RSA算法基于一个十分简单的数论事实：将两个大素数相乘十分容易，但那时想要对其乘积进行因式分解却极其困难，因此可以将乘积公开作为加密密钥。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。
原理图：
C# 代码实现：
using System;
using System.Collections.Generic;
using System.Text;
using System.Security.Cryptography;
using Microsoft.Win32;
using System.IO;
namespace SRA
{
class Program
{
static void Main(string[] args)
{
string publicKeyFile = "publicKey.txt";
string privateKeyFile = "privateKey.txt";
string publicKey = string.Empty;
string privateKey = string.Empty;
Console.WriteLine("①创建公私钥对：");
RSA.GenneralRSAKey(privateKeyFile, publicKeyFile);
publicKey = RSA.ReadPublicKey(publicKeyFile);
privateKey = RSA.ReadPrivateKey(privateKeyFile);
Console.WriteLine("公钥：" + publicKey);
Console.WriteLine("私钥：" + privateKey);
string orgStr = "HelloWord";
Console.WriteLine("②使用公钥加密字符串：");
string secStr = RSA.RSAEncrypt(publicKey, orgStr);
Console.WriteLine(secStr);
Console.WriteLine("③使用私钥解密字符串：");
Console.WriteLine(SRA.RSA.RSADecrypt(privateKey, secStr));
Console.Read();
}
}
public class RSA
{
#region ①生成公私钥对
/// <summary>
/// ①生成公私钥对
/// </summary>
/// <param name="PrivateKeyPath">私钥文件路径</param>
/// <param name="PublicKeyPath">公钥文件路径</param>
public static void GenneralRSAKey(string PrivateKeyPath, string PublicKeyPath)
{
try
{
RSACryptoServiceProvider provider = new RSACryptoServiceProvider();
CreatePrivateKeyXML(PrivateKeyPath, provider.ToXmlString(true));
CreatePublicKeyXML(PublicKeyPath, provider.ToXmlString(false));
}
catch (Exception exception)
{
throw exception;
}
}
#region 创建密钥文件
/// <summary>
/// 创建公钥文件
/// </summary>
/// <param name="path"></param>
/// <param name="publickey"></param>
public static void CreatePublicKeyXML(string path, string publickey)
{
try
{
if (File.Exists(path))
{
File.Delete(path);
}
FileStream publickeyxml = new FileStream(path, FileMode.Create);
StreamWriter sw = new StreamWriter(publickeyxml);
sw.WriteLine(publickey);
sw.Close();
publickeyxml.Close();
}
catch
{
throw;
}
}
/// <summary>
/// 创建私钥文件
/// </summary>
/// <param name="path"></param>
/// <param name="privatekey"></param>
public static void CreatePrivateKeyXML(string path, string privatekey)
{
try
{
if (File.Exists(path))
{
File.Delete(path);
}
FileStream privatekeyxml = new FileStream(path, FileMode.Create);
StreamWriter sw = new StreamWriter(privatekeyxml);
sw.WriteLine(privatekey);
sw.Close();
privatekeyxml.Close();
}
catch
{
throw;
}
}
#endregion
#endregion
#region ②读取密钥
/// <summary>
/// 读取公钥
/// </summary>
/// <param name="path"></param>
/// <returns></returns>
public static string ReadPublicKey(string path)
{
StreamReader reader = new StreamReader(path);
string publickey = reader.ReadToEnd();
reader.Close();
return publickey;
}
/// <summary>
/// 读取私钥
/// </summary>
/// <param name="path"></param>
/// <returns></returns>
public static string ReadPrivateKey(string path)
{
StreamReader reader = new StreamReader(path);
string privatekey = reader.ReadToEnd();
reader.Close();
return privatekey;
}
#endregion
#region ③加密解密
/// <summary>
/// RSA加密
/// </summary>
/// <param name="xmlPublicKey">公钥</param>
/// <param name="m_strEncryptString">MD5加密后的数据</param>
/// <returns>RSA公钥加密后的数据</returns>
public static string RSAEncrypt(string xmlPublicKey, string m_strEncryptString)
{
string str2;
try
{
RSACryptoServiceProvider provider = new RSACryptoServiceProvider();
provider.FromXmlString(xmlPublicKey);
byte[] bytes = new UnicodeEncoding().GetBytes(m_strEncryptString);
str2 = Convert.ToBase64String(provider.Encrypt(bytes, false));
}
catch (Exception exception)
{
throw exception;
}
return str2;
}
/// <summary>
/// RSA解密
/// </summary>
/// <param name="xmlPrivateKey">私钥</param>
/// <param name="m_strDecryptString">待解密的数据</param>
/// <returns>解密后的结果</returns>
public static string RSADecrypt(string xmlPrivateKey, string m_strDecryptString)
{
string str2;
try
{
RSACryptoServiceProvider provider = new RSACryptoServiceProvider();
provider.FromXmlString(xmlPrivateKey);
byte[] rgb = Convert.FromBase64String(m_strDecryptString);
byte[] buffer2 = provider.Decrypt(rgb, false);
str2 = new UnicodeEncoding().GetString(buffer2);
}
catch (Exception exception)
{
throw exception;
}
return str2;
}
#endregion
}
}
算法介绍：
算法的名字以发明者的名字命名：Ron Rivest, AdiShamir 和Leonard Adleman。早在1973年，英国国家通信总局的数学家Clifford Cocks就发现了类似的算法。但是他的发现被列为绝密，直到1998年才公诸于世。
RSA算法是一种非对称密码算法，所谓非对称，就是指该算法需要一对密钥，使用其中一个加密，则需要用另一个才能解密。
RSA的算法涉及三个参数，n、e1、e2。
其中，n是两个大质数p、q的积，n的二进制表示时所占用的位数，就是所谓的密钥长度。
e1和e2是一对相关的值，e1可以任意取，但要求e1与(p-1)*(q-1)互质；再选择e2，要求(e2*e1)mod((p-1)*(q-1))=1。
(n及e1),(n及e2)就是密钥对。
RSA加解密的算法完全相同,设A为明文，B为密文，则：A=B^e1 mod n；B=A^e2 mod n；
e1和e2可以互换使用，即：A=B^e2 mod n；B=A^e1 mod n;