我写过这个成功加密的程序。解密消息。然后我添加了代码，看看是否有另一个私钥与同一个公钥配对，事情变得令人满意。
无论如何，代码将显示所有内容。感谢您查看我的问题。
我期待我刚刚生成的公钥加密的消息，在下面的代码中，我能够通过我生成的唯一私钥解密。但在成功解密消息后，我得到了另一个可以解密消息的私钥。
我认为只是阅读代码会更容易理解我，对于缺乏细节感到遗憾。我不知道发生了什么。
如果公钥加密消息可以被许多其他私钥解密，那么为什么这种算法是安全的？
// Module
// System
#include <stdio.h>
#include <stdlib.h>
#include <unistd.h>
#include <limits.h>
#include <errno.h>
#include <string.h>
#include <time.h>
#include <math.h>
#include <gmp.h>
// sys
#include <sys/time.h>
#include <sys/file.h>
// Homemade
#include "/root/01_Code/03_C/00_Module/output_option.h"
//
// main()
int main(void){
// Value
// Basic
long Loop [1];
time_t Seed;
long Level = 8;
gmp_randstate_t Random_State; gmp_randinit_default(Random_State);
// RSA
mpz_t Buffer_mpz_1; mpz_init(Buffer_mpz_1);
mpz_t Buffer_mpz_2; mpz_init(Buffer_mpz_2);
mpz_t Prime_1; mpz_init(Prime_1);
mpz_t Prime_2; mpz_init(Prime_2);
mpz_t Phi; mpz_init(Phi);
mpz_t Common_Key; mpz_init(Common_Key);
mpz_t Public_Key; mpz_init(Public_Key);
mpz_t Private_Key; mpz_init(Private_Key);
// Implementation
// RSA init
// Prime_1
sleep(1);
time(&Seed);
gmp_randseed_ui(Random_State, Seed);
mpz_urandomb(Prime_1, Random_State, Level);
while(mpz_probab_prime_p(Prime_1, 49) != 2)
mpz_add_ui(Prime_1, Prime_1, 1);
// Prime_2
sleep(1);
time(&Seed);
gmp_randseed_ui(Random_State, Seed);
mpz_urandomb(Prime_2, Random_State, Level);
while(mpz_probab_prime_p(Prime_2, 49) != 2)
mpz_add_ui(Prime_2, Prime_2, 1);
// Phi
mpz_sub_ui(Phi, Prime_1, 1);
mpz_sub_ui(Buffer_mpz_1, Prime_2, 1);
mpz_mul( Phi, Phi, Buffer_mpz_1);
// Common_Key
mpz_mul(Common_Key, Prime_1, Prime_2);
//
// Public_Key
// Init random Public_Key
do{
sleep(1);
time(&Seed);
gmp_randseed_ui(Random_State, Seed);
mpz_urandomb(Public_Key, Random_State, Level);
}while(mpz_cmp(Public_Key, Phi) >= 0 || mpz_cmp_ui(Public_Key, 1) == 0);
mpz_set(Buffer_mpz_2, Public_Key);
// Pick Public_Key
while(1){
if(mpz_cmp(Public_Key, Phi) < 0){
mpz_gcd(Buffer_mpz_1, Public_Key, Phi);
if(mpz_cmp_ui(Buffer_mpz_1, 1) == 0) break;
mpz_add_ui(Public_Key, Public_Key, 1);
}else{
mpz_set(Public_Key, Buffer_mpz_2);
while(1){
mpz_sub_ui(Public_Key, Public_Key, 1);
if(mpz_cmp_ui(Public_Key, 1) == 0){
printf("%d\n", __LINE__);
mpz_clear(Buffer_mpz_1);
mpz_clear(Buffer_mpz_2);
mpz_clear(Prime_1);
mpz_clear(Prime_2);
mpz_clear(Phi);
mpz_clear(Common_Key);
mpz_clear(Public_Key);
mpz_clear(Private_Key);
return 1;
}
mpz_gcd(Buffer_mpz_1, Public_Key, Phi);
if(mpz_cmp_ui(Buffer_mpz_1, 1) == 0) goto l_END_PK;
}
}
}
l_END_PK:;
// Private_Key
mpz_set_ui(Buffer_mpz_1, 1);
mpz_set_ui(Private_Key, 2); char Switch = 'V';
l_AGAIN:do{
mpz_add_ui(Private_Key, Private_Key, 1);
mpz_mul(Buffer_mpz_1, Public_Key, Private_Key);
mpz_mod(Buffer_mpz_1, Buffer_mpz_1, Phi);
}while(mpz_cmp_ui(Buffer_mpz_1, 1) != 0);
if(Switch == 'V'){
Switch = 'X';
mpz_set(Buffer_mpz_2, Private_Key);
goto l_AGAIN;
}
// Encrypt & Decrypt
mpz_set_ui(Buffer_mpz_1, 88);
mpz_powm(Buffer_mpz_1, Buffer_mpz_1, Public_Key, Common_Key);
mpz_powm(Buffer_mpz_1, Buffer_mpz_1, Private_Key, Common_Key);
gmp_printf("Prime_1 %Zd\n", Prime_1);
gmp_printf("Prime_2 %Zd\n", Prime_2);
gmp_printf("Public_Key %Zd\n", Public_Key);
gmp_printf("Private_Key %Zd\n", Private_Key);
gmp_printf("Common_Key %Zd\n", Common_Key);
gmp_printf("Decrypted %Zd\n", Buffer_mpz_1);
printf("----------------------------------------------------\n");
mpz_set_ui(Buffer_mpz_1, 88);
mpz_powm(Buffer_mpz_1, Buffer_mpz_1, Public_Key, Common_Key);
mpz_powm(Buffer_mpz_1, Buffer_mpz_1, Buffer_mpz_2, Common_Key);
gmp_printf("Prime_1 %Zd\n", Prime_1);
gmp_printf("Prime_2 %Zd\n", Prime_2);
gmp_printf("Public_Key %Zd\n", Public_Key);
gmp_printf("Private_Key %Zd\n", Buffer_mpz_2);
gmp_printf("Common_Key %Zd\n", Common_Key);
gmp_printf("Decrypted %Zd\n", Buffer_mpz_1);
// Clean up
mpz_clear(Buffer_mpz_1);
mpz_clear(Buffer_mpz_2);
mpz_clear(Prime_1);
mpz_clear(Prime_2);
mpz_clear(Phi);
mpz_clear(Common_Key);
mpz_clear(Public_Key);
mpz_clear(Private_Key);
return 0;
}