bigint.cpp

RSA运算的大数库 语法简洁易懂 实用性强

/****************************************
C＋＋源文件
文件名：BigInt.cpp
用途：1024位RSA运算

作者：
版本：
平台：linux x86_64
日期：2009年 04月 23日 星期四 09:30:30 CST
****************************************/
#include "BigInt.h"

//小素数表
const static int PrimeTable[550]=
{   3,    5,    7,    11,   13,   17,   19,   23,   29,   31,
    37,   41,   43,   47,   53,   59,   61,   67,   71,   73,
    79,   83,   89,   97,   101,  103,  107,  109,  113,  127, 
    131,  137,  139,  149,  151,  157,  163,  167,  173,  179, 
    181,  191,  193,  197,  199,  211,  223,  227,  229,  233, 
    239,  241,  251,  257,  263,  269,  271,  277,  281,  283, 
    293,  307,  311,  313,  317,  331,  337,  347,  349,  353, 
    359,  367,  373,  379,  383,  389,  397,  401,  409,  419, 
    421,  431,  433,  439,  443,  449,  457,  461,  463,  467, 
    479,  487,  491,  499,  503,  509,  521,  523,  541,  547, 
    557,  563,  569,  571,  577,  587,  593,  599,  601,  607, 
    613,  617,  619,  631,  641,  643,  647,  653,  659,  661, 
    673,  677,  683,  691,  701,  709,  719,  727,  733,  739, 
    743,  751,  757,  761,  769,  773,  787,  797,  809,  811, 
    821,  823,  827,  829,  839,  853,  857,  859,  863,  877,
    881,  883,  887,  907,  911,  919,  929,  937,  941,  947, 
    953,  967,  971,  977,  983,  991,  997,  1009, 1013, 1019, 
    1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
    1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 
    1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 
    1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 
    1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,
    1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 
    1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,
    1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 
    1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 
    1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 
    1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 
    1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 
    1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 
    1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063,
    2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131, 
    2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221, 
    2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293,
    2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
    2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437, 
    2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539, 
    2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621, 
    2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689, 
    2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749, 
    2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833, 
    2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909,
    2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001,
    3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083,
    3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187, 
    3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259, 
    3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343,
    3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433, 
    3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517, 
    3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
    3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659, 
    3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733, 
    3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823, 
    3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911, 
    3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001
};

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

//解构大数对象
BigInt::~BigInt()
{
}

/****************************************************************************************
大数比较
调用方式：N.Cmp(A)
返回值：若N<A返回-1；若N=A返回0；若N>A返回1
****************************************************************************************/
int BigInt::Cmp(const BigInt& A)
{
    if(BI_Length>A.BI_Length)return 1;
    if(BI_Length<A.BI_Length)return -1;
    for(int i=BI_Length-1;i>=0;i--)
    {
        if(BI_Value[i]>A.BI_Value[i])return 1;
        if(BI_Value[i]<A.BI_Value[i])return -1;
    }
    return 0;
}

/****************************************************************************************
大数赋值
调用方式：N.Mov(A)
返回值：无，N被赋值为A
****************************************************************************************/
void BigInt::Mov(const BigInt& A)
{
    BI_Length=A.BI_Length;
    for(int i=0;i<BI_MAXLEN;i++)BI_Value[i]=A.BI_Value[i];
}

void BigInt::Mov(uint_64 A)
{
    if(A>0xffffffff)
    {
        BI_Length=2;
        BI_Value[1]=(uint_32)(A>>32);
        BI_Value[0]=(uint_32)A;
    }
    else
    {
        BI_Length=1;
        BI_Value[0]=(uint_32)A;
    }
    for(int i=BI_Length;i<BI_MAXLEN;i++)BI_Value[i]=0;
}

/****************************************************************************************
大数相加
调用形式：N.Add(A)
返回值：N+A
****************************************************************************************/
BigInt BigInt::Add(const BigInt& A)
{
    BigInt X;
    X.Mov(*this);
    usint carry=0;
    uint_64 sum=0;
    if(X.BI_Length<A.BI_Length)X.BI_Length=A.BI_Length;
    for(usint i=0;i<X.BI_Length;i++)
    {
        sum=A.BI_Value[i];
	 sum=sum+X.BI_Value[i]+carry;
        X.BI_Value[i]=(uint_32)sum;
        carry=(unsigned)(sum>>32);
    }
    X.BI_Value[X.BI_Length]=carry;
    X.BI_Length+=carry;
    return X;
}

BigInt BigInt::Add(uint_32 A)
{
    BigInt X;
    X.Mov(*this);
    uint_64 sum;
    sum=X.BI_Value[0];
    sum+=A;
    X.BI_Value[0]=(uint_32)sum;
    if(sum>0xffffffff)
    {
        usint i=1;
        while(X.BI_Value[i]==0xffffffff){X.BI_Value[i]=0;i++;}
        X.BI_Value[i]++;
        if(X.BI_Length==i)X.BI_Length++;
    }
    return X;
}

/****************************************************************************************
大数相减
调用形式：N.Sub(A)
返回值：N-A
****************************************************************************************/
BigInt BigInt::Sub(const BigInt& A) const
{
    BigInt X;
    X.Mov(*this);
    if(X.Cmp(A)<=0){X.Mov(0);return X;}
    usint carry=0;
    uint_64 num;
	usint i;
    for(i=0;i<BI_Length;i++)
    {
        if((BI_Value[i]>A.BI_Value[i])||((BI_Value[i]==A.BI_Value[i])&&(carry==0)))
        {
            X.BI_Value[i]=BI_Value[i]-carry-A.BI_Value[i];
            carry=0;
        }
        else
        {
            num=0x100000000+BI_Value[i];
            X.BI_Value[i]=(uint_32)(num-carry-A.BI_Value[i]);
            carry=1;
        }
    }
    while(X.BI_Value[X.BI_Length-1]==0)X.BI_Length--;
    return X;
}

BigInt BigInt::Sub(uint_32 A) const
{
    BigInt X;
    X.Mov(*this);
    if(X.BI_Value[0]>=A){X.BI_Value[0]-=A;return X;}
    if(X.BI_Length==1){X.Mov(0);return X;}
    uint_64 num=0x100000000+X.BI_Value[0];
    X.BI_Value[0]=(uint_32)(num-A);
    int i=1;
    while(X.BI_Value[i]==0){X.BI_Value[i]=0xffffffff;i++;}
    X.BI_Value[i]--;
    if(X.BI_Value[i]==0)X.BI_Length--;
    return X;
}

/****************************************************************************************
大数相乘
调用形式：N.Mul(A)
返回值：N*A
****************************************************************************************/
BigInt BigInt::Mul(const BigInt& A) const
{
    if(A.BI_Length==1)return Mul(A.BI_Value[0]);
	BigInt X;
	uint_64 sum,mul=0,carry=0;
	usint i,j;
	X.BI_Length=BI_Length+A.BI_Length-1;
    for(i=0;i<X.BI_Length;i++)
	{
		sum=carry;
		carry=0;
		for(j=0;j<A.BI_Length;j++)
		{
            if(((i-j)>=0)&&((i-j)<BI_Length))
			{
				mul=BI_Value[i-j];
				mul*=A.BI_Value[j];
			    carry+=mul>>32;
				mul=mul&0xffffffff;
				sum+=mul;
			}
        }
		carry+=sum>>32;
		X.BI_Value[i]=(uint_32)sum;
	}
	if(carry){X.BI_Length++;X.BI_Value[X.BI_Length-1]=(uint_32)carry;}
    return X;
}

BigInt BigInt::Mul(uint_32 A) const
{
    BigInt X;
    uint_64 mul;
    uint_32 carry=0;
    X.Mov(*this);
    for(usint i=0;i<BI_Length;i++)
    {
        mul=BI_Value[i];
        mul=mul*A+carry;
        X.BI_Value[i]=(uint_32)mul;
        carry=(uint_32)(mul>>32);
    }
    if(carry){X.BI_Length++;X.BI_Value[X.BI_Length-1]=carry;}
    return X;
}

/****************************************************************************************
大数相除
调用形式：N.Div(A)
返回值：N/A
****************************************************************************************/
BigInt BigInt::Div(const BigInt& A)
{
    if(A.BI_Length==1)return Div(A.BI_Value[0]);
    BigInt X,Y,Z;
    usint i,len;
    uint_64 num,div;
    Y.Mov(*this);
    while(Y.Cmp(A)>=0)
    {       
		div=Y.BI_Value[Y.BI_Length-1];
		num=A.BI_Value[A.BI_Length-1];
		len=Y.BI_Length-A.BI_Length;
		if((div==num)&&(len==0)){X.Mov(X.Add(1));break;}
		if((div<=num)&&len){len--;div=(div<<32)+Y.BI_Value[Y.BI_Length-2];}
		div=div/(num+1);
		Z.Mov(div);
		if(len)