MFC功能扩展：大数运算及RSA算法库
2008-08-03 21:06
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MFC功能扩展：大数运算及RSA算法库
用MFC太久，习惯了MFC风格，以至于对各种流行的大数运算及RSA库都看着不爽。。。
而MFC本身并不提供相关功能，余好事者也，曾为之扩展。
/*****************************************************************
大数运算库头文件：BigInt.h
作者：fangle.liu@gmail.com
版本：1.2 (2003.5.13)
说明：适用于MFC，1024位RSA运算
*****************************************************************/
#include <cmath>
#define BI_MAXLEN 40
#define DEC 10
#define HEX 16
//小素数表
const static int PrimeTable[1230]=
{ 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,
4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073,
4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153,
4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241,
4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327,
4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421,
4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507,
4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591,
4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663,
4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759,
4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861,
4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943,
4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009,
5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099,
5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189,
5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281,
5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393,
5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,
5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527,
5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641,
5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701,
5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801,
5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861,
5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953,
5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067,
6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143,
6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229,
6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311,
6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481,
6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577,
6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679,
6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763,
6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841,
6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947,
6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001,
7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109,
7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211,
7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307,
7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417,
7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507,
7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573,
7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649,
7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727,
7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841,
7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927,
7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039,
8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117,
8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221,
8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293,
8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389,
8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513,
8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599,
8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681,
8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747,
8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837,
8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933,
8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013,
9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127,
9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203,
9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293,
9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391,
9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461,
9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539,
9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643,
9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739,
9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817,
9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901,
9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007,10009,
};
const static CString CharTable="0123456789abcdefghijklmnopqrstuvwxyz";
class CBigInt
{
public:
//大数在0x100000000进制下的长度
unsigned m_nLength;
//用数组记录大数在0x100000000进制下每一位的值
unsigned long m_ulValue[BI_MAXLEN];
CBigInt();
/*****************************************************************
基本操作与运算
Mov，赋值运算，可赋值为大数或普通整数，可重载为运算符“=”
Cmp，比较运算，可重载为运算符“==”、“!=”、“>=”、“<=”等
Add，加，求大数与大数或大数与普通整数的和，可重载为运算符“+”
Sub，减，求大数与大数或大数与普通整数的差，可重载为运算符“-”
Mul，乘，求大数与大数或大数与普通整数的积，可重载为运算符“*”
Div，除，求大数与大数或大数与普通整数的商，可重载为运算符“/”
Mod，模，求大数与大数或大数与普通整数的模，可重载为运算符“%”
Sqr，开方，求大数的算术平方根
*****************************************************************/
void Mov(unsigned __int64 A);
void Mov(CBigInt& A);
CBigInt Add(CBigInt& A);
CBigInt Sub(CBigInt& A);
CBigInt Mul(CBigInt& A);
CBigInt Div(CBigInt& A);
CBigInt Mod(CBigInt& A);
CBigInt Sqrt();
CBigInt Add(unsigned long 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);
/*****************************************************************
输入输出
Get，从字符串按10进制或16进制格式输入到大数
Put，将大数按10进制或16进制格式输出到字符串
*****************************************************************/
void Get(CString& str, unsigned int system=HEX);
void Put(CString& str, unsigned int system=HEX);
/*****************************************************************
RSA相关运算
ModMul，布莱克雷算法求模乘
ModInv，欧几里德算法求模逆
MonPro，蒙哥马利算法求模乘
ModExp，蒙哥马利算法求模幂
TestPrime，拉宾米勒算法进行素数测试
FindPrime，产生指定长度的随机大素数
*****************************************************************/
CBigInt ModMul(CBigInt& A, CBigInt& B);
CBigInt ModInv(CBigInt& A);
CBigInt MonPro(CBigInt& A, CBigInt& B, unsigned long n);
CBigInt ModExp(CBigInt& A, CBigInt& B);
int TestPrime();
void FindPrime(int bits);
};
/*****************************************************************
大数运算库源文件：BigInt.cpp
作者：fangle.liu@gmail.com
版本：1.2 (2003.5.13)
说明：适用于MFC，1024位RSA运算
*****************************************************************/
#include "stdafx.h"
#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
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 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
调用方式：N.Mov(A)
返回值：无，N被赋值为A
****************************************************************************************/
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;
}
/****************************************************************************************
大数相加
调用形式：N.Add(A)
返回值：N+A
****************************************************************************************/
CBigInt CBigInt::Add(CBigInt& A)
{
CBigInt X;
X.Mov(*this);
unsigned carry=0;
unsigned __int64 sum=0;
if(X.m_nLength<A.m_nLength)X.m_nLength=A.m_nLength;
for(unsigned i=0;i<X.m_nLength;i++)
{
sum=A.m_ulValue[i];
sum=sum+X.m_ulValue[i]+carry;
X.m_ulValue[i]=(unsigned long)sum;
carry=(unsigned)(sum>>32);
}
X.m_ulValue[X.m_nLength]=carry;
X.m_nLength+=carry;
return X;
}
CBigInt CBigInt::Add(unsigned long A)
{
CBigInt X;
X.Mov(*this);
unsigned __int64 sum;
sum=X.m_ulValue[0];
sum+=A;
X.m_ulValue[0]=(unsigned long)sum;
if(sum>0xffffffff)
{
unsigned i=1;
while(X.m_ulValue[i]==0xffffffff){X.m_ulValue[i]=0;i++;}
X.m_ulValue[i]++;
if(X.m_nLength==i)X.m_nLength++;
}
return X;
}
/****************************************************************************************
大数相减
调用形式：N.Sub(A)
返回值：N-A
****************************************************************************************/
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
调用形式：N.Mul(A)
返回值：N*A
****************************************************************************************/
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
调用形式：N.Div(A)
返回值：N/A
****************************************************************************************/
CBigInt CBigInt::Div(CBigInt& A)
{
if(A.m_nLength==1)return Div(A.m_ulValue[0]);
CBigInt X,Y,Z;
unsigned i,len;
unsigned __int64 num,div;
Y.Mov(*this);
while(Y.Cmp(A)>=0)
{
div=Y.m_ulValue[Y.m_nLength-1];
num=A.m_ulValue[A.m_nLength-1];
len=Y.m_nLength-A.m_nLength;
if((div==num)&&(len==0)){X.Mov(X.Add(1));break;}
if((div<=num)&&len){len--;div=(div<<32)+Y.m_ulValue[Y.m_nLength-2];}
div=div/(num+1);
Z.Mov(div);
if(len)
{
Z.m_nLength+=len;
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;
int n;
n=Cmp(A);
if(n<0)return A;
if(n=0)return X;
X.Mov(*this);
while(1)
{
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){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));
n=X.Cmp(A);
if(n==0){X.Mov(0);return X;}
if(n<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=m_ulValue[i];
div+=carry*0x100000000;
carry=(unsigned long)(div%A);
}
return carry;
}
/****************************************************************************************
大数开方
调用形式：N.Sqr()
返回值：N的算术平方根
****************************************************************************************/
CBigInt CBigInt::Sqrt()
{
CBigInt X,M,N;
unsigned long m,n;
n=m_ulValue[m_nLength-1];
n=(unsigned long)sqrt((double)n);
m=n+1;
if(m_nLength==1){X.Mov(n);return X;}
N.m_nLength=m_nLength/2;
M.m_nLength=N.m_nLength;
if(m_nLength&1)
{
M.m_nLength++;
N.m_nLength++;
M.m_ulValue[M.m_nLength-1]=m;
N.m_ulValue[N.m_nLength-1]=n;
}
else
{
M.m_ulValue[M.m_nLength-1]=(m<<16);
N.m_ulValue[N.m_nLength-1]=(n<<16);
}
X.Mov(M.Add(N));
X.Mov(X.Div(2));
while(1)
{
if(Cmp(X.Mul(X))<0)M.Mov(X);
else N.Mov(X);
X.Mov(M.Sub(N));
if((X.m_ulValue[0]==1)&&(X.m_nLength==1))return N;
X.Mov(M.Add(N));
X.Mov(X.Div(2));
}
}
/****************************************************************************************
从字符串按2进制到36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
****************************************************************************************/
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]-87;
else k=0;
Mov(Add(k));
}
}
/****************************************************************************************
将大数按2进制到36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
****************************************************************************************/
void CBigInt::Put(CString& str, unsigned int system)
{
if((m_nLength==1)&&(m_ulValue[0]==0)){str="0";return;}
str="";
int a;
char ch;
CBigInt X;
X.Mov(*this);
while(X.m_ulValue[X.m_nLength-1]>0)
{
a=X.Mod(system);
ch=CharTable[a];
str.Insert(0,ch);
X.Mov(X.Div(system));
}
}
/****************************************************************************************
求模逆，即解同余方程NX%A=1，亦即解不定方程NX-AY=1的最小整数解
调用方式：N.ModInv(A)
返回值：X,满足：NX%A=1
****************************************************************************************/
CBigInt CBigInt::ModInv(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;
}
/****************************************************************************************
求模乘
调用方式：N.ModMul(A,B)
返回值：X=N*A%B
****************************************************************************************/
CBigInt CBigInt::ModMul(CBigInt& A, CBigInt& B)
{
int i,j;
CBigInt X;
X.Mov(A.Mul(m_ulValue[m_nLength-1]));
X.Mov(X.Mod(B));
for(i=m_nLength-2;i>=0;i--)
{
for(j=X.m_nLength;j>0;j--)X.m_ulValue[j]=X.m_ulValue[j-1];
X.m_ulValue[0]=0;
X.m_nLength++;
X.Mov(X.Add(A.Mul(m_ulValue[i])));
X.Mov(X.Mod(B));
}
return X;
}
/****************************************************************************************
求蒙哥马利模乘
调用方式：N.MonPro(A,B,n)，（2**(k-1)<B<2**k，R=2**k，R*R'%B=1，n*B[0]%0x100000000=-1）
返回值：X=N*A*R'%B
****************************************************************************************/
CBigInt CBigInt::MonPro(CBigInt& A, CBigInt& B, unsigned long n)
{
CBigInt X;
unsigned long T[BI_MAXLEN*2];
unsigned i,j,k;
unsigned long m,carry;
unsigned __int64 sum;
for(i=0;i<BI_MAXLEN*2;i++)T[i]=0;
k=B.m_nLength;
for(i=0;i<k;i++)
{
carry=0;
for(j=0;j<k;j++)
{
sum=A.m_ulValue[i];
sum=sum*m_ulValue[j]+T[i+j]+carry;
T[i+j]=(unsigned long)sum;
carry=(unsigned long)(sum>>32);
}
T[i+k]=carry;
}
for(i=0;i<k;i++)
{
carry=0;
m=T[i]*n;
for(j=0;j<k;j++)
{
sum=B.m_ulValue[j];
sum=sum*m+T[i+j]+carry;
T[i+j]=(unsigned long)sum;
carry=(unsigned long)(sum>>32);
}
for(j=i+k;j<k*2;j++)
{
sum=T[j];
sum+=carry;
T[j]=(unsigned long)sum;
carry=(unsigned long)(sum>>32);
if(carry==0)break;
}
}
T[k*2]=carry;
X.m_nLength=k+1;
for(i=0;i<=k;i++)X.m_ulValue[i]=T[i+k];
while(X.m_ulValue[X.m_nLength-1]==0)X.m_nLength--;
if(X.Cmp(B)>=0)X.Mov(X.Sub(B));
return X;
}
/****************************************************************************************
求模幂
调用方式：N.ModExp(A,B)
返回值：X=N**A%B
****************************************************************************************/
CBigInt CBigInt::ModExp(CBigInt& A, CBigInt& B)
{
CBigInt X,Y;
int i,k;
unsigned long n;
k=A.m_nLength*32-32;
n=A.m_ulValue[A.m_nLength-1];
while(n){n=n>>1;k++;}
Y.m_nLength=2;
Y.m_ulValue[1]=1;
X.Mov(B.m_ulValue[0]);
X.Mov(X.ModInv(Y));
X.Mov(Y.Sub(X));
n=X.m_ulValue[0];
Y.Mov(0);
Y.m_nLength=B.m_nLength+1;
Y.m_ulValue[Y.m_nLength-1]=1;
X.Mov(Y.Sub(B));
Y.Mov(ModMul(X,B));
for(i=k-1;i>=0;i--)
{
X.Mov(X.MonPro(X,B,n));
if((A.m_ulValue[i>>5]>>(i&31))&1)X.Mov(X.MonPro(Y,B,n));
}
Y.Mov(1);
X.Mov(X.MonPro(Y,B,n));
return X;
}
/****************************************************************************************
测试素数
调用方式：N.TestPrime()
返回值：若N为素数，返回0，否则返回最小质因数，若质因数不可知，返回1
****************************************************************************************/
int CBigInt::TestPrime()
{
unsigned i,pass;
if((m_ulValue[0]&1)==0)return 2;
for(i=0;i<1230;i++){if(Mod(PrimeTable[i])==0)return PrimeTable[i];}
if((m_nLength==1)&&(m_ulValue[0]<100180081))return 0;
CBigInt S,A,I,K;
K.Mov(*this);
K.m_ulValue[0]--;
for(i=0;i<5;i++)
{
pass=0;
A.Mov(rand());
S.Mov(K);
while((S.m_ulValue[0]&1)==0)
{
S.Mov(S.Div(2));
I.Mov(A.ModExp(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 1;
}
return 0;
}
/****************************************************************************************
产生随机素数
调用方法：N.FindPrime(bits)
返回值：N被赋值为一个bits位（0x100000000进制长度）的素数
****************************************************************************************/
void CBigInt::FindPrime(int bits)
{
unsigned i;
m_nLength=bits;
for(i=1;i<m_nLength;i++)m_ulValue[i]=rand()*0x10000+rand();
m_ulValue[m_nLength-1]=m_ulValue[m_nLength-1]|0x80000000;
begin:
m_ulValue[0]=rand()*0x10000+rand();
m_ulValue[0]=m_ulValue[0]|3;
for(i=0;i<500;i++){if(Mod(PrimeTable[i])==0)goto begin;}
CBigInt S,A;
S.Mov(*this);
S.m_ulValue[0]--;
for(i=0;i<S.m_nLength;i++)
{
S.m_ulValue[i]=S.m_ulValue[i]>>1;
if(S.m_ulValue[i+1]&1)S.m_ulValue[i]=S.m_ulValue[i]|0x80000000;
}
if(S.m_ulValue[S.m_nLength-1]==0)S.m_nLength--;
for(i=0;i<5;i++)
{
A.Mov(rand());
A.Mov(A.ModExp(S,*this));
A.m_ulValue[0]++;
if(((A.m_nLength!=1)||(A.m_ulValue[0]!=2))&&(Cmp(A)!=0))goto begin;
}
}
用MFC太久，习惯了MFC风格，以至于对各种流行的大数运算及RSA库都看着不爽。。。
而MFC本身并不提供相关功能，余好事者也，曾为之扩展。
/*****************************************************************
大数运算库头文件：BigInt.h
作者：fangle.liu@gmail.com
版本：1.2 (2003.5.13)
说明：适用于MFC，1024位RSA运算
*****************************************************************/
#include <cmath>
#define BI_MAXLEN 40
#define DEC 10
#define HEX 16
//小素数表
const static int PrimeTable[1230]=
{ 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,
4003, 4007, 4013, 4019, 4021, 4027, 4049, 4051, 4057, 4073,
4079, 4091, 4093, 4099, 4111, 4127, 4129, 4133, 4139, 4153,
4157, 4159, 4177, 4201, 4211, 4217, 4219, 4229, 4231, 4241,
4243, 4253, 4259, 4261, 4271, 4273, 4283, 4289, 4297, 4327,
4337, 4339, 4349, 4357, 4363, 4373, 4391, 4397, 4409, 4421,
4423, 4441, 4447, 4451, 4457, 4463, 4481, 4483, 4493, 4507,
4513, 4517, 4519, 4523, 4547, 4549, 4561, 4567, 4583, 4591,
4597, 4603, 4621, 4637, 4639, 4643, 4649, 4651, 4657, 4663,
4673, 4679, 4691, 4703, 4721, 4723, 4729, 4733, 4751, 4759,
4783, 4787, 4789, 4793, 4799, 4801, 4813, 4817, 4831, 4861,
4871, 4877, 4889, 4903, 4909, 4919, 4931, 4933, 4937, 4943,
4951, 4957, 4967, 4969, 4973, 4987, 4993, 4999, 5003, 5009,
5011, 5021, 5023, 5039, 5051, 5059, 5077, 5081, 5087, 5099,
5101, 5107, 5113, 5119, 5147, 5153, 5167, 5171, 5179, 5189,
5197, 5209, 5227, 5231, 5233, 5237, 5261, 5273, 5279, 5281,
5297, 5303, 5309, 5323, 5333, 5347, 5351, 5381, 5387, 5393,
5399, 5407, 5413, 5417, 5419, 5431, 5437, 5441, 5443, 5449,
5471, 5477, 5479, 5483, 5501, 5503, 5507, 5519, 5521, 5527,
5531, 5557, 5563, 5569, 5573, 5581, 5591, 5623, 5639, 5641,
5647, 5651, 5653, 5657, 5659, 5669, 5683, 5689, 5693, 5701,
5711, 5717, 5737, 5741, 5743, 5749, 5779, 5783, 5791, 5801,
5807, 5813, 5821, 5827, 5839, 5843, 5849, 5851, 5857, 5861,
5867, 5869, 5879, 5881, 5897, 5903, 5923, 5927, 5939, 5953,
5981, 5987, 6007, 6011, 6029, 6037, 6043, 6047, 6053, 6067,
6073, 6079, 6089, 6091, 6101, 6113, 6121, 6131, 6133, 6143,
6151, 6163, 6173, 6197, 6199, 6203, 6211, 6217, 6221, 6229,
6247, 6257, 6263, 6269, 6271, 6277, 6287, 6299, 6301, 6311,
6317, 6323, 6329, 6337, 6343, 6353, 6359, 6361, 6367, 6373,
6379, 6389, 6397, 6421, 6427, 6449, 6451, 6469, 6473, 6481,
6491, 6521, 6529, 6547, 6551, 6553, 6563, 6569, 6571, 6577,
6581, 6599, 6607, 6619, 6637, 6653, 6659, 6661, 6673, 6679,
6689, 6691, 6701, 6703, 6709, 6719, 6733, 6737, 6761, 6763,
6779, 6781, 6791, 6793, 6803, 6823, 6827, 6829, 6833, 6841,
6857, 6863, 6869, 6871, 6883, 6899, 6907, 6911, 6917, 6947,
6949, 6959, 6961, 6967, 6971, 6977, 6983, 6991, 6997, 7001,
7013, 7019, 7027, 7039, 7043, 7057, 7069, 7079, 7103, 7109,
7121, 7127, 7129, 7151, 7159, 7177, 7187, 7193, 7207, 7211,
7213, 7219, 7229, 7237, 7243, 7247, 7253, 7283, 7297, 7307,
7309, 7321, 7331, 7333, 7349, 7351, 7369, 7393, 7411, 7417,
7433, 7451, 7457, 7459, 7477, 7481, 7487, 7489, 7499, 7507,
7517, 7523, 7529, 7537, 7541, 7547, 7549, 7559, 7561, 7573,
7577, 7583, 7589, 7591, 7603, 7607, 7621, 7639, 7643, 7649,
7669, 7673, 7681, 7687, 7691, 7699, 7703, 7717, 7723, 7727,
7741, 7753, 7757, 7759, 7789, 7793, 7817, 7823, 7829, 7841,
7853, 7867, 7873, 7877, 7879, 7883, 7901, 7907, 7919, 7927,
7933, 7937, 7949, 7951, 7963, 7993, 8009, 8011, 8017, 8039,
8053, 8059, 8069, 8081, 8087, 8089, 8093, 8101, 8111, 8117,
8123, 8147, 8161, 8167, 8171, 8179, 8191, 8209, 8219, 8221,
8231, 8233, 8237, 8243, 8263, 8269, 8273, 8287, 8291, 8293,
8297, 8311, 8317, 8329, 8353, 8363, 8369, 8377, 8387, 8389,
8419, 8423, 8429, 8431, 8443, 8447, 8461, 8467, 8501, 8513,
8521, 8527, 8537, 8539, 8543, 8563, 8573, 8581, 8597, 8599,
8609, 8623, 8627, 8629, 8641, 8647, 8663, 8669, 8677, 8681,
8689, 8693, 8699, 8707, 8713, 8719, 8731, 8737, 8741, 8747,
8753, 8761, 8779, 8783, 8803, 8807, 8819, 8821, 8831, 8837,
8839, 8849, 8861, 8863, 8867, 8887, 8893, 8923, 8929, 8933,
8941, 8951, 8963, 8969, 8971, 8999, 9001, 9007, 9011, 9013,
9029, 9041, 9043, 9049, 9059, 9067, 9091, 9103, 9109, 9127,
9133, 9137, 9151, 9157, 9161, 9173, 9181, 9187, 9199, 9203,
9209, 9221, 9227, 9239, 9241, 9257, 9277, 9281, 9283, 9293,
9311, 9319, 9323, 9337, 9341, 9343, 9349, 9371, 9377, 9391,
9397, 9403, 9413, 9419, 9421, 9431, 9433, 9437, 9439, 9461,
9463, 9467, 9473, 9479, 9491, 9497, 9511, 9521, 9533, 9539,
9547, 9551, 9587, 9601, 9613, 9619, 9623, 9629, 9631, 9643,
9649, 9661, 9677, 9679, 9689, 9697, 9719, 9721, 9733, 9739,
9743, 9749, 9767, 9769, 9781, 9787, 9791, 9803, 9811, 9817,
9829, 9833, 9839, 9851, 9857, 9859, 9871, 9883, 9887, 9901,
9907, 9923, 9929, 9931, 9941, 9949, 9967, 9973, 10007,10009,
};
const static CString CharTable="0123456789abcdefghijklmnopqrstuvwxyz";
class CBigInt
{
public:
//大数在0x100000000进制下的长度
unsigned m_nLength;
//用数组记录大数在0x100000000进制下每一位的值
unsigned long m_ulValue[BI_MAXLEN];
CBigInt();
/*****************************************************************
基本操作与运算
Mov，赋值运算，可赋值为大数或普通整数，可重载为运算符“=”
Cmp，比较运算，可重载为运算符“==”、“!=”、“>=”、“<=”等
Add，加，求大数与大数或大数与普通整数的和，可重载为运算符“+”
Sub，减，求大数与大数或大数与普通整数的差，可重载为运算符“-”
Mul，乘，求大数与大数或大数与普通整数的积，可重载为运算符“*”
Div，除，求大数与大数或大数与普通整数的商，可重载为运算符“/”
Mod，模，求大数与大数或大数与普通整数的模，可重载为运算符“%”
Sqr，开方，求大数的算术平方根
*****************************************************************/
void Mov(unsigned __int64 A);
void Mov(CBigInt& A);
CBigInt Add(CBigInt& A);
CBigInt Sub(CBigInt& A);
CBigInt Mul(CBigInt& A);
CBigInt Div(CBigInt& A);
CBigInt Mod(CBigInt& A);
CBigInt Sqrt();
CBigInt Add(unsigned long 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);
/*****************************************************************
输入输出
Get，从字符串按10进制或16进制格式输入到大数
Put，将大数按10进制或16进制格式输出到字符串
*****************************************************************/
void Get(CString& str, unsigned int system=HEX);
void Put(CString& str, unsigned int system=HEX);
/*****************************************************************
RSA相关运算
ModMul，布莱克雷算法求模乘
ModInv，欧几里德算法求模逆
MonPro，蒙哥马利算法求模乘
ModExp，蒙哥马利算法求模幂
TestPrime，拉宾米勒算法进行素数测试
FindPrime，产生指定长度的随机大素数
*****************************************************************/
CBigInt ModMul(CBigInt& A, CBigInt& B);
CBigInt ModInv(CBigInt& A);
CBigInt MonPro(CBigInt& A, CBigInt& B, unsigned long n);
CBigInt ModExp(CBigInt& A, CBigInt& B);
int TestPrime();
void FindPrime(int bits);
};
/*****************************************************************
大数运算库源文件：BigInt.cpp
作者：fangle.liu@gmail.com
版本：1.2 (2003.5.13)
说明：适用于MFC，1024位RSA运算
*****************************************************************/
#include "stdafx.h"
#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
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 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
调用方式：N.Mov(A)
返回值：无，N被赋值为A
****************************************************************************************/
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;
}
/****************************************************************************************
大数相加
调用形式：N.Add(A)
返回值：N+A
****************************************************************************************/
CBigInt CBigInt::Add(CBigInt& A)
{
CBigInt X;
X.Mov(*this);
unsigned carry=0;
unsigned __int64 sum=0;
if(X.m_nLength<A.m_nLength)X.m_nLength=A.m_nLength;
for(unsigned i=0;i<X.m_nLength;i++)
{
sum=A.m_ulValue[i];
sum=sum+X.m_ulValue[i]+carry;
X.m_ulValue[i]=(unsigned long)sum;
carry=(unsigned)(sum>>32);
}
X.m_ulValue[X.m_nLength]=carry;
X.m_nLength+=carry;
return X;
}
CBigInt CBigInt::Add(unsigned long A)
{
CBigInt X;
X.Mov(*this);
unsigned __int64 sum;
sum=X.m_ulValue[0];
sum+=A;
X.m_ulValue[0]=(unsigned long)sum;
if(sum>0xffffffff)
{
unsigned i=1;
while(X.m_ulValue[i]==0xffffffff){X.m_ulValue[i]=0;i++;}
X.m_ulValue[i]++;
if(X.m_nLength==i)X.m_nLength++;
}
return X;
}
/****************************************************************************************
大数相减
调用形式：N.Sub(A)
返回值：N-A
****************************************************************************************/
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
调用形式：N.Mul(A)
返回值：N*A
****************************************************************************************/
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
调用形式：N.Div(A)
返回值：N/A
****************************************************************************************/
CBigInt CBigInt::Div(CBigInt& A)
{
if(A.m_nLength==1)return Div(A.m_ulValue[0]);
CBigInt X,Y,Z;
unsigned i,len;
unsigned __int64 num,div;
Y.Mov(*this);
while(Y.Cmp(A)>=0)
{
div=Y.m_ulValue[Y.m_nLength-1];
num=A.m_ulValue[A.m_nLength-1];
len=Y.m_nLength-A.m_nLength;
if((div==num)&&(len==0)){X.Mov(X.Add(1));break;}
if((div<=num)&&len){len--;div=(div<<32)+Y.m_ulValue[Y.m_nLength-2];}
div=div/(num+1);
Z.Mov(div);
if(len)
{
Z.m_nLength+=len;
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;
int n;
n=Cmp(A);
if(n<0)return A;
if(n=0)return X;
X.Mov(*this);
while(1)
{
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){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));
n=X.Cmp(A);
if(n==0){X.Mov(0);return X;}
if(n<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=m_ulValue[i];
div+=carry*0x100000000;
carry=(unsigned long)(div%A);
}
return carry;
}
/****************************************************************************************
大数开方
调用形式：N.Sqr()
返回值：N的算术平方根
****************************************************************************************/
CBigInt CBigInt::Sqrt()
{
CBigInt X,M,N;
unsigned long m,n;
n=m_ulValue[m_nLength-1];
n=(unsigned long)sqrt((double)n);
m=n+1;
if(m_nLength==1){X.Mov(n);return X;}
N.m_nLength=m_nLength/2;
M.m_nLength=N.m_nLength;
if(m_nLength&1)
{
M.m_nLength++;
N.m_nLength++;
M.m_ulValue[M.m_nLength-1]=m;
N.m_ulValue[N.m_nLength-1]=n;
}
else
{
M.m_ulValue[M.m_nLength-1]=(m<<16);
N.m_ulValue[N.m_nLength-1]=(n<<16);
}
X.Mov(M.Add(N));
X.Mov(X.Div(2));
while(1)
{
if(Cmp(X.Mul(X))<0)M.Mov(X);
else N.Mov(X);
X.Mov(M.Sub(N));
if((X.m_ulValue[0]==1)&&(X.m_nLength==1))return N;
X.Mov(M.Add(N));
X.Mov(X.Div(2));
}
}
/****************************************************************************************
从字符串按2进制到36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
****************************************************************************************/
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]-87;
else k=0;
Mov(Add(k));
}
}
/****************************************************************************************
将大数按2进制到36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
****************************************************************************************/
void CBigInt::Put(CString& str, unsigned int system)
{
if((m_nLength==1)&&(m_ulValue[0]==0)){str="0";return;}
str="";
int a;
char ch;
CBigInt X;
X.Mov(*this);
while(X.m_ulValue[X.m_nLength-1]>0)
{
a=X.Mod(system);
ch=CharTable[a];
str.Insert(0,ch);
X.Mov(X.Div(system));
}
}
/****************************************************************************************
求模逆，即解同余方程NX%A=1，亦即解不定方程NX-AY=1的最小整数解
调用方式：N.ModInv(A)
返回值：X,满足：NX%A=1
****************************************************************************************/
CBigInt CBigInt::ModInv(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;
}
/****************************************************************************************
求模乘
调用方式：N.ModMul(A,B)
返回值：X=N*A%B
****************************************************************************************/
CBigInt CBigInt::ModMul(CBigInt& A, CBigInt& B)
{
int i,j;
CBigInt X;
X.Mov(A.Mul(m_ulValue[m_nLength-1]));
X.Mov(X.Mod(B));
for(i=m_nLength-2;i>=0;i--)
{
for(j=X.m_nLength;j>0;j--)X.m_ulValue[j]=X.m_ulValue[j-1];
X.m_ulValue[0]=0;
X.m_nLength++;
X.Mov(X.Add(A.Mul(m_ulValue[i])));
X.Mov(X.Mod(B));
}
return X;
}
/****************************************************************************************
求蒙哥马利模乘
调用方式：N.MonPro(A,B,n)，（2**(k-1)<B<2**k，R=2**k，R*R'%B=1，n*B[0]%0x100000000=-1）
返回值：X=N*A*R'%B
****************************************************************************************/
CBigInt CBigInt::MonPro(CBigInt& A, CBigInt& B, unsigned long n)
{
CBigInt X;
unsigned long T[BI_MAXLEN*2];
unsigned i,j,k;
unsigned long m,carry;
unsigned __int64 sum;
for(i=0;i<BI_MAXLEN*2;i++)T[i]=0;
k=B.m_nLength;
for(i=0;i<k;i++)
{
carry=0;
for(j=0;j<k;j++)
{
sum=A.m_ulValue[i];
sum=sum*m_ulValue[j]+T[i+j]+carry;
T[i+j]=(unsigned long)sum;
carry=(unsigned long)(sum>>32);
}
T[i+k]=carry;
}
for(i=0;i<k;i++)
{
carry=0;
m=T[i]*n;
for(j=0;j<k;j++)
{
sum=B.m_ulValue[j];
sum=sum*m+T[i+j]+carry;
T[i+j]=(unsigned long)sum;
carry=(unsigned long)(sum>>32);
}
for(j=i+k;j<k*2;j++)
{
sum=T[j];
sum+=carry;
T[j]=(unsigned long)sum;
carry=(unsigned long)(sum>>32);
if(carry==0)break;
}
}
T[k*2]=carry;
X.m_nLength=k+1;
for(i=0;i<=k;i++)X.m_ulValue[i]=T[i+k];
while(X.m_ulValue[X.m_nLength-1]==0)X.m_nLength--;
if(X.Cmp(B)>=0)X.Mov(X.Sub(B));
return X;
}
/****************************************************************************************
求模幂
调用方式：N.ModExp(A,B)
返回值：X=N**A%B
****************************************************************************************/
CBigInt CBigInt::ModExp(CBigInt& A, CBigInt& B)
{
CBigInt X,Y;
int i,k;
unsigned long n;
k=A.m_nLength*32-32;
n=A.m_ulValue[A.m_nLength-1];
while(n){n=n>>1;k++;}
Y.m_nLength=2;
Y.m_ulValue[1]=1;
X.Mov(B.m_ulValue[0]);
X.Mov(X.ModInv(Y));
X.Mov(Y.Sub(X));
n=X.m_ulValue[0];
Y.Mov(0);
Y.m_nLength=B.m_nLength+1;
Y.m_ulValue[Y.m_nLength-1]=1;
X.Mov(Y.Sub(B));
Y.Mov(ModMul(X,B));
for(i=k-1;i>=0;i--)
{
X.Mov(X.MonPro(X,B,n));
if((A.m_ulValue[i>>5]>>(i&31))&1)X.Mov(X.MonPro(Y,B,n));
}
Y.Mov(1);
X.Mov(X.MonPro(Y,B,n));
return X;
}
/****************************************************************************************
测试素数
调用方式：N.TestPrime()
返回值：若N为素数，返回0，否则返回最小质因数，若质因数不可知，返回1
****************************************************************************************/
int CBigInt::TestPrime()
{
unsigned i,pass;
if((m_ulValue[0]&1)==0)return 2;
for(i=0;i<1230;i++){if(Mod(PrimeTable[i])==0)return PrimeTable[i];}
if((m_nLength==1)&&(m_ulValue[0]<100180081))return 0;
CBigInt S,A,I,K;
K.Mov(*this);
K.m_ulValue[0]--;
for(i=0;i<5;i++)
{
pass=0;
A.Mov(rand());
S.Mov(K);
while((S.m_ulValue[0]&1)==0)
{
S.Mov(S.Div(2));
I.Mov(A.ModExp(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 1;
}
return 0;
}
/****************************************************************************************
产生随机素数
调用方法：N.FindPrime(bits)
返回值：N被赋值为一个bits位（0x100000000进制长度）的素数
****************************************************************************************/
void CBigInt::FindPrime(int bits)
{
unsigned i;
m_nLength=bits;
for(i=1;i<m_nLength;i++)m_ulValue[i]=rand()*0x10000+rand();
m_ulValue[m_nLength-1]=m_ulValue[m_nLength-1]|0x80000000;
begin:
m_ulValue[0]=rand()*0x10000+rand();
m_ulValue[0]=m_ulValue[0]|3;
for(i=0;i<500;i++){if(Mod(PrimeTable[i])==0)goto begin;}
CBigInt S,A;
S.Mov(*this);
S.m_ulValue[0]--;
for(i=0;i<S.m_nLength;i++)
{
S.m_ulValue[i]=S.m_ulValue[i]>>1;
if(S.m_ulValue[i+1]&1)S.m_ulValue[i]=S.m_ulValue[i]|0x80000000;
}
if(S.m_ulValue[S.m_nLength-1]==0)S.m_nLength--;
for(i=0;i<5;i++)
{
A.Mov(rand());
A.Mov(A.ModExp(S,*this));
A.m_ulValue[0]++;
if(((A.m_nLength!=1)||(A.m_ulValue[0]!=2))&&(Cmp(A)!=0))goto begin;
}
}
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