Silverlight中非对称加密及数字签名RSA算法的实现

RSA算法是第一个既能用于数据加密也能用于数字签名的算法。它易于理解和操作，也很流行。它的安全性是基于大整数素因子分解的困难性，而大整数因子分解问题是数学上的著名难题，至今没有有效的方法予以解决，因此可以确保RSA算法的安全性。

    到目前Silverlight4 Beta发布为止，Silverlight中仍然没有提供非对称加密及数字签名相关的算法。而.NET Framework中提供的RSA等算法，都是通过操作系统提供的相关API实现的，没法移植到Silverlight中使用。因此很难实现一个健壮点的Silverlight纯客户端的注册验证算法。这几天抽空写了个Silverlight下可用的RSA算法，使用非对称加密和数字签名使Silverlight纯客户端的注册验证算法健壮了不少。关于这个Silverlight下可用的RSA算法的具体实现，记录在下面，欢迎大家拍砖。在进行Silverlight开发时，还可以借助一些开发工具。ComponentOne Studio for Silverlight 拥有50多个基于Microsoft Silverlight的控件，能够满足开发最流行Web界面的需要。

    RSA算法实现主要分为三部分：包括公钥和私钥的产生，非对称加密和解密，数字签名和验证，下面将逐个介绍RSA算法的工作原理及我的实现方法。

 

 

    1，公钥和私钥的产生

    随意选择两个大素数p、q，p不等于q，计算n = p * q。
    随机选择一个整数e，满足e和( p – 1 ) * ( q – 1 )互质。(注：e很容易选择，如3, 17, 65537等都可以。.NET Framework中e默认选择的就是65537)
利用Euclid算法计算解密密钥d,满足
      e * d ≡ 1 ( mod ( p - 1 ) * ( q - 1 ) )
    其中n和d也要互质。

    其中e和n就是公钥，d和n就是私钥。P、q销毁。

    在.NET Framework的RSA算法中，e对应RSAParameters.Exponent；d对应RSAParameters.D；n对应RSAParameters.ModulusExponent。.NET Framework中的RSA算法默认使用1024位长的密钥。公钥和私钥是利用.NET Framework的RSACryptoServiceProvider生成公钥xml文件和私钥xml文件来实现的。生成公钥和私钥xml文件的程序本身不是Silverlight程序。

 

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RSACryptoServiceProvider rsa = new RSACryptoServiceProvider();
 
    //生成公钥XML字符串
    string publicKeyXmlString = rsa.ToXmlString(false);
 
    //生成私钥XML字符串
    string privateKeyXmlString = rsa.ToXmlString(true);

 

 

公钥和私钥将从生成的公钥xml文件和私钥xml文件中导入。

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public class RSAPublicKey
    {
        public byte[] Modulus;
        public byte[] Exponent;
 
        public static RSAPublicKey FromXmlString(string xmlString)
        {
            if (string.IsNullOrEmpty(xmlString))
            {
                return null;
            }
 
            try
            {
                using (XmlReader reader = XmlReader.Create(new StringReader(xmlString)))
                {
                    if (!reader.ReadToFollowing("RSAKeyValue"))
                    {
                        return null;
                    }
 
                    if (reader.LocalName != "Modulus" && !reader.ReadToFollowing("Modulus"))
                    {
                        return null;
                    }
                    string modulus = reader.ReadElementContentAsString();
 
                    if (reader.LocalName != "Exponent" && !reader.ReadToFollowing("Exponent"))
                    {
                        return null;
                    }
                    string exponent = reader.ReadElementContentAsString();
 
                    RSAPublicKey publicKey = new RSAPublicKey();
                    publicKey.Modulus = Convert.FromBase64String(modulus);
                    publicKey.Exponent = Convert.FromBase64String(exponent);
 
                    return publicKey;
                }
            }
            catch
            {
                return null;
            }
        }       
    }

 

 

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public class RSAPrivateKey
    {
        public byte[] Modulus;
        public byte[] D;
 
        public static RSAPrivateKey FromXmlString(string xmlString)
        {
            if (string.IsNullOrEmpty(xmlString))
            {
                return null;
            }
 
            try
            {
                using (XmlReader reader = XmlReader.Create(new StringReader(xmlString)))
                {
                    if (!reader.ReadToFollowing("RSAKeyValue"))
                    {
                        return null;
                    }
 
                    if (reader.LocalName != "Modulus" && !reader.ReadToFollowing("Modulus"))
                    {
                        return null;
                    }
                    string modulus = reader.ReadElementContentAsString();
 
                    if (reader.LocalName != "D" && !reader.ReadToFollowing("D"))
                    {
                        return null;
                    }
                    string d = reader.ReadElementContentAsString();
 
                    RSAPrivateKey privateKey = new RSAPrivateKey();
                    privateKey.Modulus = Convert.FromBase64String(modulus);
                    privateKey.D = Convert.FromBase64String(d);
 
                    return privateKey;
                }
            }
            catch
            {
                return null;
            }
        }       
    }

 

 

2，非对称加密和解密
    私钥加密m（二进制表示）时，首先把m分成长s的数据块 m1, m2 ... mi，其中 2^s <= n, s 尽可能的大。执行如下计算：
        ci = mi ^ d (mod n)
    公钥解密c（二进制表示）时，也需要将c分成长s的数据块c1, c2 ... ci，执行如下计算：
        mi = ci ^ e (mod n)

    在某些情况下，也会使用公钥加密->私钥解密。原理和私钥加密->公钥解密一样。下面是私钥计算和公钥计算的算法。其中利用到了Chew Keong TAN的BigInteger类。.NET Framework 4中提供的BigInteger.ModPow方法好像有问题。 

 

 

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private static byte[] Compute(byte[] data, RSAPublicKey publicKey, int blockSize)
        {
            //
            // 公钥加密/解密公式为：ci = mi^e ( mod n )           
            //
            // 先将 m（二进制表示）分成数据块 m1, m2, ..., mi ，然后进行运算。
            //
            BigInteger e = new BigInteger(publicKey.Exponent);
            BigInteger n = new BigInteger(publicKey.Modulus);
 
            int blockOffset = 0;
            using (MemoryStream stream = new MemoryStream())
            {
                while (blockOffset < data.Length)
                {
                    int blockLen = Math.Min(blockSize, data.Length - blockOffset);
                    byte[] blockData = new byte[blockLen];
                    Buffer.BlockCopy(data, blockOffset, blockData, 0, blockLen);
 
                    BigInteger mi = new BigInteger(blockData);
                    BigInteger ci = mi.modPow(e, n);//ci = mi^e ( mod n )
 
                    byte[] block = ci.getBytes();
                    stream.Write(block, 0, block.Length);
                    blockOffset += blockLen;
                }
 
                return stream.ToArray();
            }
        }
 
        private static byte[] Compute(byte[] data, RSAPrivateKey privateKey, int blockSize)
        {
            //
            // 私钥加密/解密公式为：mi = ci^d ( mod n )
            //
            // 先将 c（二进制表示）分成数据块 c1, c2, ..., ci ，然后进行运算。           
            //
            BigInteger d = new BigInteger(privateKey.D);
            BigInteger n = new BigInteger(privateKey.Modulus);
 
            int blockOffset = 0;
 
            using (MemoryStream stream = new MemoryStream())
            {
                while (blockOffset < data.Length)
                {
                    int blockLen = Math.Min(blockSize, data.Length - blockOffset);
                    byte[] blockData = new byte[blockLen];
                    Buffer.BlockCopy(data, blockOffset, blockData, 0, blockLen);
 
                    BigInteger ci = new BigInteger(blockData);
                    BigInteger mi = ci.modPow(d, n);//mi = ci^d ( mod n )
 
                    byte[] block = mi.getBytes();
                    stream.Write(block, 0, block.Length);
                    blockOffset += blockLen;
                }
 
                return stream.ToArray();
            }
        }

 

 

下面是私钥加密->公钥解密的实现。

 

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public static byte[] Encrypt(byte[] data, RSAPublicKey publicKey)
        {
            if (data == null)
            {
                throw new ArgumentNullException("data");
            }
 
            if (publicKey == null)
            {
                throw new ArgumentNullException("publicKey");
            }
 
            int blockSize = publicKey.Modulus.Length - 1;
            return Compute(data, publicKey, blockSize);
        }
 
        public static byte[] Decrypt(byte[] data, RSAPrivateKey privateKey)
        {
            if (data == null)
            {
                throw new ArgumentNullException("data");
            }
 
            if (privateKey == null)
            {
                throw new ArgumentNullException("privateKey");
            }
 
            int blockSize = privateKey.Modulus.Length;
            return Compute(data, privateKey, blockSize);
        }

 

 

下面是公钥加密->私钥解密的实现。 

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public static byte[] Encrypt(byte[] data, RSAPrivateKey privateKey)
        {
            if (data == null)
            {
                throw new ArgumentNullException("data");
            }
 
            if (privateKey == null)
            {
                throw new ArgumentNullException("privateKey");
            }
 
            int blockSize = privateKey.Modulus.Length - 1;
            return Compute(data, privateKey, blockSize);
        }
 
        public static byte[] Decrypt(byte[] data, RSAPublicKey publicKey)
        {
            if (data == null)
            {
                throw new ArgumentNullException("data");
            }
 
            if (publicKey == null)
            {
                throw new ArgumentNullException("publicKey");
            }
 
            int blockSize = publicKey.Modulus.Length;
            return Compute(data, publicKey, blockSize);
        }
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3，数字签名和验证
    私钥签名数据m时，先对m进行hash计算，得到计算结果h。然后将h使用私钥加密，得到加密后的密文s即为签名。
    公钥验证签名s时，先将m进行hash计算，得到计算结果h。然后使用公钥解密s得到结果h’。如果h==h’即验证成功，否则验证失败。

    在某些情况下，也会使用公钥签名->私钥验证。原理和私钥签名->公钥验证一样。

    下面是私钥签名->公钥验证的实现。 

 

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public static byte[] Sign(byte[] data, RSAPublicKey publicKey, HashAlgorithm hash)
       {
           if (data == null)
           {
               throw new ArgumentNullException("data");
           }
 
           if (publicKey == null)
           {
               throw new ArgumentNullException("publicKey");
           }
 
           if (hash == null)
           {
               throw new ArgumentNullException("hash");
           }
 
           byte[] hashData = hash.ComputeHash(data);
           byte[] signature = Encrypt(hashData, publicKey);
           return signature;
       }
 
       public static bool Verify(byte[] data, RSAPrivateKey privateKey, HashAlgorithm hash, byte[] signature)
       {
           if (data == null)
           {
               throw new ArgumentNullException("data");
           }
 
           if (privateKey == null)
           {
               throw new ArgumentNullException("privateKey");
           }
 
           if (hash == null)
           {
               throw new ArgumentNullException("hash");
           }
 
           if (signature == null)
           {
               throw new ArgumentNullException("signature");
           }
 
           byte[] hashData = hash.ComputeHash(data);
           byte[] signatureHashData = Decrypt(signature, privateKey);
 
           if (signatureHashData != null && signatureHashData.Length == hashData.Length)
           {
               for (int i = 0; i < signatureHashData.Length; i++)
               {
                   if (signatureHashData[i] != hashData[i])
                   {
                       return false;
                   }
               }
               return true;
           }
 
           return false;
       }

 

 

下面是公钥签名->私钥验证的实现。

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public static byte[] Sign(byte[] data, RSAPrivateKey privateKey, HashAlgorithm hash)
        {
            if (data == null)
            {
                throw new ArgumentNullException("data");
            }
 
            if (privateKey == null)
            {
                throw new ArgumentNullException("privateKey");
            }
 
            if (hash == null)
            {
                throw new ArgumentNullException("hash");
            }
 
            byte[] hashData = hash.ComputeHash(data);
            byte[] signature = Encrypt(hashData, privateKey);
            return signature;
        }
 
        public static bool Verify(byte[] data, RSAPublicKey publicKey, HashAlgorithm hash, byte[] signature)
        {
            if (data == null)
            {
                throw new ArgumentNullException("data");
            }
 
            if (publicKey == null)
            {
                throw new ArgumentNullException("publicKey");
            }
 
            if (hash == null)
            {
                throw new ArgumentNullException("hash");
            }
 
            if (signature == null)
            {
                throw new ArgumentNullException("signature");
            }
 
            byte[] hashData = hash.ComputeHash(data);
 
            byte[] signatureHashData = Decrypt(signature, publicKey);
 
            if (signatureHashData != null && signatureHashData.Length == hashData.Length)
            {
                for (int i = 0; i < signatureHashData.Length; i++)
                {
                    if (signatureHashData[i] != hashData[i])
                    {
                        return false;
                    }
                }
                return true;
            }
 
            return false;
        }<br><br><br>
posted @   葡萄城技术团队  阅读(1546)  评论(4)  编辑  收藏  举报
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