227 lines
7.7 KiB
C++
227 lines
7.7 KiB
C++
//
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// Created by 29019 on 2020/1/5.
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//
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#include "rsa.h"
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#include <iostream>
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#include <stdlib.h>
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#include <time.h>
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#include <math.h>
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using namespace std;
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//小素数表
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const static int PrimeTable[550]=
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{ 3, 5, 7, 11, 13, 17, 19, 23, 29, 31,
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37, 41, 43, 47, 53, 59, 61, 67, 71, 73,
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79, 83, 89, 97, 101, 103, 107, 109, 113, 127,
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131, 137, 139, 149, 151, 157, 163, 167, 173, 179,
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181, 191, 193, 197, 199, 211, 223, 227, 229, 233,
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239, 241, 251, 257, 263, 269, 271, 277, 281, 283,
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293, 307, 311, 313, 317, 331, 337, 347, 349, 353,
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359, 367, 373, 379, 383, 389, 397, 401, 409, 419,
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421, 431, 433, 439, 443, 449, 457, 461, 463, 467,
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479, 487, 491, 499, 503, 509, 521, 523, 541, 547,
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557, 563, 569, 571, 577, 587, 593, 599, 601, 607,
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613, 617, 619, 631, 641, 643, 647, 653, 659, 661,
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673, 677, 683, 691, 701, 709, 719, 727, 733, 739,
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743, 751, 757, 761, 769, 773, 787, 797, 809, 811,
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821, 823, 827, 829, 839, 853, 857, 859, 863, 877,
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881, 883, 887, 907, 911, 919, 929, 937, 941, 947,
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953, 967, 971, 977, 983, 991, 997, 1009, 1013, 1019,
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1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087,
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1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153,
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1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229,
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1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297,
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1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381,
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1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453,
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1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523,
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1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597,
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1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663,
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1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741,
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1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823,
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1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901,
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1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993,
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1997, 1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053, 2063,
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2069, 2081, 2083, 2087, 2089, 2099, 2111, 2113, 2129, 2131,
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2137, 2141, 2143, 2153, 2161, 2179, 2203, 2207, 2213, 2221,
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2237, 2239, 2243, 2251, 2267, 2269, 2273, 2281, 2287, 2293,
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2297, 2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357, 2371,
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2377, 2381, 2383, 2389, 2393, 2399, 2411, 2417, 2423, 2437,
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2441, 2447, 2459, 2467, 2473, 2477, 2503, 2521, 2531, 2539,
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2543, 2549, 2551, 2557, 2579, 2591, 2593, 2609, 2617, 2621,
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2633, 2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687, 2689,
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2693, 2699, 2707, 2711, 2713, 2719, 2729, 2731, 2741, 2749,
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2753, 2767, 2777, 2789, 2791, 2797, 2801, 2803, 2819, 2833,
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2837, 2843, 2851, 2857, 2861, 2879, 2887, 2897, 2903, 2909,
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2917, 2927, 2939, 2953, 2957, 2963, 2969, 2971, 2999, 3001,
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3011, 3019, 3023, 3037, 3041, 3049, 3061, 3067, 3079, 3083,
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3089, 3109, 3119, 3121, 3137, 3163, 3167, 3169, 3181, 3187,
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3191, 3203, 3209, 3217, 3221, 3229, 3251, 3253, 3257, 3259,
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3271, 3299, 3301, 3307, 3313, 3319, 3323, 3329, 3331, 3343,
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3347, 3359, 3361, 3371, 3373, 3389, 3391, 3407, 3413, 3433,
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3449, 3457, 3461, 3463, 3467, 3469, 3491, 3499, 3511, 3517,
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3527, 3529, 3533, 3539, 3541, 3547, 3557, 3559, 3571, 3581,
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3583, 3593, 3607, 3613, 3617, 3623, 3631, 3637, 3643, 3659,
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3671, 3673, 3677, 3691, 3697, 3701, 3709, 3719, 3727, 3733,
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3739, 3761, 3767, 3769, 3779, 3793, 3797, 3803, 3821, 3823,
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3833, 3847, 3851, 3853, 3863, 3877, 3881, 3889, 3907, 3911,
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3917, 3919, 3923, 3929, 3931, 3943, 3947, 3967, 3989, 4001
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};
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static int Mod(uint8_t *dat,int size,int table){
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}
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/*
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目前的做法是基于费马素性检测
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假如a是整数，p是质数，且a,p互质(即两者只有一个公约数1)，那么a的(p-1)次方除以p的余数恒等于1。
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也就是说, 如果p为素数, 那么对于任何a<p, 有
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a ^ p % p == a 成立
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而它的逆命题则至少有1/2的概率成立
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那么我们就可以通过多次素性检测, 来减少假素数出现的概率
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而素数定理, 又指出了素数的密度与ln(x)成反比, 也就是说, 我们可以先随机生成一个n bit的整数, 如果不是素数, 则继续向后取, 那么, 大概取n个数, 就能碰到一个素数
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*/
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BigInt GetPrime(int bits)
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{
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unsigned i;
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BigInt ret(bits/8);
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uint8_t *m_ulValue = ret.Data();
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int m_nLength = bits;
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begin:
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for(i=0;i<m_nLength;i++)
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m_ulValue[i] = rand()*0x10000 + rand();
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m_ulValue[0] = m_ulValue[0] | 1;
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for(i = m_nLength - 1;i > 0;i--)
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{
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m_ulValue[i] = m_ulValue[i]<<1;
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if(m_ulValue[i-1]&0x80000000)
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m_ulValue[i]++;
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}
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m_ulValue[0]=m_ulValue[0]<<1;
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m_ulValue[0]++;
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for(i = 0; i <550;i++)
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{
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if(Mod(PrimeTable[i]) == 0)
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goto begin;
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}
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//CBigInt S,A,I,K;
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//K.Mov(*this);
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//K.m_ulValue[0]--;
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for(i=0;i<5;i++)
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{
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//A.Mov(rand()*rand());
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//S.Mov(K.Div(2));
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//I.Mov(A.RsaTrans(S,*this));
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//if(((I.m_nLength!=1) || (I.m_ulValue[0]!=1))&&(I.Cmp(K)!=0))
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// goto begin;
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}
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}
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// 生成伪素数
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const int MAX_ROW = 50;
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size_t Pseudoprime()
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{
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bool ifprime = false;
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size_t a = 0;
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int arr[MAX_ROW]; //数组arr为{3，4，5，6...52}
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for (int i = 0; i<MAX_ROW; ++i)
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{
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arr[i] = i+3;
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}
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while (!ifprime)
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{
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srand((unsigned)time(0));
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ifprime = true;
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a = (rand()%10000)*2+3; //生成一个范围在3到2003里的奇数
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for (int j = 0; j<MAX_ROW; ++j)
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{
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if (a%arr[j] == 0)
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{
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ifprime = false;
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break;
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}
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}
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}
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return a;
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}
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size_t repeatMod(size_t base, size_t n, size_t mod)//模重复平方算法求(b^n)%m
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{
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size_t a = 1;
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while(n)
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{
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if(n&1)
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{
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a = (a*base)%mod;
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}
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base = (base*base)%mod;
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n = n>>1;
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}
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return a;
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}
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//Miller-Rabin素数检测
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bool rabinmiller(size_t n, size_t k)
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{
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int s = 0;
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int temp = n-1;
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while ((temp & 0x1) == 0 && temp)
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{
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temp = temp>>1;
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s++;
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} //将n-1表示为(2^s)*t
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size_t t = temp;
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while(k--) //判断k轮误判概率不大于(1/4)^k
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{
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srand((unsigned)time(0));
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size_t b = rand()%(n-2)+2; //生成一个b(2≤a ≤n-2)
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size_t y = repeatMod(b,t,n);
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if (y == 1 || y == (n-1))
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return true;
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for(int j = 1; j<=(s-1) && y != (n-1); ++j)
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{
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y = repeatMod(y,2,n);
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if (y == 1)
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return false;
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}
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if ( y != (n-1))
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return false;
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}
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return true;
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}
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BigInt::BigInt(int size) {
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memset(this->mDat,0,size);
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}
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BigInt::BigInt(int size, uint8_t *dat) {
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memcpy(this->mDat,dat,size);
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}
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bool BigInt::operator=(BigInt &cmp) {
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return memcmp((const void *)cmp.Data(),
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(const void *)this->Data(),this->mSize);
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}
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BigInt BigInt::operator>(const BigInt &) {
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return BigInt(0);
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}
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BigInt BigInt::operator<(const BigInt &) {
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return BigInt(0);
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}
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BigInt BigInt::operator^(const BigInt &) {
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return BigInt(0);
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}
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string BigInt::ToString() {
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return std::__cxx11::string();
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}
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const uint8_t *BigInt::Data() {
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return mDat;
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}
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