{
buffer[bufLen] = (uint)carry;
bufLen++;
}
}
count -= shiftAmount;
}
return bufLen;
} //***********************************************************************
// Overloading of unary >> operators
//*********************************************************************** public static BigInteger operator >>(BigInteger bi1, int shiftVal)
{
BigInteger result = new BigInteger(bi1);
result.dataLength = shiftRight(result.data, shiftVal); if ((bi1.data[maxLength - ] & 0x80000000) != ) // negative
{
for (int i = maxLength - ; i >= result.dataLength; i--)
result.data[i] = 0xFFFFFFFF; uint mask = 0x80000000;
for (int i = ; i < ; i++)
{
if ((result.data[result.dataLength - ] & mask) != )
break; result.data[result.dataLength - ] |= mask;
mask >>= ;
}
result.dataLength = maxLength;
} return result;
} private static int shiftRight(uint[] buffer, int shiftVal)
{
int shiftAmount = ;
int invShift = ;
int bufLen = buffer.Length; while (bufLen > && buffer[bufLen - ] == )
bufLen--; //Console.WriteLine("bufLen = " + bufLen + " buffer.Length = " + buffer.Length); for (int count = shiftVal; count > ;)
{
if (count < shiftAmount)
{
shiftAmount = count;
invShift = - shiftAmount;
} //Console.WriteLine("shiftAmount = {0}", shiftAmount); ulong carry = ;
for (int i = bufLen - ; i >= ; i--)
{
ulong val = ((ulong)buffer[i]) >> shiftAmount;
val |= carry; carry = ((ulong)buffer[i]) << invShift;
buffer[i] = (uint)(val);
} count -= shiftAmount;
} while (bufLen > && buffer[bufLen - ] == )
bufLen--; return bufLen;
} //***********************************************************************
// Overloading of the NOT operator (1's complement)
//*********************************************************************** public static BigInteger operator ~(BigInteger bi1)
{
BigInteger result = new BigInteger(bi1); for (int i = ; i < maxLength; i++)
result.data[i] = (uint)(~(bi1.data[i])); result.dataLength = maxLength; while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--; return result;
} //***********************************************************************
// Overloading of the NEGATE operator (2's complement)
//*********************************************************************** public static BigInteger operator -(BigInteger bi1)
{
// handle neg of zero separately since it'll cause an overflow
// if we proceed. if (bi1.dataLength == && bi1.data[] == )
return (new BigInteger()); BigInteger result = new BigInteger(bi1); // 1's complement
for (int i = ; i < maxLength; i++)
result.data[i] = (uint)(~(bi1.data[i])); // add one to result of 1's complement
long val, carry = ;
int index = ; while (carry != && index < maxLength)
{
val = (long)(result.data[index]);
val++; result.data[index] = (uint)(val & 0xFFFFFFFF);
carry = val >> ; index++;
} if ((bi1.data[maxLength - ] & 0x80000000) == (result.data[maxLength - ] & 0x80000000))
throw (new ArithmeticException("Overflow in negation.\n")); result.dataLength = maxLength; while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--;
return result;
} //***********************************************************************
// Overloading of equality operator
//*********************************************************************** public static bool operator ==(BigInteger bi1, BigInteger bi2)
{
return bi1.Equals(bi2);
} public static bool operator !=(BigInteger bi1, BigInteger bi2)
{
return !(bi1.Equals(bi2));
} public override bool Equals(object o)
{
BigInteger bi = (BigInteger)o; if (this.dataLength != bi.dataLength)
return false; for (int i = ; i < this.dataLength; i++)
{
if (this.data[i] != bi.data[i])
return false;
}
return true;
} public override int GetHashCode()
{
return this.ToString().GetHashCode();
} //***********************************************************************
// Overloading of inequality operator
//*********************************************************************** public static bool operator >(BigInteger bi1, BigInteger bi2)
{
int pos = maxLength - ; // bi1 is negative, bi2 is positive
if ((bi1.data[pos] & 0x80000000) != && (bi2.data[pos] & 0x80000000) == )
return false; // bi1 is positive, bi2 is negative
else if ((bi1.data[pos] & 0x80000000) == && (bi2.data[pos] & 0x80000000) != )
return true; // same sign
int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
for (pos = len - ; pos >= && bi1.data[pos] == bi2.data[pos]; pos--) ; if (pos >= )
{
if (bi1.data[pos] > bi2.data[pos])
return true;
return false;
}
return false;
} public static bool operator <(BigInteger bi1, BigInteger bi2)
{
int pos = maxLength - ; // bi1 is negative, bi2 is positive
if ((bi1.data[pos] & 0x80000000) != && (bi2.data[pos] & 0x80000000) == )
return true; // bi1 is positive, bi2 is negative
else if ((bi1.data[pos] & 0x80000000) == && (bi2.data[pos] & 0x80000000) != )
return false; // same sign
int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength;
for (pos = len - ; pos >= && bi1.data[pos] == bi2.data[pos]; pos--) ; if (pos >= )
{
if (bi1.data[pos] < bi2.data[pos])
return true;
return false;
}
return false;
} public static bool operator >=(BigInteger bi1, BigInteger bi2)
{
return (bi1 == bi2 || bi1 > bi2);
} public static bool operator <=(BigInteger bi1, BigInteger bi2)
{
return (bi1 == bi2 || bi1 < bi2);
} //***********************************************************************
// Private function that supports the division of two numbers with
// a divisor that has more than 1 digit.
//
// Algorithm taken from [1]
//*********************************************************************** private static void multiByteDivide(BigInteger bi1, BigInteger bi2,
BigInteger outQuotient, BigInteger outRemainder)
{
uint[] result = new uint[maxLength]; int remainderLen = bi1.dataLength + ;
uint[] remainder = new uint[remainderLen]; uint mask = 0x80000000;
uint val = bi2.data[bi2.dataLength - ];
int shift = , resultPos = ; while (mask != && (val & mask) == )
{
shift++; mask >>= ;
} //Console.WriteLine("shift = {0}", shift);
//Console.WriteLine("Before bi1 Len = {0}, bi2 Len = {1}", bi1.dataLength, bi2.dataLength); for (int i = ; i < bi1.dataLength; i++)
remainder[i] = bi1.data[i];
shiftLeft(remainder, shift);
bi2 = bi2 << shift; /*
Console.WriteLine("bi1 Len = {0}, bi2 Len = {1}", bi1.dataLength, bi2.dataLength);
Console.WriteLine("dividend = " + bi1 + "\ndivisor = " + bi2);
for(int q = remainderLen - 1; q >= 0; q--)
Console.Write("{0:x2}", remainder[q]);
Console.WriteLine();
*/ int j = remainderLen - bi2.dataLength;
int pos = remainderLen - ; ulong firstDivisorByte = bi2.data[bi2.dataLength - ];
ulong secondDivisorByte = bi2.data[bi2.dataLength - ]; int divisorLen = bi2.dataLength + ;
uint[] dividendPart = new uint[divisorLen]; while (j > )
{
ulong dividend = ((ulong)remainder[pos] << ) + (ulong)remainder[pos - ];
//Console.WriteLine("dividend = {0}", dividend); ulong q_hat = dividend / firstDivisorByte;
ulong r_hat = dividend % firstDivisorByte; //Console.WriteLine("q_hat = {0:X}, r_hat = {1:X}", q_hat, r_hat); bool done = false;
while (!done)
{
done = true; if (q_hat == 0x100000000 ||
(q_hat * secondDivisorByte) > ((r_hat << ) + remainder[pos - ]))
{
q_hat--;
r_hat += firstDivisorByte; if (r_hat < 0x100000000)
done = false;
}
} for (int h = ; h < divisorLen; h++)
dividendPart[h] = remainder[pos - h]; BigInteger kk = new BigInteger(dividendPart);
BigInteger ss = bi2 * (long)q_hat; //Console.WriteLine("ss before = " + ss);
while (ss > kk)
{
q_hat--;
ss -= bi2;
//Console.WriteLine(ss);
}
BigInteger yy = kk - ss; //Console.WriteLine("ss = " + ss);
//Console.WriteLine("kk = " + kk);
//Console.WriteLine("yy = " + yy); for (int h = ; h < divisorLen; h++)
remainder[pos - h] = yy.data[bi2.dataLength - h]; /*
Console.WriteLine("dividend = ");
for(int q = remainderLen - 1; q >= 0; q--)
Console.Write("{0:x2}", remainder[q]);
Console.WriteLine("\n************ q_hat = {0:X}\n", q_hat);
*/ result[resultPos++] = (uint)q_hat; pos--;
j--;
} outQuotient.dataLength = resultPos;
int y = ;
for (int x = outQuotient.dataLength - ; x >= ; x--, y++)
outQuotient.data[y] = result[x];
for (; y < maxLength; y++)
outQuotient.data[y] = ; while (outQuotient.dataLength > && outQuotient.data[outQuotient.dataLength - ] == )
outQuotient.dataLength--; if (outQuotient.dataLength == )
outQuotient.dataLength = ; outRemainder.dataLength = shiftRight(remainder, shift); for (y = ; y < outRemainder.dataLength; y++)
outRemainder.data[y] = remainder[y];
for (; y < maxLength; y++)
outRemainder.data[y] = ;
} //***********************************************************************
// Private function that supports the division of two numbers with
// a divisor that has only 1 digit.
//*********************************************************************** private static void singleByteDivide(BigInteger bi1, BigInteger bi2,
BigInteger outQuotient, BigInteger outRemainder)
{
uint[] result = new uint[maxLength];
int resultPos = ; // copy dividend to reminder
for (int i = ; i < maxLength; i++)
outRemainder.data[i] = bi1.data[i];
outRemainder.dataLength = bi1.dataLength; while (outRemainder.dataLength > && outRemainder.data[outRemainder.dataLength - ] == )
outRemainder.dataLength--; ulong divisor = (ulong)bi2.data[];
int pos = outRemainder.dataLength - ;
ulong dividend = (ulong)outRemainder.data[pos]; //Console.WriteLine("divisor = " + divisor + " dividend = " + dividend);
//Console.WriteLine("divisor = " + bi2 + "\ndividend = " + bi1); if (dividend >= divisor)
{
ulong quotient = dividend / divisor;
result[resultPos++] = (uint)quotient; outRemainder.data[pos] = (uint)(dividend % divisor);
}
pos--; while (pos >= )
{
//Console.WriteLine(pos); dividend = ((ulong)outRemainder.data[pos + ] << ) + (ulong)outRemainder.data[pos];
ulong quotient = dividend / divisor;
result[resultPos++] = (uint)quotient; outRemainder.data[pos + ] = ;
outRemainder.data[pos--] = (uint)(dividend % divisor);
//Console.WriteLine(">>>> " + bi1);
} outQuotient.dataLength = resultPos;
int j = ;
for (int i = outQuotient.dataLength - ; i >= ; i--, j++)
outQuotient.data[j] = result[i];
for (; j < maxLength; j++)
outQuotient.data[j] = ; while (outQuotient.dataLength > && outQuotient.data[outQuotient.dataLength - ] == )
outQuotient.dataLength--; if (outQuotient.dataLength == )
outQuotient.dataLength = ; while (outRemainder.dataLength > && outRemainder.data[outRemainder.dataLength - ] == )
outRemainder.dataLength--;
} //***********************************************************************
// Overloading of division operator
//*********************************************************************** public static BigInteger operator /(BigInteger bi1, BigInteger bi2)
{
BigInteger quotient = new BigInteger();
BigInteger remainder = new BigInteger(); int lastPos = maxLength - ;
bool divisorNeg = false, dividendNeg = false; if ((bi1.data[lastPos] & 0x80000000) != ) // bi1 negative
{
bi1 = -bi1;
dividendNeg = true;
}
if ((bi2.data[lastPos] & 0x80000000) != ) // bi2 negative
{
bi2 = -bi2;
divisorNeg = true;
} if (bi1 < bi2)
{
return quotient;
} else
{
if (bi2.dataLength == )
singleByteDivide(bi1, bi2, quotient, remainder);
else
multiByteDivide(bi1, bi2, quotient, remainder); if (dividendNeg != divisorNeg)
return -quotient; return quotient;
}
} //***********************************************************************
// Overloading of modulus operator
//*********************************************************************** public static BigInteger operator %(BigInteger bi1, BigInteger bi2)
{
BigInteger quotient = new BigInteger();
BigInteger remainder = new BigInteger(bi1); int lastPos = maxLength - ;
bool dividendNeg = false; if ((bi1.data[lastPos] & 0x80000000) != ) // bi1 negative
{
bi1 = -bi1;
dividendNeg = true;
}
if ((bi2.data[lastPos] & 0x80000000) != ) // bi2 negative
bi2 = -bi2; if (bi1 < bi2)
{
return remainder;
} else
{
if (bi2.dataLength == )
singleByteDivide(bi1, bi2, quotient, remainder);
else
multiByteDivide(bi1, bi2, quotient, remainder); if (dividendNeg)
return -remainder; return remainder;
}
} //***********************************************************************
// Overloading of bitwise AND operator
//*********************************************************************** public static BigInteger operator &(BigInteger bi1, BigInteger bi2)
{
BigInteger result = new BigInteger(); int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; for (int i = ; i < len; i++)
{
uint sum = (uint)(bi1.data[i] & bi2.data[i]);
result.data[i] = sum;
} result.dataLength = maxLength; while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--; return result;
} //***********************************************************************
// Overloading of bitwise OR operator
//*********************************************************************** public static BigInteger operator |(BigInteger bi1, BigInteger bi2)
{
BigInteger result = new BigInteger(); int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; for (int i = ; i < len; i++)
{
uint sum = (uint)(bi1.data[i] | bi2.data[i]);
result.data[i] = sum;
} result.dataLength = maxLength; while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--; return result;
} //***********************************************************************
// Overloading of bitwise XOR operator
//*********************************************************************** public static BigInteger operator ^(BigInteger bi1, BigInteger bi2)
{
BigInteger result = new BigInteger(); int len = (bi1.dataLength > bi2.dataLength) ? bi1.dataLength : bi2.dataLength; for (int i = ; i < len; i++)
{
uint sum = (uint)(bi1.data[i] ^ bi2.data[i]);
result.data[i] = sum;
} result.dataLength = maxLength; while (result.dataLength > && result.data[result.dataLength - ] == )
result.dataLength--; return result;
} //***********************************************************************
// Returns max(this, bi)
//*********************************************************************** public BigInteger max(BigInteger bi)
{
if (this > bi)
return (new BigInteger(this));
else
return (new BigInteger(bi));
} //***********************************************************************
// Returns min(this, bi)
//*********************************************************************** public BigInteger min(BigInteger bi)
{
if (this < bi)
return (new BigInteger(this));
else
return (new BigInteger(bi)); } //***********************************************************************
// Returns the absolute value
//*********************************************************************** public BigInteger abs()
{
if ((this.data[maxLength - ] & 0x80000000) != )
return (-this);
else
return (new BigInteger(this));
} //***********************************************************************
// Returns a string representing the BigInteger in base 10.
//*********************************************************************** public override string ToString()
{
return ToString();
} //***********************************************************************
// Returns a string representing the BigInteger in sign-and-magnitude
// format in the specified radix.
//
// Example
// -------
// If the value of BigInteger is -255 in base 10, then
// ToString(16) returns "-FF"
//
//*********************************************************************** public string ToString(int radix)
{
if (radix < || radix > )
throw (new ArgumentException("Radix must be >= 2 and <= 36")); string charSet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ";
string result = ""; BigInteger a = this; bool negative = false;
if ((a.data[maxLength - ] & 0x80000000) != )
{
negative = true;
try
{
a = -a;
}
catch (Exception) { }
} BigInteger quotient = new BigInteger();
BigInteger remainder = new BigInteger();
BigInteger biRadix = new BigInteger(radix); if (a.dataLength == && a.data[] == )
result = "";
else
{
while (a.dataLength > || (a.dataLength == && a.data[] != ))
{
singleByteDivide(a, biRadix, quotient, remainder); if (remainder.data[] < )
result = remainder.data[] + result;
else
result = charSet[(int)remainder.data[] - ] + result; a = quotient;
}
if (negative)
result = "-" + result;
} return result;
} //***********************************************************************
// Returns a hex string showing the contains of the BigInteger
//
// Examples
// -------
// 1) If the value of BigInteger is 255 in base 10, then
// ToHexString() returns "FF"
//
// 2) If the value of BigInteger is -255 in base 10, then
// ToHexString() returns ".....FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF01",
// which is the 2's complement representation of -255.
//
//*********************************************************************** public string ToHexString()
{
string result = data[dataLength - ].ToString("X"); for (int i = dataLength - ; i >= ; i--)
{
result += data[i].ToString("X8");
} return result;
} //***********************************************************************
// Modulo Exponentiation
//*********************************************************************** public BigInteger modPow(BigInteger exp, BigInteger n)
{
if ((exp.data[maxLength - ] & 0x80000000) != )
throw (new ArithmeticException("Positive exponents only.")); BigInteger resultNum = ;
BigInteger tempNum;
bool thisNegative = false; if ((this.data[maxLength - ] & 0x80000000) != ) // negative this
{
tempNum = -this % n;
thisNegative = true;
}
else
tempNum = this % n; // ensures (tempNum * tempNum) < b^(2k) if ((n.data[maxLength - ] & 0x80000000) != ) // negative n
n = -n; // calculate constant = b^(2k) / m
BigInteger constant = new BigInteger(); int i = n.dataLength << ;
constant.data[i] = 0x00000001;
constant.dataLength = i + ; constant = constant / n;
int totalBits = exp.bitCount();
int count = ; // perform squaring and multiply exponentiation
for (int pos = ; pos < exp.dataLength; pos++)
{
uint mask = 0x01;
//Console.WriteLine("pos = " + pos); for (int index = ; index < ; index++)
{
if ((exp.data[pos] & mask) != )
resultNum = BarrettReduction(resultNum * tempNum, n, constant); mask <<= ; tempNum = BarrettReduction(tempNum * tempNum, n, constant); if (tempNum.dataLength == && tempNum.data[] == )
{
if (thisNegative && (exp.data[] & 0x1) != ) //odd exp
return -resultNum;
return resultNum;
}
count++;
if (count == totalBits)
break;
}
} if (thisNegative && (exp.data[] & 0x1) != ) //odd exp
return -resultNum; return resultNum;
} //***********************************************************************
// Fast calculation of modular reduction using Barrett's reduction.
// Requires x < b^(2k), where b is the base. In this case, base is
// 2^32 (uint).
//
// Reference [4]
//*********************************************************************** private BigInteger BarrettReduction(BigInteger x, BigInteger n, BigInteger constant)
{
int k = n.dataLength,
kPlusOne = k + ,
kMinusOne = k - ; BigInteger q1 = new BigInteger(); // q1 = x / b^(k-1)
for (int i = kMinusOne, j = ; i < x.dataLength; i++, j++)
q1.data[j] = x.data[i];
q1.dataLength = x.dataLength - kMinusOne;
if (q1.dataLength <= )
q1.dataLength = ; BigInteger q2 = q1 * constant;
BigInteger q3 = new BigInteger(); // q3 = q2 / b^(k+1)
for (int i = kPlusOne, j = ; i < q2.dataLength; i++, j++)
q3.data[j] = q2.data[i];
q3.dataLength = q2.dataLength - kPlusOne;
if (q3.dataLength <= )
q3.dataLength = ; // r1 = x mod b^(k+1)
// i.e. keep the lowest (k+1) words
BigInteger r1 = new BigInteger();
int lengthToCopy = (x.dataLength > kPlusOne) ? kPlusOne : x.dataLength;
for (int i = ; i < lengthToCopy; i++)
r1.data[i] = x.data[i];
r1.dataLength = lengthToCopy; // r2 = (q3 * n) mod b^(k+1)
// partial multiplication of q3 and n BigInteger r2 = new BigInteger();
for (int i = ; i < q3.dataLength; i++)
{
if (q3.data[i] == ) continue; ulong mcarry = ;
int t = i;
for (int j = ; j < n.dataLength && t < kPlusOne; j++, t++)
{
// t = i + j
ulong val = ((ulong)q3.data[i] * (ulong)n.data[j]) +
(ulong)r2.data[t] + mcarry; r2.data[t] = (uint)(val & 0xFFFFFFFF);
mcarry = (val >> );
} if (t < kPlusOne)
r2.data[t] = (uint)mcarry;
}
r2.dataLength = kPlusOne;
while (r2.dataLength > && r2.data[r2.dataLength - ] == )
r2.dataLength--; r1 -= r2;
if ((r1.data[maxLength - ] & 0x80000000) != ) // negative
{
BigInteger val = new BigInteger();
val.data[kPlusOne] = 0x00000001;
val.dataLength = kPlusOne + ;
r1 += val;
} while (r1 >= n)
r1 -= n; return r1;
} //***********************************************************************
// Returns gcd(this, bi)
//*********************************************************************** public BigInteger gcd(BigInteger bi)
{
BigInteger x;
BigInteger y; if ((data[maxLength - ] & 0x80000000) != ) // negative
x = -this;
else
x = this; if ((bi.data[maxLength - ] & 0x80000000) != ) // negative
y = -bi;
else
y = bi; BigInteger g = y; while (x.dataLength > || (x.dataLength == && x.data[] != ))
{
g = x;
x = y % x;
y = g;
} return g;
} //***********************************************************************
// Populates "this" with the specified amount of random bits
//*********************************************************************** public void genRandomBits(int bits, Random rand)
{
int dwords = bits >> ;
int remBits = bits & 0x1F; if (remBits != )
dwords++; if (dwords > maxLength)
throw (new ArithmeticException("Number of required bits > maxLength.")); for (int i = ; i < dwords; i++)
data[i] = (uint)(rand.NextDouble() * 0x100000000); for (int i = dwords; i < maxLength; i++)
data[i] = ; if (remBits != )
{
uint mask = (uint)(0x01 << (remBits - ));
data[dwords - ] |= mask; mask = (uint)(0xFFFFFFFF >> ( - remBits));
data[dwords - ] &= mask;
}
else
data[dwords - ] |= 0x80000000; dataLength = dwords; if (dataLength == )
dataLength = ;
} //***********************************************************************
// Returns the position of the most significant bit in the BigInteger.
//
// Eg. The result is 0, if the value of BigInteger is 0...0000 0000
// The result is 1, if the value of BigInteger is 0...0000 0001
// The result is 2, if the value of BigInteger is 0...0000 0010
// The result is 2, if the value of BigInteger is 0...0000 0011
//
//*********************************************************************** public int bitCount()
{
while (dataLength > && data[dataLength - ] == )
dataLength--; uint value = data[dataLength - ];
uint mask = 0x80000000;
int bits = ; while (bits > && (value & mask) == )
{
bits--;
mask >>= ;
}
bits += ((dataLength - ) << ); return bits;
} //***********************************************************************
// Probabilistic prime test based on Fermat's little theorem
//
// for any a < p (p does not divide a) if
// a^(p-1) mod p != 1 then p is not prime.
//
// Otherwise, p is probably prime (pseudoprime to the chosen base).
//
// Returns
// -------
// True if "this" is a pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
// Note - this method is fast but fails for Carmichael numbers except
// when the randomly chosen base is a factor of the number.
//
//*********************************************************************** public bool FermatLittleTest(int confidence)
{
BigInteger thisVal;
if ((this.data[maxLength - ] & 0x80000000) != ) // negative
thisVal = -this;
else
thisVal = this; if (thisVal.dataLength == )
{
// test small numbers
if (thisVal.data[] == || thisVal.data[] == )
return false;
else if (thisVal.data[] == || thisVal.data[] == )
return true;
} if ((thisVal.data[] & 0x1) == ) // even numbers
return false; int bits = thisVal.bitCount();
BigInteger a = new BigInteger();
BigInteger p_sub1 = thisVal - (new BigInteger());
Random rand = new Random(); for (int round = ; round < confidence; round++)
{
bool done = false; while (!done) // generate a < n
{
int testBits = ; // make sure "a" has at least 2 bits
while (testBits < )
testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0
if (byteLen > || (byteLen == && a.data[] != ))
done = true;
} // check whether a factor exists (fix for version 1.03)
BigInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == && gcdTest.data[] != )
return false; // calculate a^(p-1) mod p
BigInteger expResult = a.modPow(p_sub1, thisVal); int resultLen = expResult.dataLength; // is NOT prime is a^(p-1) mod p != 1 if (resultLen > || (resultLen == && expResult.data[] != ))
{
//Console.WriteLine("a = " + a.ToString());
return false;
}
} return true;
} //***********************************************************************
// Probabilistic prime test based on Rabin-Miller's
//
// for any p > 0 with p - 1 = 2^s * t
//
// p is probably prime (strong pseudoprime) if for any a < p,
// 1) a^t mod p = 1 or
// 2) a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
//
// Otherwise, p is composite.
//
// Returns
// -------
// True if "this" is a strong pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
//*********************************************************************** public bool RabinMillerTest(int confidence)
{
BigInteger thisVal;
if ((this.data[maxLength - ] & 0x80000000) != ) // negative
thisVal = -this;
else
thisVal = this; if (thisVal.dataLength == )
{
// test small numbers
if (thisVal.data[] == || thisVal.data[] == )
return false;
else if (thisVal.data[] == || thisVal.data[] == )
return true;
} if ((thisVal.data[] & 0x1) == ) // even numbers
return false; // calculate values of s and t
BigInteger p_sub1 = thisVal - (new BigInteger());
int s = ; for (int index = ; index < p_sub1.dataLength; index++)
{
uint mask = 0x01; for (int i = ; i < ; i++)
{
if ((p_sub1.data[index] & mask) != )
{
index = p_sub1.dataLength; // to break the outer loop
break;
}
mask <<= ;
s++;
}
} BigInteger t = p_sub1 >> s; int bits = thisVal.bitCount();
BigInteger a = new BigInteger();
Random rand = new Random(); for (int round = ; round < confidence; round++)
{
bool done = false; while (!done) // generate a < n
{
int testBits = ; // make sure "a" has at least 2 bits
while (testBits < )
testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0
if (byteLen > || (byteLen == && a.data[] != ))
done = true;
} // check whether a factor exists (fix for version 1.03)
BigInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == && gcdTest.data[] != )
return false; BigInteger b = a.modPow(t, thisVal); /*
Console.WriteLine("a = " + a.ToString(10));
Console.WriteLine("b = " + b.ToString(10));
Console.WriteLine("t = " + t.ToString(10));
Console.WriteLine("s = " + s);
*/ bool result = false; if (b.dataLength == && b.data[] == ) // a^t mod p = 1
result = true; for (int j = ; result == false && j < s; j++)
{
if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
{
result = true;
break;
} b = (b * b) % thisVal;
} if (result == false)
return false;
}
return true;
} //***********************************************************************
// Probabilistic prime test based on Solovay-Strassen (Euler Criterion)
//
// p is probably prime if for any a < p (a is not multiple of p),
// a^((p-1)/2) mod p = J(a, p)
//
// where J is the Jacobi symbol.
//
// Otherwise, p is composite.
//
// Returns
// -------
// True if "this" is a Euler pseudoprime to randomly chosen
// bases. The number of chosen bases is given by the "confidence"
// parameter.
//
// False if "this" is definitely NOT prime.
//
//*********************************************************************** public bool SolovayStrassenTest(int confidence)
{
BigInteger thisVal;
if ((this.data[maxLength - ] & 0x80000000) != ) // negative
thisVal = -this;
else
thisVal = this; if (thisVal.dataLength == )
{
// test small numbers
if (thisVal.data[] == || thisVal.data[] == )
return false;
else if (thisVal.data[] == || thisVal.data[] == )
return true;
} if ((thisVal.data[] & 0x1) == ) // even numbers
return false; int bits = thisVal.bitCount();
BigInteger a = new BigInteger();
BigInteger p_sub1 = thisVal - ;
BigInteger p_sub1_shift = p_sub1 >> ; Random rand = new Random(); for (int round = ; round < confidence; round++)
{
bool done = false; while (!done) // generate a < n
{
int testBits = ; // make sure "a" has at least 2 bits
while (testBits < )
testBits = (int)(rand.NextDouble() * bits); a.genRandomBits(testBits, rand); int byteLen = a.dataLength; // make sure "a" is not 0
if (byteLen > || (byteLen == && a.data[] != ))
done = true;
} // check whether a factor exists (fix for version 1.03)
BigInteger gcdTest = a.gcd(thisVal);
if (gcdTest.dataLength == && gcdTest.data[] != )
return false; // calculate a^((p-1)/2) mod p BigInteger expResult = a.modPow(p_sub1_shift, thisVal);
if (expResult == p_sub1)
expResult = -; // calculate Jacobi symbol
BigInteger jacob = Jacobi(a, thisVal); //Console.WriteLine("a = " + a.ToString(10) + " b = " + thisVal.ToString(10));
//Console.WriteLine("expResult = " + expResult.ToString(10) + " Jacob = " + jacob.ToString(10)); // if they are different then it is not prime
if (expResult != jacob)
return false;
} return true;
} //***********************************************************************
// Implementation of the Lucas Strong Pseudo Prime test.
//
// Let n be an odd number with gcd(n,D) = 1, and n - J(D, n) = 2^s * d
// with d odd and s >= 0.
//
// If Ud mod n = 0 or V2^r*d mod n = 0 for some 0 <= r < s, then n
// is a strong Lucas pseudoprime with parameters (P, Q). We select
// P and Q based on Selfridge.
//
// Returns True if number is a strong Lucus pseudo prime.
// Otherwise, returns False indicating that number is composite.
//*********************************************************************** public bool LucasStrongTest()
{
BigInteger thisVal;
if ((this.data[maxLength - ] & 0x80000000) != ) // negative
thisVal = -this;
else
thisVal = this; if (thisVal.dataLength == )
{
// test small numbers
if (thisVal.data[] == || thisVal.data[] == )
return false;
else if (thisVal.data[] == || thisVal.data[] == )
return true;
} if ((thisVal.data[] & 0x1) == ) // even numbers
return false; return LucasStrongTestHelper(thisVal);
} private bool LucasStrongTestHelper(BigInteger thisVal)
{
// Do the test (selects D based on Selfridge)
// Let D be the first element of the sequence
// 5, -7, 9, -11, 13, ... for which J(D,n) = -1
// Let P = 1, Q = (1-D) / 4 long D = , sign = -, dCount = ;
bool done = false; while (!done)
{
int Jresult = BigInteger.Jacobi(D, thisVal); if (Jresult == -)
done = true; // J(D, this) = 1
else
{
if (Jresult == && Math.Abs(D) < thisVal) // divisor found
return false; if (dCount == )
{
// check for square
BigInteger root = thisVal.sqrt();
if (root * root == thisVal)
return false;
} //Console.WriteLine(D);
D = (Math.Abs(D) + ) * sign;
sign = -sign;
}
dCount++;
} long Q = ( - D) >> ; /*
Console.WriteLine("D = " + D);
Console.WriteLine("Q = " + Q);
Console.WriteLine("(n,D) = " + thisVal.gcd(D));
Console.WriteLine("(n,Q) = " + thisVal.gcd(Q));
Console.WriteLine("J(D|n) = " + BigInteger.Jacobi(D, thisVal));
*/ BigInteger p_add1 = thisVal + ;
int s = ; for (int index = ; index < p_add1.dataLength; index++)
{
uint mask = 0x01; for (int i = ; i < ; i++)
{
if ((p_add1.data[index] & mask) != )
{
index = p_add1.dataLength; // to break the outer loop
break;
}
mask <<= ;
s++;
}
} BigInteger t = p_add1 >> s; // calculate constant = b^(2k) / m
// for Barrett Reduction
BigInteger constant = new BigInteger(); int nLen = thisVal.dataLength << ;
constant.data[nLen] = 0x00000001;
constant.dataLength = nLen + ; constant = constant / thisVal; BigInteger[] lucas = LucasSequenceHelper(, Q, t, thisVal, constant, );
bool isPrime = false; if ((lucas[].dataLength == && lucas[].data[] == ) ||
(lucas[].dataLength == && lucas[].data[] == ))
{
// u(t) = 0 or V(t) = 0
isPrime = true;
} for (int i = ; i < s; i++)
{
if (!isPrime)
{
// doubling of index
lucas[] = thisVal.BarrettReduction(lucas[] * lucas[], thisVal, constant);
lucas[] = (lucas[] - (lucas[] << )) % thisVal; //lucas[1] = ((lucas[1] * lucas[1]) - (lucas[2] << 1)) % thisVal; if ((lucas[].dataLength == && lucas[].data[] == ))
isPrime = true;
} lucas[] = thisVal.BarrettReduction(lucas[] * lucas[], thisVal, constant); //Q^k
} if (isPrime) // additional checks for composite numbers
{
// If n is prime and gcd(n, Q) == 1, then
// Q^((n+1)/2) = Q * Q^((n-1)/2) is congruent to (Q * J(Q, n)) mod n BigInteger g = thisVal.gcd(Q);
if (g.dataLength == && g.data[] == ) // gcd(this, Q) == 1
{
if ((lucas[].data[maxLength - ] & 0x80000000) != )
lucas[] += thisVal; BigInteger temp = (Q * BigInteger.Jacobi(Q, thisVal)) % thisVal;
if ((temp.data[maxLength - ] & 0x80000000) != )
temp += thisVal; if (lucas[] != temp)
isPrime = false;
}
} return isPrime;
} //***********************************************************************
// Determines whether a number is probably prime, using the Rabin-Miller's
// test. Before applying the test, the number is tested for divisibility
// by primes < 2000
//
// Returns true if number is probably prime.
//*********************************************************************** public bool isProbablePrime(int confidence)
{
BigInteger thisVal;
if ((this.data[maxLength - ] & 0x80000000) != ) // negative
thisVal = -this;
else
thisVal = this; // test for divisibility by primes < 2000
for (int p = ; p < primesBelow2000.Length; p++)
{
BigInteger divisor = primesBelow2000[p]; if (divisor >= thisVal)
break; BigInteger resultNum = thisVal % divisor;
if (resultNum.IntValue() == )
{
/*
Console.WriteLine("Not prime! Divisible by {0}\n",
primesBelow2000[p]);
*/
return false;
}
} if (thisVal.RabinMillerTest(confidence))
return true;
else
{
//Console.WriteLine("Not prime! Failed primality test\n");
return false;
}
} //***********************************************************************
// Determines whether this BigInteger is probably prime using a
// combination of base 2 strong pseudoprime test and Lucas strong
// pseudoprime test.
//
// The sequence of the primality test is as follows,
//
// 1) Trial divisions are carried out using prime numbers below 2000.
// if any of the primes divides this BigInteger, then it is not prime.
//
// 2) Perform base 2 strong pseudoprime test. If this BigInteger is a
// base 2 strong pseudoprime, proceed on to the next step.
//
// 3) Perform strong Lucas pseudoprime test.
//
// Returns True if this BigInteger is both a base 2 strong pseudoprime
// and a strong Lucas pseudoprime.
//
// For a detailed discussion of this primality test, see [6].
//
//*********************************************************************** public bool isProbablePrime()
{
BigInteger thisVal;
if ((this.data[maxLength - ] & 0x80000000) != ) // negative
thisVal = -this;
else
thisVal = this; if (thisVal.dataLength == )
{
// test small numbers
if (thisVal.data[] == || thisVal.data[] == )
return false;
else if (thisVal.data[] == || thisVal.data[] == )
return true;
} if ((thisVal.data[] & 0x1) == ) // even numbers
return false; // test for divisibility by primes < 2000
for (int p = ; p < primesBelow2000.Length; p++)
{
BigInteger divisor = primesBelow2000[p]; if (divisor >= thisVal)
break; BigInteger resultNum = thisVal % divisor;
if (resultNum.IntValue() == )
{
//Console.WriteLine("Not prime! Divisible by {0}\n",
// primesBelow2000[p]); return false;
}
} // Perform BASE 2 Rabin-Miller Test // calculate values of s and t
BigInteger p_sub1 = thisVal - (new BigInteger());
int s = ; for (int index = ; index < p_sub1.dataLength; index++)
{
uint mask = 0x01; for (int i = ; i < ; i++)
{
if ((p_sub1.data[index] & mask) != )
{
index = p_sub1.dataLength; // to break the outer loop
break;
}
mask <<= ;
s++;
}
} BigInteger t = p_sub1 >> s; int bits = thisVal.bitCount();
BigInteger a = ; // b = a^t mod p
BigInteger b = a.modPow(t, thisVal);
bool result = false; if (b.dataLength == && b.data[] == ) // a^t mod p = 1
result = true; for (int j = ; result == false && j < s; j++)
{
if (b == p_sub1) // a^((2^j)*t) mod p = p-1 for some 0 <= j <= s-1
{
result = true;
break;
} b = (b * b) % thisVal;
} // if number is strong pseudoprime to base 2, then do a strong lucas test
if (result)
result = LucasStrongTestHelper(thisVal); return result;
} //***********************************************************************
// Returns the lowest 4 bytes of the BigInteger as an int.
//*********************************************************************** public int IntValue()
{
return (int)data[];
} //***********************************************************************
// Returns the lowest 8 bytes of the BigInteger as a long.
//*********************************************************************** public long LongValue()
{
long val = ; val = (long)data[];
try
{ // exception if maxLength = 1
val |= (long)data[] << ;
}
catch (Exception)
{
if ((data[] & 0x80000000) != ) // negative
val = (int)data[];
} return val;
} //***********************************************************************
// Computes the Jacobi Symbol for a and b.
// Algorithm adapted from [3] and [4] with some optimizations
//*********************************************************************** public static int Jacobi(BigInteger a, BigInteger b)
{
// Jacobi defined only for odd integers
if ((b.data[] & 0x1) == )
throw (new ArgumentException("Jacobi defined only for odd integers.")); if (a >= b) a %= b;
if (a.dataLength == && a.data[] == ) return ; // a == 0
if (a.dataLength == && a.data[] == ) return ; // a == 1 if (a < )
{
if ((((b - ).data[]) & 0x2) == ) //if( (((b-1) >> 1).data[0] & 0x1) == 0)
return Jacobi(-a, b);
else
return -Jacobi(-a, b);
} int e = ;
for (int index = ; index < a.dataLength; index++)
{
uint mask = 0x01; for (int i = ; i < ; i++)
{
if ((a.data[index] & mask) != )
{
index = a.dataLength; // to break the outer loop
break;
}
mask <<= ;
e++;
}
} BigInteger a1 = a >> e; int s = ;
if ((e & 0x1) != && ((b.data[] & 0x7) == || (b.data[] & 0x7) == ))
s = -; if ((b.data[] & 0x3) == && (a1.data[] & 0x3) == )
s = -s; if (a1.dataLength == && a1.data[] == )
return s;
else
return (s * Jacobi(b % a1, a1));
} //***********************************************************************
// Generates a positive BigInteger that is probably prime.
//*********************************************************************** public static BigInteger genPseudoPrime(int bits, int confidence, Random rand)
{
BigInteger result = new BigInteger();
bool done = false; while (!done)
{
result.genRandomBits(bits, rand);
result.data[] |= 0x01; // make it odd // prime test
done = result.isProbablePrime(confidence);
}
return result;
} //***********************************************************************
// Generates a random number with the specified number of bits such
// that gcd(number, this) = 1
//*********************************************************************** public BigInteger genCoPrime(int bits, Random rand)
{
bool done = false;
BigInteger result = new BigInteger(); while (!done)
{
result.genRandomBits(bits, rand);
//Console.WriteLine(result.ToString(16)); // gcd test
BigInteger g = result.gcd(this);
if (g.dataLength == && g.data[] == )
done = true;
} return result;
} //***********************************************************************
// Returns the modulo inverse of this. Throws ArithmeticException if
// the inverse does not exist. (i.e. gcd(this, modulus) != 1)
//*********************************************************************** public BigInteger modInverse(BigInteger modulus)
{
BigInteger[] p = { , };
BigInteger[] q = new BigInteger[]; // quotients
BigInteger[] r = { , }; // remainders int step = ; BigInteger a = modulus;
BigInteger b = this; while (b.dataLength > || (b.dataLength == && b.data[] != ))
{
BigInteger quotient = new BigInteger();
BigInteger remainder = new BigInteger(); if (step > )
{
BigInteger pval = (p[] - (p[] * q[])) % modulus;
p[] = p[];
p[] = pval;
} if (b.dataLength == )
singleByteDivide(a, b, quotient, remainder);
else
multiByteDivide(a, b, quotient, remainder); /*
Console.WriteLine(quotient.dataLength);
Console.WriteLine("{0} = {1}({2}) + {3} p = {4}", a.ToString(10),
b.ToString(10), quotient.ToString(10), remainder.ToString(10),
p[1].ToString(10));
*/ q[] = q[];
r[] = r[];
q[] = quotient; r[] = remainder; a = b;
b = remainder; step++;
} if (r[].dataLength > || (r[].dataLength == && r[].data[] != ))
throw (new ArithmeticException("No inverse!")); BigInteger result = ((p[] - (p[] * q[])) % modulus); if ((result.data[maxLength - ] & 0x80000000) != )
result += modulus; // get the least positive modulus return result;
} //***********************************************************************
// Returns the value of the BigInteger as a byte array. The lowest
// index contains the MSB.
//*********************************************************************** public byte[] getBytes()
{
int numBits = bitCount(); int numBytes = numBits >> ;
if ((numBits & 0x7) != )
numBytes++; byte[] result = new byte[numBytes]; //Console.WriteLine(result.Length); int pos = ;
uint tempVal, val = data[dataLength - ]; if ((tempVal = (val >> & 0xFF)) != )
result[pos++] = (byte)tempVal;
if ((tempVal = (val >> & 0xFF)) != )
result[pos++] = (byte)tempVal;
if ((tempVal = (val >> & 0xFF)) != )
result[pos++] = (byte)tempVal;
if ((tempVal = (val & 0xFF)) != )
result[pos++] = (byte)tempVal; for (int i = dataLength - ; i >= ; i--, pos += )
{
val = data[i];
result[pos + ] = (byte)(val & 0xFF);
val >>= ;
result[pos + ] = (byte)(val & 0xFF);
val >>= ;
result[pos + ] = (byte)(val & 0xFF);
val >>= ;
result[pos] = (byte)(val & 0xFF);
} return result;
} //***********************************************************************
// Sets the value of the specified bit to 1
// The Least Significant Bit position is 0.
//*********************************************************************** public void setBit(uint bitNum)
{
uint bytePos = bitNum >> ; // divide by 32
byte bitPos = (byte)(bitNum & 0x1F); // get the lowest 5 bits uint mask = (uint) << bitPos;
this.data[bytePos] |= mask; if (bytePos >= this.dataLength)
this.dataLength = (int)bytePos + ;
} //***********************************************************************
// Sets the value of the specified bit to 0
// The Least Significant Bit position is 0.
//*********************************************************************** public void unsetBit(uint bitNum)
{
uint bytePos = bitNum >> ; if (bytePos < this.dataLength)
{
byte bitPos = (byte)(bitNum & 0x1F); uint mask = (uint) << bitPos;
uint mask2 = 0xFFFFFFFF ^ mask; this.data[bytePos] &= mask2; if (this.dataLength > && this.data[this.dataLength - ] == )
this.dataLength--;
}
} //***********************************************************************
// Returns a value that is equivalent to the integer square root
// of the BigInteger.
//
// The integer square root of "this" is defined as the largest integer n
// such that (n * n) <= this
//
//*********************************************************************** public BigInteger sqrt()
{
uint numBits = (uint)this.bitCount(); if ((numBits & 0x1) != ) // odd number of bits
numBits = (numBits >> ) + ;
else
numBits = (numBits >> ); uint bytePos = numBits >> ;
byte bitPos = (byte)(numBits & 0x1F); uint mask; BigInteger result = new BigInteger();
if (bitPos == )
mask = 0x80000000;
else
{
mask = (uint) << bitPos;
bytePos++;
}
result.dataLength = (int)bytePos; for (int i = (int)bytePos - ; i >= ; i--)
{
while (mask != )
{
// guess
result.data[i] ^= mask; // undo the guess if its square is larger than this
if ((result * result) > this)
result.data[i] ^= mask; mask >>= ;
}
mask = 0x80000000;
}
return result;
} //***********************************************************************
// Returns the k_th number in the Lucas Sequence reduced modulo n.
//
// Uses index doubling to speed up the process. For example, to calculate V(k),
// we maintain two numbers in the sequence V(n) and V(n+1).
//
// To obtain V(2n), we use the identity
// V(2n) = (V(n) * V(n)) - (2 * Q^n)
// To obtain V(2n+1), we first write it as
// V(2n+1) = V((n+1) + n)
// and use the identity
// V(m+n) = V(m) * V(n) - Q * V(m-n)
// Hence,
// V((n+1) + n) = V(n+1) * V(n) - Q^n * V((n+1) - n)
// = V(n+1) * V(n) - Q^n * V(1)
// = V(n+1) * V(n) - Q^n * P
//
// We use k in its binary expansion and perform index doubling for each
// bit position. For each bit position that is set, we perform an
// index doubling followed by an index addition. This means that for V(n),
// we need to update it to V(2n+1). For V(n+1), we need to update it to
// V((2n+1)+1) = V(2*(n+1))
//
// This function returns
// [0] = U(k)
// [1] = V(k)
// [2] = Q^n
//
// Where U(0) = 0 % n, U(1) = 1 % n
// V(0) = 2 % n, V(1) = P % n
//*********************************************************************** public static BigInteger[] LucasSequence(BigInteger P, BigInteger Q,
BigInteger k, BigInteger n)
{
if (k.dataLength == && k.data[] == )
{
BigInteger[] result = new BigInteger[]; result[] = ; result[] = % n; result[] = % n;
return result;
} // calculate constant = b^(2k) / m
// for Barrett Reduction
BigInteger constant = new BigInteger(); int nLen = n.dataLength << ;
constant.data[nLen] = 0x00000001;
constant.dataLength = nLen + ; constant = constant / n; // calculate values of s and t
int s = ; for (int index = ; index < k.dataLength; index++)
{
uint mask = 0x01; for (int i = ; i < ; i++)
{
if ((k.data[index] & mask) != )
{
index = k.dataLength; // to break the outer loop
break;
}
mask <<= ;
s++;
}
} BigInteger t = k >> s; //Console.WriteLine("s = " + s + " t = " + t);
return LucasSequenceHelper(P, Q, t, n, constant, s);
} //***********************************************************************
// Performs the calculation of the kth term in the Lucas Sequence.
// For details of the algorithm, see reference [9].
//
// k must be odd. i.e LSB == 1
//*********************************************************************** private static BigInteger[] LucasSequenceHelper(BigInteger P, BigInteger Q,
BigInteger k, BigInteger n,
BigInteger constant, int s)
{
BigInteger[] result = new BigInteger[]; if ((k.data[] & 0x00000001) == )
throw (new ArgumentException("Argument k must be odd.")); int numbits = k.bitCount();
uint mask = (uint)0x1 << ((numbits & 0x1F) - ); // v = v0, v1 = v1, u1 = u1, Q_k = Q^0 BigInteger v = % n, Q_k = % n,
v1 = P % n, u1 = Q_k;
bool flag = true; for (int i = k.dataLength - ; i >= ; i--) // iterate on the binary expansion of k
{
//Console.WriteLine("round");
while (mask != )
{
if (i == && mask == 0x00000001) // last bit
break; if ((k.data[i] & mask) != ) // bit is set
{
// index doubling with addition u1 = (u1 * v1) % n; v = ((v * v1) - (P * Q_k)) % n;
v1 = n.BarrettReduction(v1 * v1, n, constant);
v1 = (v1 - ((Q_k * Q) << )) % n; if (flag)
flag = false;
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); Q_k = (Q_k * Q) % n;
}
else
{
// index doubling
u1 = ((u1 * v) - Q_k) % n; v1 = ((v * v1) - (P * Q_k)) % n;
v = n.BarrettReduction(v * v, n, constant);
v = (v - (Q_k << )) % n; if (flag)
{
Q_k = Q % n;
flag = false;
}
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
} mask >>= ;
}
mask = 0x80000000;
} // at this point u1 = u(n+1) and v = v(n)
// since the last bit always 1, we need to transform u1 to u(2n+1) and v to v(2n+1) u1 = ((u1 * v) - Q_k) % n;
v = ((v * v1) - (P * Q_k)) % n;
if (flag)
flag = false;
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant); Q_k = (Q_k * Q) % n; for (int i = ; i < s; i++)
{
// index doubling
u1 = (u1 * v) % n;
v = ((v * v) - (Q_k << )) % n; if (flag)
{
Q_k = Q % n;
flag = false;
}
else
Q_k = n.BarrettReduction(Q_k * Q_k, n, constant);
} result[] = u1;
result[] = v;
result[] = Q_k; return result;
} //***********************************************************************
// Tests the correct implementation of the /, %, * and + operators
//*********************************************************************** public static void MulDivTest(int rounds)
{
Random rand = new Random();
byte[] val = new byte[];
byte[] val2 = new byte[]; for (int count = ; count < rounds; count++)
{
// generate 2 numbers of random length
int t1 = ;
while (t1 == )
t1 = (int)(rand.NextDouble() * ); int t2 = ;
while (t2 == )
t2 = (int)(rand.NextDouble() * ); bool done = false;
while (!done)
{
for (int i = ; i < ; i++)
{
if (i < t1)
val[i] = (byte)(rand.NextDouble() * );
else
val[i] = ; if (val[i] != )
done = true;
}
} done = false;
while (!done)
{
for (int i = ; i < ; i++)
{
if (i < t2)
val2[i] = (byte)(rand.NextDouble() * );
else
val2[i] = ; if (val2[i] != )
done = true;
}
} while (val[] == )
val[] = (byte)(rand.NextDouble() * );
while (val2[] == )
val2[] = (byte)(rand.NextDouble() * ); Console.WriteLine(count);
BigInteger bn1 = new BigInteger(val, t1);
BigInteger bn2 = new BigInteger(val2, t2); // Determine the quotient and remainder by dividing
// the first number by the second. BigInteger bn3 = bn1 / bn2;
BigInteger bn4 = bn1 % bn2; // Recalculate the number
BigInteger bn5 = (bn3 * bn2) + bn4; // Make sure they're the same
if (bn5 != bn1)
{
Console.WriteLine("Error at " + count);
Console.WriteLine(bn1 + "\n");
Console.WriteLine(bn2 + "\n");
Console.WriteLine(bn3 + "\n");
Console.WriteLine(bn4 + "\n");
Console.WriteLine(bn5 + "\n");
return;
}
}
} //***********************************************************************
// Tests the correct implementation of the modulo exponential function
// using RSA encryption and decryption (using pre-computed encryption and
// decryption keys).
//*********************************************************************** public static void RSATest(int rounds)
{
Random rand = new Random();
byte[] val = new byte[]; // private and public key
BigInteger bi_e = new BigInteger("a932b948feed4fb2b692609bd22164fc9edb59fae7880cc1eaff7b3c9626b7e5b241c27a974833b2622ebe09beb451917663d47232488f23a117fc97720f1e7", );
BigInteger bi_d = new BigInteger("4adf2f7a89da93248509347d2ae506d683dd3a16357e859a980c4f77a4e2f7a01fae289f13a851df6e9db5adaa60bfd2b162bbbe31f7c8f828261a6839311929d2cef4f864dde65e556ce43c89bbbf9f1ac5511315847ce9cc8dc92470a747b8792d6a83b0092d2e5ebaf852c85cacf34278efa99160f2f8aa7ee7214de07b7", );
BigInteger bi_n = new BigInteger("e8e77781f36a7b3188d711c2190b560f205a52391b3479cdb99fa010745cbeba5f2adc08e1de6bf38398a0487c4a73610d94ec36f17f3f46ad75e17bc1adfec99839589f45f95ccc94cb2a5c500b477eb3323d8cfab0c8458c96f0147a45d27e45a4d11d54d77684f65d48f15fafcc1ba208e71e921b9bd9017c16a5231af7f", ); Console.WriteLine("e =\n" + bi_e.ToString());
Console.WriteLine("\nd =\n" + bi_d.ToString());
Console.WriteLine("\nn =\n" + bi_n.ToString() + "\n"); for (int count = ; count < rounds; count++)
{
// generate data of random length
int t1 = ;
while (t1 == )
t1 = (int)(rand.NextDouble() * ); bool done = false;
while (!done)
{
for (int i = ; i < ; i++)
{
if (i < t1)
val[i] = (byte)(rand.NextDouble() * );
else
val[i] = ; if (val[i] != )
done = true;
}
} while (val[] == )
val[] = (byte)(rand.NextDouble() * ); Console.Write("Round = " + count); // encrypt and decrypt data
BigInteger bi_data = new BigInteger(val, t1);
BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n); // compare
if (bi_decrypted != bi_data)
{
Console.WriteLine("\nError at round " + count);
Console.WriteLine(bi_data + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
} } //***********************************************************************
// Tests the correct implementation of the modulo exponential and
// inverse modulo functions using RSA encryption and decryption. The two
// pseudoprimes p and q are fixed, but the two RSA keys are generated
// for each round of testing.
//*********************************************************************** public static void RSATest2(int rounds)
{
Random rand = new Random();
byte[] val = new byte[]; byte[] pseudoPrime1 = {
(byte)0x85, (byte)0x84, (byte)0x64, (byte)0xFD, (byte)0x70, (byte)0x6A,
(byte)0x9F, (byte)0xF0, (byte)0x94, (byte)0x0C, (byte)0x3E, (byte)0x2C,
(byte)0x74, (byte)0x34, (byte)0x05, (byte)0xC9, (byte)0x55, (byte)0xB3,
(byte)0x85, (byte)0x32, (byte)0x98, (byte)0x71, (byte)0xF9, (byte)0x41,
(byte)0x21, (byte)0x5F, (byte)0x02, (byte)0x9E, (byte)0xEA, (byte)0x56,
(byte)0x8D, (byte)0x8C, (byte)0x44, (byte)0xCC, (byte)0xEE, (byte)0xEE,
(byte)0x3D, (byte)0x2C, (byte)0x9D, (byte)0x2C, (byte)0x12, (byte)0x41,
(byte)0x1E, (byte)0xF1, (byte)0xC5, (byte)0x32, (byte)0xC3, (byte)0xAA,
(byte)0x31, (byte)0x4A, (byte)0x52, (byte)0xD8, (byte)0xE8, (byte)0xAF,
(byte)0x42, (byte)0xF4, (byte)0x72, (byte)0xA1, (byte)0x2A, (byte)0x0D,
(byte)0x97, (byte)0xB1, (byte)0x31, (byte)0xB3,
}; byte[] pseudoPrime2 = {
(byte)0x99, (byte)0x98, (byte)0xCA, (byte)0xB8, (byte)0x5E, (byte)0xD7,
(byte)0xE5, (byte)0xDC, (byte)0x28, (byte)0x5C, (byte)0x6F, (byte)0x0E,
(byte)0x15, (byte)0x09, (byte)0x59, (byte)0x6E, (byte)0x84, (byte)0xF3,
(byte)0x81, (byte)0xCD, (byte)0xDE, (byte)0x42, (byte)0xDC, (byte)0x93,
(byte)0xC2, (byte)0x7A, (byte)0x62, (byte)0xAC, (byte)0x6C, (byte)0xAF,
(byte)0xDE, (byte)0x74, (byte)0xE3, (byte)0xCB, (byte)0x60, (byte)0x20,
(byte)0x38, (byte)0x9C, (byte)0x21, (byte)0xC3, (byte)0xDC, (byte)0xC8,
(byte)0xA2, (byte)0x4D, (byte)0xC6, (byte)0x2A, (byte)0x35, (byte)0x7F,
(byte)0xF3, (byte)0xA9, (byte)0xE8, (byte)0x1D, (byte)0x7B, (byte)0x2C,
(byte)0x78, (byte)0xFA, (byte)0xB8, (byte)0x02, (byte)0x55, (byte)0x80,
(byte)0x9B, (byte)0xC2, (byte)0xA5, (byte)0xCB,
}; BigInteger bi_p = new BigInteger(pseudoPrime1);
BigInteger bi_q = new BigInteger(pseudoPrime2);
BigInteger bi_pq = (bi_p - ) * (bi_q - );
BigInteger bi_n = bi_p * bi_q; for (int count = ; count < rounds; count++)
{
// generate private and public key
BigInteger bi_e = bi_pq.genCoPrime(, rand);
BigInteger bi_d = bi_e.modInverse(bi_pq); Console.WriteLine("\ne =\n" + bi_e.ToString());
Console.WriteLine("\nd =\n" + bi_d.ToString());
Console.WriteLine("\nn =\n" + bi_n.ToString() + "\n"); // generate data of random length
int t1 = ;
while (t1 == )
t1 = (int)(rand.NextDouble() * ); bool done = false;
while (!done)
{
for (int i = ; i < ; i++)
{
if (i < t1)
val[i] = (byte)(rand.NextDouble() * );
else
val[i] = ; if (val[i] != )
done = true;
}
} while (val[] == )
val[] = (byte)(rand.NextDouble() * ); Console.Write("Round = " + count); // encrypt and decrypt data
BigInteger bi_data = new BigInteger(val, t1);
BigInteger bi_encrypted = bi_data.modPow(bi_e, bi_n);
BigInteger bi_decrypted = bi_encrypted.modPow(bi_d, bi_n); // compare
if (bi_decrypted != bi_data)
{
Console.WriteLine("\nError at round " + count);
Console.WriteLine(bi_data + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
} } //***********************************************************************
// Tests the correct implementation of sqrt() method.
//*********************************************************************** public static void SqrtTest(int rounds)
{
Random rand = new Random();
for (int count = ; count < rounds; count++)
{
// generate data of random length
int t1 = ;
while (t1 == )
t1 = (int)(rand.NextDouble() * ); Console.Write("Round = " + count); BigInteger a = new BigInteger();
a.genRandomBits(t1, rand); BigInteger b = a.sqrt();
BigInteger c = (b + ) * (b + ); // check that b is the largest integer such that b*b <= a
if (c <= a)
{
Console.WriteLine("\nError at round " + count);
Console.WriteLine(a + "\n");
return;
}
Console.WriteLine(" <PASSED>.");
}
} #endregion
}
}
调用方法
static void test()
{
string str = "{\"sc\":\"his51\",\"no\":\"1\",\"na\":\"管理员\"}";
System.Diagnostics.Debug.Print("明文：\r\n" + str + "\r\n");
RSAHelper.RSAKey keyPair = RSAHelper.GetRASKey();
System.Diagnostics.Debug.Print("公钥：\r\n" + keyPair.PublicKey + "\r\n");
System.Diagnostics.Debug.Print("私钥：\r\n" + keyPair.PrivateKey + "\r\n"); string en = RSAHelper.EncryptString(str, keyPair.PrivateKey);
System.Diagnostics.Debug.Print("公钥加密后：\r\n" + en + "\r\n"); var de = RSAHelper.DecryptString(en, keyPair.PublicKey);
System.Diagnostics.Debug.Print("解密：\r\n" + de + "\r\n");
Console.ReadKey();
}
输出demo
明文：
{"sc":"his51","no":"","na":"管理员"} 公钥：
AwEAAcVDSgexdQkY2OOZ2cs8Q2O9oFg0Gw1DkUofZ8w3keihXanlmluLAvIUTfUpSq1bmDvlM3jnxbc9uHpCMpVk4hPnnLcZvIy8JcSg1B1jHHSeLIW1MBh5VuHIYvSkBm3+S26sU5MMqLUq46YW74jKWbLy4kXSBEmiE0zJLlE7g9ap 私钥：
gJCIFuvAF/JMZE2O4kbIps+jlqJJuzBiu0dF73VvmdaKtOfQtOIx3jykp+HjGTYfkFECRE5n8zOpY0sgyZMwUXveki9tcglOQiF6bPCkhBaK1S4j/UYTAxxMfgQzsMN32C6RP2RUwSMb3u4hAGPfMMwj5ySmijx8REyNa42t5wgBxUNKB7F1CRjY45nZyzxDY72gWDQbDUORSh9nzDeR6KFdqeWaW4sC8hRN9SlKrVuYO+UzeOfFtz24ekIylWTiE+ectxm8jLwlxKDUHWMcdJ4shbUwGHlW4chi9KQGbf5LbqxTkwyotSrjphbviMpZsvLiRdIESaITTMkuUTuD1qk= 公钥加密后：
61631DE036DE7F4E4083375FC708B7DB57DBE73B4BFED4F4C902EFF1A3F0D57C307937163D84EA2792EDE5D52280092A1555C33C314A6A862000C7448CBCFD6E8E8E1A6E0505A4020AD8AFF8434D68B97BD80558DD118D6C5AF674D1246BB3A6567FF8A1C678DCFBF6411D7869508758C3EF11FC1A09A14A750EB748CB056EA3 解密：
{"sc":"his51","no":"","na":"管理员"}
公钥加密，私钥解密。
【加解密专辑】对接触到的PGP、RSA、AES加解密算法整理的更多相关文章
- RSA,AES加解密算法的实现
目录 Python实现RSA公钥加密算法 RSA公钥加密算法原理 RSA算法的Python实现 AES加解密算法实现 AES加解密算法原理 AES加解密算法Python实现 参考文献 Python实现 ...
- 简述前后端项目RSA+AES加解密
一.登录机制 在项目中,我们可以大致得出一个登录的过程,主要分为 登录验证.登录保持.退出三个部分.登录验证是指客户端提供用户名和密码,向服务器提出登录请求,服务器判断客户端是否可以登录并向客户端确 ...
- 学习加密(四)spring boot 使用RSA+AES混合加密,前后端传递参数加解密
学习加密(四)spring boot 使用RSA+AES混合加密,前后端传递参数加解密 技术标签: RSA AES RSA AES 混合加密 整合 前言: 为了提高安全性采用了RS ...
- java使用RSA与AES加密解密
首先了解下,什么是堆成加密,什么是非对称加密? 对称加密:加密与解密的密钥是相同的,加解密速度很快,比如AES 非对称加密:加密与解密的秘钥是不同的,速度较慢,比如RSA 先看代码(先会用在研究) 相 ...
- AES加解密程序的实现
AES加解密程序的实现正常情况,用户不能访问sys.dbms_crypto,需要DBA授权:grant execute on dbms_crypto to crm;建立加解密的PKG_AES包:CRE ...
- DES，AeS加解密，MD5，SHA加密
1.DES一共就有4个参数参与运作:明文.密文.密钥.向量.其中这4者的关系可以理解为: 密文=明文+密钥+向量: 明文=密文-密钥-向量: 为什么要向量这个参数呢?因为如果有一篇文章,有几个词重复, ...
- c# Aes加解密和对象序列化
aes加解密 public class AesCryptto { private string key = "hjyf57468jhmuist"; private string i ...
- Java、C#双语版配套AES加解密示例
这年头找个正经能用的东西那是真难,网上一搜索一大堆,正经能用的没几个,得,最后还是得靠自己,正巧遇上需要AES加解密的地方了,而且还是Java和C#间的相互加解密操作,这里做个备忘 这里采用的加解 ...
- AES加解密算法Qt实现
[声明] (1) 本文源码 在一位未署名网友源码基础上,利用Qt编程,实现了AES加解密算法,并添加了文件加解密功能.在此表示感谢!该源码仅供学习交流,请勿用于商业目的. (2) 图片及描述 除图1外 ...
随机推荐
- BIO、NIO、AIO系列一：NIO
一.几个基本概念 1.同步.异步.阻塞.非阻塞 同步:用户触发IO操作,你发起了请求就得等着对方给你返回结果,你不能走,针对调用方的,你发起了请求你等 异步:触发触发了IO操作,即发起了请求以后可以做 ...
- e795. 获得和设置JSlider的值
// To create a slider, see e794 创建JSlider组件 // Get the current value int value = slider.getValue(); ...
- memcached -- 运行memcached
Memcached 运行 Memcached命令的运行: $ /usr/local/memcached/bin/memcached -h 注意:如果使用自动安装, memcached 命令位于 /us ...
- Java与编码问题串讲之二–如何理解java采用Unicode编码
Java开发者必须牢记:在Java中字符仅以一种形式存在,那就是Unicode(不选择任何特定的编码,直接使用他们在字符集中的编号,这是统一的唯一方法).由于java采用unicode编码,char ...
- 核心动画——Core Animation
一. CALayer (一). CALayer简单介绍 在iOS中,你能看得见摸得着的东西基本上都是UIView,比方一个button.一个文本标签.一个文本输入框.一个图标等等.这些都是UIView ...
- HTML5 FileReader
利用HTML5中的FileReader类,动态切换af中Panel的背景,动态设置img元素的图片 1 if(FileReader){ 2 $('.panel').on("tap" ...
- 【转】Gulp入门基础教程
Gulp入门基础教程 原文在此 前言最近流行前端构建工具,苦于之前使用Grunt,代码很难阅读,现在出了Gulp, 真是摆脱了痛苦.发现了一篇很好的Gulp英文教程,整理翻译给大家看看. 为什么使用G ...
- 安卓开发笔记——ListView加载性能优化ViewHolder
在前不久做安卓项目的时候,其中有个功能是爬取某网站上的新闻信息,用ListView展示,虽然做了分页,但还是觉得达不到理想流畅效果. 上网查阅了些资料,发现一些挺不错的总结,这里记录下,便于复习. 当 ...
- Objective-C语法之字符串NSString去掉前后空格或回车符（可以是NSCharacterSet类型的其它字符）
main.m #import <Foundation/Foundation.h> #import "NSString+Trim.h" int main(int argc ...
- jenkins 如何处理windows batch command
这两天一直被一个问题困扰. 在jenkins的windows batch command 测试好的,拿到bat文件中,再从Execute Windows Batch command 中调用这个bat, ...