我正在尝试实现自己的RSA加密引擎。给定这些RSA算法值:
p = 61. // A prime number.
q = 53. // Also a prime number.
n = 3233. // p * q.
totient = 3120. // (p - 1) * (q - 1)
e = 991. // Co-prime to the totient (co-prime to 3120).
d = 1231. // d * e = 1219921, which is equal to the relation where 1 + k * totient = 1219921 when k = 391.
我正在尝试编写一种方法来加密字符串中的每个字节并返回加密的字符串:
public string Encrypt(string m, Encoding encoding)
{
byte[] bytes = encoding.GetBytes(m);
for (int i = 0; i < bytes.Length; i++)
{
bytes[i] = (byte)BigInteger.ModPow(bytes[i], e, n);
}
string encryptedString = encoding.GetString(bytes);
Console.WriteLine("Encrypted {0} as {1}.", m, encryptedString);
return encryptedString;
}
这里明显的问题是BigInteger.ModPow(bytes[i], e, n)
可能太大而无法容纳字节空间。它可能导致值超过8位。您如何解决此问题,同时仍然能够将加密的字节字符串解密回常规字符串?
更新:即使从byte []到byte []进行加密,您也会遇到以下情况:使用RSA算法加密该字节超出了字节的大小限制:
public byte[] Encrypt(string m, Encoding encoding)
{
byte[] bytes = encoding.GetBytes(m);
for (int i = 0; i < bytes.Length; i++)
{
bytes[i] = (byte)BigInteger.ModPow(bytes[i], e, n);
}
return bytes;
}
更新:我的问题是,加密将导致比初始输入字符串更多的字节数:
public byte[] Encrypt(string m, Encoding encoding)
{
byte[] bytes = encoding.GetBytes(m);
byte[] returnBytes = new byte[0];
for (int i = 0; i < bytes.Length; i++)
{
byte[] result = BigInteger.ModPow(bytes[i], (BigInteger)e, n).ToByteArray();
int preSize = returnBytes.Length;
Array.Resize(ref returnBytes, returnBytes.Length + result.Length);
result.CopyTo(returnBytes, preSize);
}
return returnBytes;
}
public string Decrypt(byte[] c, Encoding encoding)
{
byte[] returnBytes = new byte[0];
for (int i = 0; i < c.Length; i++)
{
byte[] result = BigInteger.ModPow(c[i], d, n).ToByteArray();
int preSize = returnBytes.Length;
Array.Resize(ref returnBytes, returnBytes.Length + result.Length);
result.CopyTo(returnBytes, preSize);
}
string decryptedString = encoding.GetString(returnBytes);
return decryptedString;
}
如果您运行如下代码:
byte[] encryptedBytes = engine.Encrypt("Hello, world.", Encoding.UTF8);
Console.WriteLine(engine.Decrypt(encryptedBytes, Encoding.UTF8));
输出将是这样的:
?♥D
?♥→☻►♦→☻►♦oD♦8? ?♠oj?♠→☻►♦;♂?♠♂♠?♠
显然,输出不是原始字符串,因为我不能一次尝试解密每个字节,因为有时两个或更多字节的密文代表一个整数的值,我需要将其解密回一个字节。原始字符串...所以我想知道处理这个问题的标准机制是什么。
注意:我更新了此答案。请向下滚动至该更新,以了解应如何实际实施该更新,因为此第一种方法不是进行RSA加密的正确方法。
我可以想到的一种方法是这样的(但可能不符合标准),而且请注意,这不能填充:
public byte[] Encrypt(string m, Encoding encoding)
{
byte[] bytes = encoding.GetBytes(m);
byte[] returnBytes = new byte[0];
for (int i = 0; i < bytes.Length; i++)
{
byte[] result = BigInteger.ModPow(bytes[i], (BigInteger)e, n).ToByteArray();
int preSize = returnBytes.Length;
Array.Resize(ref returnBytes, returnBytes.Length + result.Length + 1);
(new byte[] { (byte)(result.Length) }).CopyTo(returnBytes, preSize);
result.CopyTo(returnBytes, preSize + 1);
}
return returnBytes;
}
public string Decrypt(byte[] c, Encoding encoding)
{
byte[] returnBytes = new byte[0];
for (int i = 0; i < c.Length; i++)
{
int dataLength = (int)c[i];
byte[] result = new byte[dataLength];
for (int j = 0; j < dataLength; j++)
{
i++;
result[j] = c[i];
}
BigInteger integer = new BigInteger(result);
byte[] integerResult = BigInteger.ModPow(integer, d, n).ToByteArray();
int preSize = returnBytes.Length;
Array.Resize(ref returnBytes, returnBytes.Length + integerResult.Length);
integerResult.CopyTo(returnBytes, preSize);
}
string decryptedString = encoding.GetString(returnBytes);
return decryptedString;
}
这有可能成为跨平台的,因为您可以选择使用其他数据类型来表示e或n,并将其传递给这样的C#后端服务。这是一个测试:
string stringToEncrypt = "Mary had a little lamb.";
Console.WriteLine("Encrypting the string: {0}", stringToEncrypt);
byte[] encryptedBytes = engine.Encrypt(stringToEncrypt, Encoding.UTF8);
Console.WriteLine("Encrypted text: {0}", Encoding.UTF8.GetString(encryptedBytes));
Console.WriteLine("Decrypted text: {0}", engine.Decrypt(encryptedBytes, Encoding.UTF8));
输出:
Encrypting the string: Mary had a little lamb.
Encrypted text: ☻6☻1♦☻j☻☻&♀☻g♦☻t☻☻1♦☻? ☻g♦☻1♦☻g♦☻?♥☻?☻☻7☺☻7☺☻?♥☻?♂☻g♦☻?♥☻1♦☻$☺☻
c ☻?☻
Decrypted text: Mary had a little lamb.
更新:我前面说的一切在RSA的实现中都是完全错误的。错,错,错!这是进行RSA加密的正确方法:
举个例子:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Numerics;
using System.Security.Cryptography;
using System.Text;
using System.Threading.Tasks;
namespace BytePadder
{
class Program
{
const int p = 61;
const int q = 53;
const int n = 3233;
const int totient = 3120;
const int e = 991;
const int d = 1231;
static void Main(string[] args)
{
// ---------------------- RSA Example I ----------------------
// Shows how an integer gets encrypted and decrypted.
BigInteger integer = 1000;
BigInteger encryptedInteger = Encrypt(integer);
Console.WriteLine("Encrypted Integer: {0}", encryptedInteger);
BigInteger decryptedInteger = Decrypt(encryptedInteger);
Console.WriteLine("Decrypted Integer: {0}", decryptedInteger);
// --------------------- RSA Example II ----------------------
// Shows how a string gets encrypted and decrypted.
string unencryptedString = "A";
BigInteger integer2 = new BigInteger(Encoding.UTF8.GetBytes(unencryptedString));
Console.WriteLine("String as Integer: {0}", integer2);
BigInteger encryptedInteger2 = Encrypt(integer2);
Console.WriteLine("String as Encrypted Integer: {0}", encryptedInteger2);
BigInteger decryptedInteger2 = Decrypt(encryptedInteger2);
Console.WriteLine("String as Decrypted Integer: {0}", decryptedInteger2);
string decryptedIntegerAsString = Encoding.UTF8.GetString(decryptedInteger2.ToByteArray());
Console.WriteLine("Decrypted Integer as String: {0}", decryptedIntegerAsString);
Console.ReadLine();
}
static BigInteger Encrypt(BigInteger integer)
{
if (integer < n)
{
return BigInteger.ModPow(integer, e, n);
}
throw new Exception("The integer must be less than the value of n in order to be decypherable!");
}
static BigInteger Decrypt(BigInteger integer)
{
return BigInteger.ModPow(integer, d, n);
}
}
}
输出示例:
Encrypted Integer: 1989
Decrypted Integer: 1000
String as Integer: 65
String as Encrypted Integer: 1834
String as Decrypted Integer: 65
Decrypted Integer as String: A
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