密码学RSA算法通过C++实现

[sunner543]

这段程序如题，有谁能帮我解释下最后一段的RSA各行的意思。谢谢哈。


//头文件BigInt.h

#ifndef BIGINT_H
#define BIGINT_H


#define BI_MAXLEN 8

class CBigInt
{
public:
unsigned m_nLength;
unsigned long m_ulValue[BI_MAXLEN];
CBigInt();

void Mov(unsigned __int64 A);
void Mov(CBigInt& A);
CBigInt Sub(CBigInt& A);
CBigInt Mul(CBigInt& A);
CBigInt Mod(CBigInt& A);
CBigInt Sub(unsigned long A);
CBigInt Mul(unsigned long A);
CBigInt Div(unsigned long A);
unsigned long Mod(unsigned long A);
int Cmp(CBigInt& A);
CBigInt ModExp(CBigInt& A, CBigInt& B);
};

#endif

//原文件BigInt.cpp

#include "BigInt.h"

//构造大数对象并初始化为零
CBigInt::CBigInt()
{
m_nLength=1;
for(int i=0;i <BI_MAXLEN;i++)m_ulValue[i]=0;
}


//大数比较
int CBigInt::Cmp(CBigInt& A)
{
if(m_nLength>A.m_nLength)return 1;
if(m_nLength <A.m_nLength)return -1;
for(int i=m_nLength-1;i>=0;i--)
{
if(m_ulValue[i]>A.m_ulValue[i])return 1;
if(m_ulValue[i] <A.m_ulValue[i])return -1;
}
return 0;
}

//大数赋值
void CBigInt::Mov(CBigInt& A)
{
m_nLength=A.m_nLength;
for(int i=0;i <BI_MAXLEN;i++)
m_ulValue[i]=A.m_ulValue[i];
}
void CBigInt::Mov(unsigned __int64 A)
{
if(A>0xffffffff)
{
m_nLength=2;
m_ulValue[1]=(unsigned long)(A>>32);
m_ulValue[0]=(unsigned long)A;
}
else
{
m_nLength=1;
m_ulValue[0]=(unsigned long)A;
}
for(int i=m_nLength;i <BI_MAXLEN;i++)m_ulValue[i]=0;
}

//大数相减
CBigInt CBigInt::Sub(CBigInt& A)
{
CBigInt X;
X.Mov(*this);
if(X.Cmp(A) <=0){X.Mov(0);return X;}
unsigned carry=0;
unsigned __int64 num;
unsigned i;
for(i=0;i <m_nLength;i++)
{
if((m_ulValue[i]>A.m_ulValue[i]) ¦ ¦((m_ulValue[i]==A.m_ulValue[i])&&(carry==0)))
{
X.m_ulValue[i]=m_ulValue[i]-carry-A.m_ulValue[i];
carry=0;
}
else
{
num=0x100000000+m_ulValue[i];
X.m_ulValue[i]=(unsigned long)(num-carry-A.m_ulValue[i]);
carry=1;
}
}
while(X.m_ulValue[X.m_nLength-1]==0)X.m_nLength--;
return X;
}


CBigInt CBigInt::Sub(unsigned long A)
{
CBigInt X;
X.Mov(*this);
if(X.m_ulValue[0]>=A){X.m_ulValue[0]-=A;return X;}
if(X.m_nLength==1){X.Mov(0);return X;}
unsigned __int64 num=0x100000000+X.m_ulValue[0];
X.m_ulValue[0]=(unsigned long)(num-A);
int i=1;
while(X.m_ulValue[i]==0){X.m_ulValue[i]=0xffffffff;i++;}
X.m_ulValue[i]--;
if(X.m_ulValue[i]==0)X.m_nLength--;
return X;
}

//大数相乘
CBigInt CBigInt::Mul(CBigInt& A)
{
if(A.m_nLength==1)return Mul(A.m_ulValue[0]);
CBigInt X;
unsigned __int64 sum,mul=0,carry=0;
unsigned i,j;
X.m_nLength=m_nLength+A.m_nLength-1;
for(i=0;i <X.m_nLength;i++)
{
sum=carry;
carry=0;
for(j=0;j <A.m_nLength;j++)
{
if(((i-j)>=0)&&((i-j) <m_nLength))
{
mul=m_ulValue[i-j];
mul*=A.m_ulValue[j];
carry+=mul>>32;
mul=mul&0xffffffff;
sum+=mul;
}
}
carry+=sum>>32;
X.m_ulValue[i]=(unsigned long)sum;
}
if(carry){X.m_nLength++;X.m_ulValue[X.m_nLength-1]=(unsigned long)carry;}
return X;
}


CBigInt CBigInt::Mul(unsigned long A)
{
CBigInt X;
unsigned __int64 mul;
unsigned long carry=0;
X.Mov(*this);
for(unsigned i=0;i <m_nLength;i++)
{
mul=m_ulValue[i];
mul=mul*A+carry;
X.m_ulValue[i]=(unsigned long)mul;
carry=(unsigned long)(mul>>32);
}
if(carry){X.m_nLength++;X.m_ulValue[X.m_nLength-1]=carry;}
return X;
}

//大数相除
CBigInt CBigInt::Div(unsigned long A)
{
CBigInt X;
X.Mov(*this);
if(X.m_nLength==1){X.m_ulValue[0]=X.m_ulValue[0]/A;return X;}
unsigned __int64 div,mul;
unsigned long carry=0;
for(int i=X.m_nLength-1;i>=0;i--)
{
div=carry;
div=(div < <32)+X.m_ulValue[i];
X.m_ulValue[i]=(unsigned long)(div/A);
mul=(div/A)*A;
carry=(unsigned long)(div-mul);
}
if(X.m_ulValue[X.m_nLength-1]==0)X.m_nLength--;
return X;
}


//大数求模
CBigInt CBigInt::Mod(CBigInt& A)
{
if(A.m_nLength==1)
{
CBigInt X;
X.m_ulValue[0]=Mod(A.m_ulValue[0]);
return X;
}
CBigInt X,Y;
int len;
unsigned __int64 num,div;
unsigned long carry=0;
X.Mov(*this);
while(X.Cmp(A)>0)
{
if(X.m_ulValue[X.m_nLength-1]>A.m_ulValue[A.m_nLength-1])
{
len=X.m_nLength-A.m_nLength;
div=X.m_ulValue[X.m_nLength-1]/(A.m_ulValue[A.m_nLength-1]+1);
}
else if(X.m_nLength>A.m_nLength)
{
len=X.m_nLength-A.m_nLength-1;
num=X.m_ulValue[X.m_nLength-1];
num=(num < <32)+X.m_ulValue[X.m_nLength-2];
if(A.m_ulValue[A.m_nLength-1]==0xffffffff)div=(num>>32);
else div=num/(A.m_ulValue[A.m_nLength-1]+1);
}
else
{
X.Mov(X.Sub(A));
break;
}
Y.Mov(div);
Y.Mov(Y.Mul(A));
Y.m_nLength+=len;
for(int i=Y.m_nLength-1;i>=len;i--) Y.m_ulValue[i]=Y.m_ulValue[i-len];
for(i=0;i <len;i++) Y.m_ulValue[i]=0;
X.Mov(X.Sub(Y));
}
if(X.Cmp(A)==0)X.Mov(0);
return X;
}

unsigned long CBigInt::Mod(unsigned long A)
{
if(m_nLength==1)return(m_ulValue[0]%A);
unsigned __int64 div;
unsigned long carry=0;
for(int i=m_nLength-1;i>=0;i--)
{
div=carry*0x100000000+m_ulValue[i];
carry=(unsigned long)(div-((div/A)*A));
}
return carry;
}


//蒙哥马利算法求模幂
CBigInt CBigInt::ModExp(CBigInt& A, CBigInt& B)
{
CBigInt X,Y,Z;
X.Mov(1);
Y.Mov(*this);
Z.Mov(A);
while((Z.m_nLength!=1) ¦ ¦Z.m_ulValue[0])
{
if(Z.m_ulValue[0]&1)
{
Z.Mov(Z.Sub(1));
X.Mov(X.Mul(Y));
X.Mov(X.Mod(B));
}
else
{
Z.Mov(Z.Div(2));
Y.Mov(Y.Mul(Y));
Y.Mov(Y.Mod(B));
}
}
return X;
}

//原文件主程序RSA.cpp

#include "BigInt.h"
#include <stdio.h>

int main(int argc, char* argv[])
{
CBigInt m,e,n,d,c,m1;
int i;

m.m_nLength=4;
m.m_ulValue[3]=0x0;
m.m_ulValue[2]=0x0;
m.m_ulValue[1]=0x0;
m.m_ulValue[0]=0x45e;

printf("The initial plainttext m is:\n");
for(i=BI_MAXLEN-5;i>=0;i--)
printf("%x\n",m.m_ulValue[i]);


e.m_nLength=1;
e.m_ulValue[0]=0x34703;

n.m_nLength=4;
n.m_ulValue[3]=0x78CDED41;
n.m_ulValue[2]=0xF71A0BF9;
n.m_ulValue[1]=0xA1F36E0A;
n.m_ulValue[0]=0x60F3EE89;


c.Mov(m.ModExp(e,n));

printf("The ciphertext encrypted c is:\n");
for(i=BI_MAXLEN-5;i>=0;i--)
printf("%x\n",c.m_ulValue[i]);


d.m_nLength=4;
d.m_ulValue[3]=0x4C9327F3;
d.m_ulValue[2]=0x70B028FD;
d.m_ulValue[1]=0x08D56387;
d.m_ulValue[0]=0xFCC6161B;

m1.Mov(c.ModExp(d,n));

printf("The plainttext decrypted m1 is:\n");
for(i=BI_MAXLEN-5;i>=0;i--)
printf("%x\n",m1.m_ulValue[i]);



return 0;
}

[mjzg89]

额，这个我不太擅长哦

[oo]

[Quote=引用 1 楼 Supper_Jerry 的回复:]
直接向mathe提问。到数据结构算法版
分给我留下。
[/Quote]

[vvpisces]

自己google一下算法，然后对应代码看呀！

[sunner543]

直接向mathe提问。到数据结构算法版
分给我留下。
什么意思。虽然不懂。但是分还是给你了。可以的话解释一下。刚加的论坛。C++菜鸟

[sunner543]

算法懂得。但是代码看不懂。C++菜鸟

[Supper_Jerry]

直接向mathe提问。到数据结构算法版
分给我留下。