RSA 算法是第一个能同时用于加密和数字签名的算法,也易于理解和操作。 RSA是被研究得最广泛的公钥算法,从提出到现在已近二十年,经历了各种攻击的考验,逐渐为人们接受,普遍认为是目前最优秀的公钥方案之一。RSA的安全 性依赖于大数的因子分解,但并没有从理论上证明破译RSA的难度与大数分解难度等价。
    RSA的安全性依赖于大数分解。公钥和私钥都是两个大素数( 大于 100个十进制位)的函数。据猜测,从一个密钥和密文推断出明文的难度等同于分解两个大素数的积。 
    密钥对的产生。选择两个大素数,p 和q 。计算: 
                        n = p * q 
    然后随机选择加密密钥e(PS:最常用的e值有3,17和65537,微软就是使用的65537,采用3个中的任何一个都不存在安全问题),要求 e 和 ( p - 1 ) * ( q - 1 ) 互质。最后,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。数e和n是公钥,d是私钥。两个素数p和q不再需要,应该丢弃,不要让任何人知道。 
    加密信息 m(二进制表示)时,首先把m分成等长数据块 m1 ,m2,..., mi ,块长s,其中 2^s <= n, s 尽可能的大。对应的密文是: 
                       ci = mi^e ( mod n ) ( a ) 
    解密时作如下计算: 
                       mi = ci^d ( mod n ) ( b )

    .NET提供常用的加密算法类,支持RSA的类是RSACryptoServiceProvider(命名空 间:System.Security.Cryptography),但只支持公钥加密,私钥解密。RSACryptoServiceProvider类包 括:Modulus、Exponent、P、Q、DP、DQ、InverseQ、D等8个属性,其中Modulus和Exponent就是公 钥,Modulus和D就是私钥,RSACryptoServiceProvider类提供导出公钥的方法,也提供导出私钥的方法,但导出的私钥包含上面 8个属性,显然要用RSACryptoServiceProvider实现私钥加密公钥是不可行的。

    从RSA的原理来看,公钥加密私钥解密和私钥加密公钥解密应该是等价的,在某些情况下,比如共享软件加密,我们需要用私钥加密注册码或注册文件,发给用户,用户用公钥解密注册码或注册文件进行合法性验证。

    本 人利用网上找的一个C#版的大整数类BigInteger(本人认为这是偶发现的效率最高的一个C#版大整数类)来实现私钥加密公钥加密(事实上也完全支 持公租加密私钥解密),但没有使用类BigInteger的大素数生成函数,而是直接使用类RSACryptoServiceProvider来生成大素 数。其中加密函数和解密函数的实现如下:

                /*
                 功能:用指定的私钥(n,d)加密指定字符串source
                
*/

                
private string EncryptString(string source, BigInteger d, BigInteger n)
                
{
                        
int len = source.Length;
                        
int len1 = 0;
                        
int blockLen = 0;
                        
if ((len % 128) == 0)
                                len1
= len / 128;
                        
else
                                len1
= len / 128 + 1;
                        
string block = "";
                        
string temp = "";
                        
for (int i = 0; i < len1; i++)
                        
{
                                
if (len >= 128)
                                        blockLen
= 128;
                                
else
                                        blockLen
= len;
                                block
= source.Substring(i * 128, blockLen);
                                
byte[] oText = System.Text.Encoding.Default.GetBytes(block);
                                BigInteger biText
= new BigInteger(oText);
                                BigInteger biEnText
= biText.modPow(d, n);
                                
string temp1 = biEnText.ToHexString();
                                temp
+= temp1;
                                len
-= blockLen;
                        }

                        
return temp;
                }


                
/*
                 功能:用指定的公钥(n,e)解密指定字符串source
                
*/

                
private string DecryptString(string source, BigInteger e, BigInteger n)
                
{
                        
int len = source.Length;
                        
int len1 = 0;
                        
int blockLen = 0;
                        
if ((len % 256) == 0)
                                len1
= len / 256;
                        
else
                                len1
= len / 256 + 1;
                        
string block = "";
                        
string temp = "";
                        
for (int i = 0; i < len1; i++)
                        
{
                                
if (len >= 256)
                                        blockLen
= 256;
                                
else
                                        blockLen
= len;
                                block
= source.Substring(i * 256, blockLen);
                                BigInteger biText
= new BigInteger(block, 16);
                                BigInteger biEnText
= biText.modPow(e, n);
                                
string temp1 = System.Text.Encoding.Default.GetString(biEnText.getBytes());
                                temp
+= temp1;
                                len
-= blockLen;
                        }

                        
return temp;
                }

     加密过程和解密过程代码如下所示:

                /*
                 加密过程,其中d、n是RSACryptoServiceProvider生成的D、Modulus
                
*/

                
private string EncryptProcess(string source, string d, string n)
                
{
                        
byte[] N = Convert.FromBase64String(n);
                        
byte[] D = Convert.FromBase64String(d);
                        BigInteger biN
= new BigInteger(N);
                        BigInteger biD
= new BigInteger(D);
                        
return EncryptString(source, biD, biN);
                }


                
/*
                 解密过程,其中e、n是RSACryptoServiceProvider生成的Exponent、Modulus
                
*/

                
private string DecryptProcess(string source, string e, string n)
                
{
                        
byte[] N = Convert.FromBase64String(n);
                        
byte[] E = Convert.FromBase64String(e);
                        BigInteger biN
= new BigInteger(N);
                        BigInteger biE
= new BigInteger(E);
                        
return DecryptString(source, biE, biN);
                }

     以上方法经本人实际使用,效果良好,希望对朋友们有帮助。

 

     PS:文中所用大整数类下载地址:http://www.hugesoft.net/ContentPage.aspx?p1=010001&p2=201(PS:原文此链接失效应使用原地址http://www.codeproject.com/KB/cs/biginteger.aspx)


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