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#include<gmp.h> #include<time.h> #include<fstream> #include<string.h> #include <string> #include<iostream> #include <cstdio> #include <ctime> #include <cstring> #include <cstdlib> using namespace std; //输入字符串转换 string strToNum(char str[]){ int len = strlen(str); string num[len]; string returnstr = ""; for(int i = 0;i < len; i++){ if(str[i] == '0') num[i] = "00"; else if(str[i] == '1') num[i] = "01"; else if(str[i] == '2') num[i] = "02"; else if(str[i] == '3') num[i] = "03"; else if(str[i] == '4') num[i] = "04"; else if(str[i] == '5') num[i] = "05"; else if(str[i] == '6') num[i] = "06"; else if(str[i] == '7') num[i] = "07"; else if(str[i] == '8') num[i] = "08"; else if(str[i] == '9') num[i] = "09"; else if(str[i] == 'a') num[i] = "10"; else if(str[i] == 'b') num[i] = "11"; else if(str[i] == 'c') num[i] = "12"; else if(str[i] == 'd') num[i] = "13"; else if(str[i] == 'e') num[i] = "14"; else if(str[i] == 'f') num[i] = "15"; else if(str[i] == 'g') num[i] = "16"; else if(str[i] == 'h') num[i] = "17"; else if(str[i] == 'i') num[i] = "18"; else if(str[i] == 'j') num[i] = "19"; else if(str[i] == 'k') num[i] = "20"; else if(str[i] == 'l') num[i] = "21"; else if(str[i] == 'm') num[i] = "22"; else if(str[i] == 'n') num[i] = "23"; else if(str[i] == 'o') num[i] = "24"; else if(str[i] == 'p') num[i] = "25"; else if(str[i] == 'q') num[i] = "26"; else if(str[i] == 'r') num[i] = "27"; else if(str[i] == 's') num[i] = "28"; else if(str[i] == 't') num[i] = "29"; else if(str[i] == 'u') num[i] = "30"; else if(str[i] == 'v') num[i] = "31"; else if(str[i] == 'w') num[i] = "32"; else if(str[i] == 'x') num[i] = "33"; else if(str[i] == 'y') num[i] = "34"; else if(str[i] == 'z') num[i] = "35"; else if(str[i] == 'A') num[i] = "36"; else if(str[i] == 'B') num[i] = "37"; else if(str[i] == 'C') num[i] = "38"; else if(str[i] == 'D') num[i] = "39"; else if(str[i] == 'E') num[i] = "40"; else if(str[i] == 'F') num[i] = "41"; else if(str[i] == 'G') num[i] = "42"; else if(str[i] == 'H') num[i] = "43"; else if(str[i] == 'I') num[i] = "44"; else if(str[i] == 'J') num[i] = "45"; else if(str[i] == 'K') num[i] = "46"; else if(str[i] == 'L') num[i] = "47"; else if(str[i] == 'M') num[i] = "48"; else if(str[i] == 'N') num[i] = "49"; else if(str[i] == 'O') num[i] = "50"; else if(str[i] == 'P') num[i] = "51"; else if(str[i] == 'Q') num[i] = "52"; else if(str[i] == 'R') num[i] = "53"; else if(str[i] == 'S') num[i] = "54"; else if(str[i] == 'T') num[i] = "55"; else if(str[i] == 'U') num[i] = "56"; else if(str[i] == 'V') num[i] = "57"; else if(str[i] == 'W') num[i] = "58"; else if(str[i] == 'X') num[i] = "59"; else if(str[i] == 'Y') num[i] = "60"; else if(str[i] == 'Z') num[i] = "61"; returnstr.append(num[i]); } return returnstr; } int main(){ /* * p q ：大素数 * n : p*q * m : (p - 1)(q - 1) * e : 𝑔𝑐𝑑(𝑒,m) = 1 （取e为40297） * 𝑑𝑒 ≡ 1 𝑚𝑜𝑑 m * 公钥 𝑃𝐾 = {𝑒, 𝑛}，私钥 𝑆𝐾 = {𝑑, 𝑛} * M :明文 C_pub：公钥加密密文 C_pv: 私钥加密密文 * M_pv: 私钥解密密文 M_pub: 公钥解密密文 */ mpz_t p, q, n, m, e, d, M, C_pub, C_pv, M_pub, M_pv, r; mpz_init(p); mpz_init(q); mpz_init(m); mpz_init(n); mpz_init_set_ui(e, 40297); mpz_init(d); mpz_init(M); mpz_init(C_pub); mpz_init(C_pv); mpz_init(M_pub); mpz_init(M_pv); mpz_init_set_str(r,"340282366920938463463374607431768211456",10); //2^128 gmp_randstate_t grt; gmp_randinit_default(grt); gmp_randseed_ui(grt, time(NULL)); do{ mpz_urandomb(p, grt, 1024);//随机生成一个0-2^1024的一个数 mpz_urandomb(q, grt, 1024); }while(mpz_cmp(p,r)<0 || mpz_cmp(q,r)< 0); //保证p q 不小于2^128 mpz_nextprime(p, p);//找到邻近的素数p mpz_nextprime(q, q);//找到邻近的素数q mpz_mul(n, p, q); //计算n=p*q mpz_sub_ui(p, p, 1);//p-1 mpz_sub_ui(q, q, 1);//q-1 mpz_mul(m, p, q);//m = (p-1)(q-1) mpz_invert(d, e, m);//计算d\ gmp_printf("%s %ZX\n\n", "p为:", p); gmp_printf("%s %ZX\n\n", "q为:", q); gmp_printf("%s %ZX\n\n", "n为:", n); gmp_printf("%s %ZX\n\n", "𝜙(𝑛)为:", m); gmp_printf("%s %ZX\n\n", "d为:", d); gmp_printf("%s %ZX\n\n", "e为:", e); char text[255] = ""; printf("请输入明文\n"); scanf("%[^\n]",&text); string retext = strToNum(text); // printf("%s \n",retext.c_str()); mpz_set_str(M, retext.c_str(), 10); gmp_printf("%s %ZX\n\n", "明文M转换后的十六进制表示为:", M); mpz_powm(C_pub, M, e, n); //计算公钥加密 C_pub=M^e mod n; gmp_printf("%s %ZX\n\n", "公钥加密结果C_pub为:", C_pub); mpz_powm(M_pv, C_pub, d, n); //计算私钥解密 M_pv=C_pub^d mod n; gmp_printf("%s %ZX\n\n","私钥解密结果M_pv为", M_pv); mpz_powm(C_pv, M, d, n); //计算私钥加密 C_pv=M^d mod n; gmp_printf("%s %ZX\n\n", "私钥加密结果C_pv为:", C_pv); mpz_powm(M_pub, C_pv, e, n); //计算公钥解密 M_pub=C_pv^e mod n; gmp_printf("%s %ZX\n\n","公钥解密结果M_pub为", M_pub); }