bigint.cpp

简单的RSA算法的加密解密程序

			for(i=Z.m_nLength-1;i>=len;i--)Z.m_ulValue[i]=Z.m_ulValue[i-len];
			for(i=0;i<len;i++)Z.m_ulValue[i]=0;
		}
		X.Mov(X.Add(Z));
        Y.Mov(Y.Sub(A.Mul(Z)));
    }
    return X;
}

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
调用形式：N.Mod(A)
返回值：N%A
****************************************************************************************/
CBigInt CBigInt::Mod(CBigInt& A)
{
    CBigInt X,Y;
	unsigned __int64 div,num;
    unsigned long carry=0;
	unsigned i,len;
    X.Mov(*this);
    while(X.Cmp(A)>=0)
    {
		div=X.m_ulValue[X.m_nLength-1];
		num=A.m_ulValue[A.m_nLength-1];
		len=X.m_nLength-A.m_nLength;
		if((div==num)&&(len==0)){X.Mov(X.Sub(A));break;}
		if((div<=num)&&len){len--;div=(div<<32)+X.m_ulValue[X.m_nLength-2];}
		div=div/(num+1);
		Y.Mov(div);
		Y.Mov(A.Mul(Y));
		if(len)
		{
			Y.m_nLength+=len;
			for(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));
    }
    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=m_ulValue[i];
		div+=carry*0x100000000;
        carry=(unsigned long)(div%A);
    }
    return carry;
}

/****************************************************************************************
从字符串按设定进制格式输入到大数
调用格式：N.Get(str,sys)
返回值：N被赋值为相应大数
sys即进制数
****************************************************************************************/
void CBigInt::Get(CString& str, unsigned int system)
{
    int len=str.GetLength(),k;
    Mov(0);
    for(int i=0;i<len;i++)
    {
       Mov(Mul(system));
       if((str[i]>='0')&&(str[i]<='9'))k=str[i]-48;
       else if((str[i]>='A')&&(str[i]<='Z'))k=str[i]-55;
       else if((str[i]>='a')&&(str[i]<='z'))k=str[i]-61;
       else k=62;
	   //if ((str[i]>=42)&&(str[i]<=122)) k=str[i]-42;
	   //else k=62;
       Mov(Add(k));
    }
}

/****************************************************************************************
从字符串按设定进制格式输入到大数
调用格式：N.GetLast(str,sys)
返回值：N被赋值为相应大数
sys即进制数
****************************************************************************************/
void CBigInt::GetLast(CString& str, unsigned int system)
{
    int len=str.GetLength(),k;
    Mov(0);
    for(int i=0;i<len;i++)
    {
       Mov(Mul(system));
       if((str[i]>='0')&&(str[i]<='9'))k=str[i];//-48;
       else if((str[i]>='A')&&(str[i]<='Z'))k=str[i];//-55;
       else if((str[i]>='a')&&(str[i]<='z'))k=str[i];//-87;
       else k=0;
	   
       Mov(Add(k));
    }
}

/****************************************************************************************
将大数按设定进制格式输出为字符串
调用格式：N.Put(str,sys)
返回值：无，参数str被赋值为N的sys进制字符串
sys即进制数
****************************************************************************************/
void CBigInt::Put(CString& str, unsigned int system)
{
    if((m_nLength==1)&&(m_ulValue[0]==0)){str="0";return;}
	str="";
    CString t="0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz ";
    int a;
    char ch;
    CBigInt X;
    X.Mov(*this);
    while(X.m_ulValue[X.m_nLength-1]>0)
    {
        a=X.Mod(system);
        ch=t[a];
        str.Insert(0,ch);
        X.Mov(X.Div(system));
    }
}

/****************************************************************************************
求不定方程ax-by=1的最小整数解
调用方式：N.Euc(A)
返回值：X,满足：NX mod A=1
****************************************************************************************/
CBigInt CBigInt::Euc(CBigInt& A)
{
	CBigInt M,E,X,Y,I,J;
    int x,y;
	M.Mov(A);
	E.Mov(*this);
	X.Mov(0);
	Y.Mov(1);
	x=y=1;
	while((E.m_nLength!=1)||(E.m_ulValue[0]!=0))
	{
		I.Mov(M.Div(E));
		J.Mov(M.Mod(E));
		M.Mov(E);
		E.Mov(J);
		J.Mov(Y);
		Y.Mov(Y.Mul(I));
		if(x==y)
		{
		    if(X.Cmp(Y)>=0)Y.Mov(X.Sub(Y));
			else{Y.Mov(Y.Sub(X));y=0;}
		}
		else{Y.Mov(X.Add(Y));x=1-x;y=1-y;}
		X.Mov(J);
	}
	if(x==0)X.Mov(A.Sub(X));
	return X;
}

/****************************************************************************************
求乘方的模
调用方式：N.RsaTrans(A,B)
返回值：X=N^A MOD B
****************************************************************************************/
CBigInt CBigInt::RsaTrans(CBigInt& A, CBigInt& B)
{
    CBigInt X,Y;
	int i,j,k;
	unsigned n;
	unsigned long num;
	k=A.m_nLength*32-32;
	num=A.m_ulValue[A.m_nLength-1];
	while(num){num=num>>1;k++;}
	X.Mov(*this);
	for(i=k-2;i>=0;i--)
	{
		Y.Mov(X.Mul(X.m_ulValue[X.m_nLength-1]));
		Y.Mov(Y.Mod(B));
        for(n=1;n<X.m_nLength;n++)
		{          
			for(j=Y.m_nLength;j>0;j--)Y.m_ulValue[j]=Y.m_ulValue[j-1];
			Y.m_ulValue[0]=0;
			Y.m_nLength++;
			Y.Mov(Y.Add(X.Mul(X.m_ulValue[X.m_nLength-n-1])));
			Y.Mov(Y.Mod(B));
		}
		X.Mov(Y);
		if((A.m_ulValue[i>>5]>>(i&31))&1)
		{
		    Y.Mov(Mul(X.m_ulValue[X.m_nLength-1]));
		    Y.Mov(Y.Mod(B));
            for(n=1;n<X.m_nLength;n++)
			{          
			    for(j=Y.m_nLength;j>0;j--)Y.m_ulValue[j]=Y.m_ulValue[j-1];
			    Y.m_ulValue[0]=0;
			    Y.m_nLength++;
			    Y.Mov(Y.Add(Mul(X.m_ulValue[X.m_nLength-n-1])));
			    Y.Mov(Y.Mod(B));
			}
		    X.Mov(Y);
		}
	}
    return X;
}

/****************************************************************************************
拉宾米勒算法测试素数    正确率达99.99%
调用方式：N.Rab()
返回值：若N为素数，返回1，否则返回0     
****************************************************************************************/
int CBigInt::Rab()
{
    unsigned i,j,pass;    
    CBigInt S,A,I,K;
    K.Mov(*this);
	K.m_ulValue[0]--;
    for(i=0;i<5;i++)
    {
        pass=0;
        A.Mov(rand()*rand());
		S.Mov(K);
        while((S.m_ulValue[0]&1)==0)
		{
            for(j=0;j<S.m_nLength;j++)
			{
			    S.m_ulValue[j]=S.m_ulValue[j]>>1;
			    if(S.m_ulValue[j+1]&1)S.m_ulValue[j]=S.m_ulValue[j]|0x80000000;
			}
		    if(S.m_ulValue[S.m_nLength-1]==0)S.m_nLength--;
			I.Mov(A.RsaTrans(S,*this));
			if(I.Cmp(K)==0){pass=1;break;}
		}
		if((I.m_nLength==1)&&(I.m_ulValue[0]==1))pass=1;
		if(pass==0)return 0;
	}
    return 1;
}

/****************************************************************************************
产生随机素数
调用方法：N.GetPrime(bits)
返回值：N被赋值为一个bits位（0x100000000进制长度）的素数
****************************************************************************************/
void CBigInt::GetPrime(int bits)
{
    unsigned i;
    m_nLength=bits;
begin:
	for(i=0;i<m_nLength;i++)m_ulValue[i]=rand()*0x10000+rand();
    m_ulValue[0]=m_ulValue[0]|1;
	for(i=m_nLength-1;i>0;i--)
	{
		m_ulValue[i]=m_ulValue[i]<<1;
		if(m_ulValue[i-1]&0x80000000)m_ulValue[i]++;
	}
	m_ulValue[0]=m_ulValue[0]<<1;
	m_ulValue[0]++;
    for(i=0;i<550;i++){if(Mod(PrimeTable[i])==0)goto begin;}
    CBigInt K;
    K.Mov(*this);	
	if(K.Rab()==0) goto begin;
}