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【C/C++】非对称加密算法的原理
作者:哲天 / 发布于2016/6/27/ 807
/*
 *    本代码只实现一个简单的RSA加密算法。生成基本的公钥和密钥。 
 *
 * 让我写这个的想法是，在工作中很多人都会使用，用Java PHP C C++ ...
 *
 * 总之有各种各样的语言，但很多使用的人并不明白期中的原理，只有当我们明
 *
 * 白期中的数学原理后，就可以最小化的实现我们自己的加解密算法,所以本节
 *
 * 代码实只体现数学原理，并不考虑实际的应用。
 *
 * ********************************************************************/
 
#include <stdio.h>
#include <time.h>
#include <math.h>
#include <stdbool.h>
 
 
typedef struct
{
    int m_nPublic;  // Public key
    int m_nPrivate; // Private key
    int m_nCircle;  // Circle the number
}SecretKey;
 
 
/*
 *  JudgePrimeNumber is a tool function.
 *
 ***********************************************************************/
bool
JudgePrimeNumber( int nNumber )
{
    /*
     * Function : To determine whether unNumber is a prime number?
     * Percondition : NULL
     * Postcondition: Is to return true,no return false.
     * *************************************************************/
    int i = 2;
    while( i < nNumber )
    {
        if( nNumber % i == 0 )
            break;
        i++;
    }
    if( i == nNumber )
        return true;
    else
        return false;
}
 
int
GenerateRandomNumber( int nMin, int nMax )
{
    /*
     * Function : Generate a greater than nMin random number less than nMax.
     * Percondition : nMax > nMin; 
     * Postcondition: Return a random number.
     * *************************************************************/
    int nRandom, i = nMax - nMin;
 
    srand( time( 0 ) );
    while( i < nMax ){
        nRandom = rand() % nMax;
        if( nMin < nRandom )
            return nRandom;
        i++;
    }
    return 0;
}
 
int
GenerateRandomPrimeNumber( int nMin )
{
 
    /*
     * Function : Generate a prime number of random.
     * Percondition : 0 < nMin  < 900
     * Postcondition: Return a random prime number.
     * *************************************************************/
    int i, nRandom = 0;
    for( i = nMin ; i < 1000; i++ )
        if( JudgePrimeNumber( i ) )
            return i;
    return 0;
}
 
int
LeastCommonMultiple( int nA,int nB )
{
 
    /*
     * Function : Seek nA and nB common multiple
     * Percondition : NULL
     * Postcondition: Return nA and nB common multiple
     * *************************************************************/
    int i;
     
    for( i = 1; ; i++ )
        if( i % nA == 0 && i % nB ==0 )
            break;
    return i;
}
 
int
Gcd( int nx, int ny )
{
    /*
     * Function     : Seek nx and ny greatest common divisor.
     *
     * ************************************************************/
    if( nx < ny )
        return Gcd( ny, nx );
    if( 0 == ny )
        return nx;
    else
    {
        if( 0 == ( nx % 2 ) )
        {
            if( 0 == ( ny % 2 ) )
                return ( Gcd( nx >> 1,ny >> 1 ) << 1 );
            else
                return Gcd( nx >> 1, ny );
 
        }
        else
        {
             
            if( 0 == ( ny % 2 ) )
                return Gcd( nx ,ny >> 1 );
            else
                return Gcd( ny, nx - ny );
        }
    }
}
 
int
GreatestCommonDivisor( int nNumber )
{
    /*
     * Function : Generate the Greatest common divisor of 1 and 
     *        nNumber number;
     * Percondition : NULL
     * Postcondition: Return the Greatest common divisor of 1 and
     *        nNumber number;
     * *************************************************************/
    int nTemp = 0,nRet = 0;
    nTemp = GenerateRandomNumber( 50,100 );
     
    while( nTemp < 200 )
    {
        nRet = Gcd( nTemp, nNumber );
        if( nRet == 1 )
            return nTemp;
        nTemp++;
    }
    return 0;
}
 
int
IndexCalculate( int nNumber, int nIndex,int nMod )
{
    /*
     * Function : nNumber ^ nIndex % nMod
     * Percondition : nNumber < nMod
     * Postcondition: Return nNumber ^ nIndex % nMode is values.
     * *************************************************************/
    int nt = 1,nTemp = nNumber;
     
    while( nIndex != 0 )
    {
        if( 1 == nIndex % 2 )
            nt = nt * nTemp % nMod;
        nTemp = nTemp * nTemp % nMod;
        nIndex /= 2;
    }
    return nt;
}
 
/*
 *
 * Use GenerateSecretKey function generate secret key.
 *
 * Use Encryption function encryption express.
 *
 * Use DecryptFuction function decrypt ciphertext.
 *
 * *********************************************************************/
 
int
Encryption( int nExpress,SecretKey sk)
{
    /*
     * Function : Use sk encryption express.
     * Percondition : n < 
     * Postcondition: Return ciphertext.
     * *************************************************************/
    int nCiphertext = 0;
    nCiphertext = IndexCalculate( nExpress,sk.m_nPublic,sk.m_nCircle);
    return nCiphertext;
}
 
int
Decrypt( int nCiphertext,SecretKey sk)
{
    /*
     * Function : Use sk decrypt ciphertext
     * Percondition : 
     * Postcondition: Return express.
     * *************************************************************/
    int nExpress = 0;
    nExpress = IndexCalculate( nCiphertext, sk.m_nPrivate, sk.m_nCircle );
    return nExpress;
}
 
void
PrintKey( SecretKey sk )
{
    /*
     * Function : Print secret key
     *
     * *************************************************************/
    printf("公钥：%.2d %.2d\n密钥：%.2d %.2d\n ",sk.m_nPublic,\
            sk.m_nCircle, sk.m_nPrivate,sk.m_nCircle);
 
}
 
SecretKey
GenerateSecretKey( void )
{
    /*
     * Function : Generate public key and private key.
     * Percondition : NULL
     * Postcondition: Return secret key.
     * *************************************************************/
    int na = 0, nb = 0, nTemp, i = 0;
    SecretKey stKey = {0};
 
    na = GenerateRandomPrimeNumber( GenerateRandomNumber( 10,50 ) );    
    nb = GenerateRandomPrimeNumber( GenerateRandomNumber( 70,100 ) );
 
    stKey.m_nCircle = na * nb;
 
    nTemp = LeastCommonMultiple( na - 1, nb - 1 );
    stKey.m_nPublic = GreatestCommonDivisor( nTemp );
 
    i = GenerateRandomNumber( 10, 50 );
    while( i++ )
    {
        if( ( stKey.m_nPublic * i ) % nTemp == 1 )
        {
            stKey.m_nPrivate = i;
            break;
        }
    }
    return stKey;
}
 
 
 
/*
 *  main函数中只提供实现实例。
 *
 ***********************************************************************/
int
main(void)
{   
    int nText,nTemp = 0;
    SecretKey stKey = {0};
    stKey = GenerateSecretKey();
    while( stKey.m_nPrivate == stKey.m_nPublic )
        stKey = GenerateSecretKey();
    PrintKey( stKey );
    printf("请输入明文(%d < Number < -%d)：",stKey.m_nCircle - 2, \
            stKey.m_nCircle - 2 );
    scanf("%d",&nTemp);
    nText = Encryption( nTemp, stKey );
    printf(" 密文: %d \n",nText );
    nText = Decrypt( nText, stKey );
    printf(" 明文: %d \n",nText );
     
    return 0;
}
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