C语言实现RSA算法加解密

使用c语言实现了RSA加解密算法，可以加解密文件和字符串。

rsa算法原理

• 选择两个大素数p和q；
• 计算n = p * q;
• 计算φ(n)=(p-1)(q-1)；
• 选择与φ(n)互素的整数d；
• 由de=1 mod φ(n)计算得到e；
• 公钥是(e, n), 私钥是(d, n);
• 假设明文是M（一个整数），则密文C =??mod n，此为加密过程；
• 解密过程为M =??mod n;

rsa.h

#pragma once
#include <iostream>
#include <fstream>
#include <tommath.h>
#include <time.h>
#include <Windows.h>
#include <string>

#define SUBKEY_LENGTH 78  //  >512 bit

#define FILE_NAME_LENGTH 99

#define PLAINTEXT_LENGTH 64

#define BINARY_LENGTH 512

using namespace std;



void initial();

int Get_char_bit(char c, int pos);

void Create_prime_number(mp_int *number);

void Generate_key(char *key_name);

void Write_key_2_File(char *file_name, mp_int *key, mp_int *n);

void ADD_0(char *binary, int mode);

void rsa_decrypt(char *src, char *dst, char *key_name, int mode);

void rsa_encrypt(char *src, char *dst, char *key_name, int mode);

void mp_print(mp_int *number);

void Get_key_from_file(mp_int *key, mp_int *n, char *key_name, int mode);

void Create_number(mp_int *number, int mode);

int Miller_rabin(mp_int *number);

void Char_2_binary(char *text, char *binary, int len);

void Binary_2_char(char *binary, char *text, int binary_len);

void quick_pow(mp_int *a, mp_int *b, mp_int *c, mp_int *d);

int Get_file_length(char *filename);

rsa.cpp

#include "rsa.h"

mp_int two;
mp_int five;
mp_int zero;
mp_int one;



int Get_char_bit(char c, int pos)
{
	return ((c >> (7 - pos)) & 1);
}



// mode 0: number of n digits
// mode 1: 2 <= number <= n - 2  for miller rabin test
void Create_number(mp_int *number, int mode)
{
	int i;
	
	srand((unsigned)time(NULL));

	char temp_number[SUBKEY_LENGTH + 1];

	temp_number[0] = rand() % 9 + 1 + 48;

	if (0 == mode)
	{
		int temp;
		for (i = 1; i <= SUBKEY_LENGTH - 2; i++)
			temp_number[i] = rand() % 10 + 48;

		temp = rand() % 10;
		if (0 == temp % 2)
			temp++;

		if (5 == temp)
			temp = 7;

		temp_number[SUBKEY_LENGTH - 1] = temp + 48;

		temp_number[SUBKEY_LENGTH] = '\0';
	}
	else if (1 == mode)
	{
		int digit = rand() % (SUBKEY_LENGTH - 2) + 2;

		for (i = 1; i <= digit - 1; i++)
			temp_number[i] = rand() % 10 + 48;

		temp_number[digit] = '\0';
	}

	mp_read_radix(number, temp_number, 10);
}



int Miller_rabin(mp_int *number)
{
	int result;
	mp_int base;
	mp_init_size(&base, SUBKEY_LENGTH);
	
	Create_number(&base, 1);

	mp_prime_miller_rabin(number, &base, &result);

	mp_clear(&base);

	return result;
}



void Create_prime_number(mp_int *number)
{
	mp_int r;
	mp_init(&r);

	int time = 100;
	int result;
	int i;

	Create_number(number, 0);

	while (1)
	{
		mp_prime_is_divisible(number, &result);

		if (0 != result)
		{
			do
			{
				mp_add(number, &two, number);
				mp_mod(number, &five, &r);
			} while (MP_EQ == mp_cmp_mag(&zero, &r));

			continue;
		}

		for (i = 0; i < time; i++)
		{
			if (!Miller_rabin(number))
				break;
		}

		if (i == time)
			return;
		else
		{
			do
			{
				mp_add(number, &two, number);
				mp_mod(number, &five, &r);
			} while (MP_EQ == mp_cmp_mag(&zero, &r));
		}
	}
}



void Generate_key(char *key_name)
{
	mp_int p, q, n, f, e, d;

	mp_init_size(&p, SUBKEY_LENGTH);
	mp_init_size(&q, SUBKEY_LENGTH);
	mp_init_size(&n, SUBKEY_LENGTH * 2);
	mp_init_size(&f, SUBKEY_LENGTH * 2);
	mp_init_size(&d, SUBKEY_LENGTH * 2);
	mp_init_size(&e, SUBKEY_LENGTH * 2);

	Create_prime_number(&p);
	Sleep(1000);
	Create_prime_number(&q);

	mp_mul(&p, &q, &n);

	mp_sub(&p, &one, &p);
	mp_sub(&q, &one, &q);

	mp_mul(&p, &q, &f);

	mp_set_int(&d, 127);

	mp_int gcd;
	mp_init_size(&gcd, SUBKEY_LENGTH * 2);

	do
	{
		mp_add(&d, &two, &d);
		mp_gcd(&d, &f, &gcd);
	} while (MP_EQ != mp_cmp_mag(&gcd, &one));

	mp_invmod(&d, &f, &e);

	char PUBLIC_KEY[FILE_NAME_LENGTH] = "d:\\public_key_";
	char PRIVATE_KEY[FILE_NAME_LENGTH] = "d:\\private_key_";


	strcat(PUBLIC_KEY, key_name);
	strcat(PRIVATE_KEY, key_name);

	Write_key_2_File(PUBLIC_KEY, &d, &n);
	Write_key_2_File(PRIVATE_KEY, &e, &n);

	mp_clear_multi(&p, &q, &e, &d, &f, &n, &gcd, NULL);
}



void initial()
{
	mp_init_set_int(&two, 2);
	mp_init_set_int(&five, 5);
	mp_init_set_int(&zero, 0);
	mp_init_set_int(&one, 1);
}



void Write_key_2_File(char *file_name, mp_int *key, mp_int *n)
{
	remove(file_name);
	FILE *fp = fopen(file_name, "w+");

	if (NULL == fp)
	{
		cout << "open file error!" << endl;
		return;
	}

	char key_str[SUBKEY_LENGTH * 2 + 1];
	char n_str[SUBKEY_LENGTH * 2 + 1];

	mp_toradix(key, key_str, 10);
	mp_toradix(n, n_str, 10);

	fprintf(fp, "%s\n", n_str);
	fprintf(fp, "%s", key_str);

	fclose(fp);
}



void mp_print(mp_int *number)
{
	char str[SUBKEY_LENGTH * 2 + 1];
	mp_toradix(number, str, 10);
	cout << str << endl;
}



// mode 0: get public key
// mode 1: get private key

void Get_key_from_file(mp_int *key, mp_int *n, char *key_name, int mode)
{
	FILE *fp = NULL;

	char PUBLIC_KEY[FILE_NAME_LENGTH] = "";
	char PRIVATE_KEY[FILE_NAME_LENGTH] = "";


	if (0 == mode)
	{
		strcat(PUBLIC_KEY, key_name);
		fp = fopen(PUBLIC_KEY, "r+");
	}
	else if (1 == mode)
	{
		strcat(PRIVATE_KEY, key_name);
		fp = fopen(PRIVATE_KEY, "r+");
	}


	if (NULL == fp)
	{
		cout << "open file error!" << endl;
		return;
	}

	char key_str[SUBKEY_LENGTH * 2 + 1];
	char n_str[SUBKEY_LENGTH * 2 + 1];

	fscanf(fp, "%s\n", n_str);
	fscanf(fp, "%s", key_str);

	mp_read_radix(n, n_str, 10);
	mp_read_radix(key, key_str, 10);

	fclose(fp);
}



void Char_2_binary(char *text, char *binary, int len)
{
	int i;
	int j;
	int k = 0;
	for (i = 0; i <= len - 1; i++)
	{
		for (j = 0; j <= 7; j++)
			binary[k++] = Get_char_bit(text[i], j) + '0';
	}

	binary[k] = '\0';
}



void Binary_2_char(char *binary, char *text, int binary_len)
{
	int i;
	int j = 0;
	int k = 0;
	int sum = 0;

	for (i = 0; i <= binary_len - 1; i++)
	{
		sum = sum + pow(2, 7 - j)*(int)((binary[i]) - '0');
		j++;

		if (8 == j)
		{
			text[k++] = sum;
			sum = 0;
			j = 0;
		}
	}
}



// mode 0: encrypt char*
// mode 1: encrypt file
void rsa_encrypt(char *src, char *dst, char *key_name, int mode)
{
	mp_int n;
	mp_int public_key;
	mp_int plain_number;
	mp_int cipher_number;

	mp_init_size(&n, SUBKEY_LENGTH * 2);
	mp_init_size(&public_key, SUBKEY_LENGTH * 2);
	mp_init_size(&plain_number, SUBKEY_LENGTH * 2);
	mp_init_size(&cipher_number, SUBKEY_LENGTH * 2);

	Get_key_from_file(&public_key, &n, key_name, 0);

	char plain_text[PLAINTEXT_LENGTH + 1];
	char cipher_text[PLAINTEXT_LENGTH + 2];

	char plain_binary[BINARY_LENGTH + 1];
	char cipher_binary[BINARY_LENGTH + 9];

	int i;
	int j;
	int k;
	int l;

	if (0 == mode)
	{
		int round = ceil(strlen(src) / 64.0);
		
		for (i = 0; i < round; i++)
		{
			for (l = 0; l <= BINARY_LENGTH; l++)
				plain_binary[l] = '\0';

			for (l = 0; l <= BINARY_LENGTH + 8; l++)
				cipher_binary[l] = '\0';

			for (l = 0; l <= PLAINTEXT_LENGTH; l++)
				plain_text[l] = '\0';

			for (l = 0; l <= PLAINTEXT_LENGTH + 1; l++)
				cipher_text[l] = '\0';

			for (j = 0; j <= PLAINTEXT_LENGTH - 1; j++)
			{
				plain_text[j] = src[i * PLAINTEXT_LENGTH + j];

				if ('\0' == plain_text[j])
				{
					for (k = j + 1; k <= PLAINTEXT_LENGTH - 1; k++)
						plain_text[k] = '\0';
					break;
				}
			}

			plain_text[PLAINTEXT_LENGTH] = '\0';

			Char_2_binary(plain_text, plain_binary, PLAINTEXT_LENGTH);

			mp_zero(&plain_number);
			mp_read_radix(&plain_number, plain_binary, 2);

			mp_zero(&cipher_number);

			// ----------------------------------------------------------------
			mp_exptmod(&plain_number, &public_key, &n, &cipher_number);

			//quick_pow(&plain_number, &public_key, &n, &cipher_number);
			// ----------------------------------------------------------------

			mp_toradix(&cipher_number, cipher_binary, 2);

			ADD_0(cipher_binary, 0);

			Binary_2_char(cipher_binary, cipher_text, BINARY_LENGTH + 8);

			for (l = 0; l <= PLAINTEXT_LENGTH; l++)
				dst[i*(PLAINTEXT_LENGTH + 1) + l] = cipher_text[l];
		}
		
		dst[round * (PLAINTEXT_LENGTH + 1)] = '\0';

		mp_clear_multi(&n, &public_key, &plain_number, &cipher_number, NULL);

	}
	else if (1 == mode)
	{
		ifstream fin;
		ofstream fout;
			
		fin.open(src, ios::binary);
		fout.open(dst, ios::binary);

		char ch;

		int i = 0;
		int len = Get_file_length(src) % 64;
		fout << len << endl;

		while (1)
		{
			fin.get(ch);
			plain_text[i++] = ch;

			if (i == PLAINTEXT_LENGTH || fin.eof())
			{
				if (i == PLAINTEXT_LENGTH)
					plain_text[i] = '\0';
				else
				{
					for (k = i - 1; k <= PLAINTEXT_LENGTH; k++)
						plain_text[k] = '\0';
				}
				
				for (l = 0; l <= BINARY_LENGTH; l++)
					plain_binary[l] = '\0';

				for (l = 0; l <= BINARY_LENGTH + 8; l++)
					cipher_binary[l] = '\0';

				for (l = 0; l <= PLAINTEXT_LENGTH + 1; l++)
					cipher_text[l] = '\0';

				Char_2_binary(plain_text, plain_binary, PLAINTEXT_LENGTH);

				mp_zero(&plain_number);
				mp_read_radix(&plain_number, plain_binary, 2);

				mp_zero(&cipher_number);

				// ----------------------------------------------------------------
				mp_exptmod(&plain_number, &public_key, &n, &cipher_number);

				//quick_pow(&plain_number, &public_key, &n, &cipher_number);
				// ----------------------------------------------------------------

				mp_toradix(&cipher_number, cipher_binary, 2);

				ADD_0(cipher_binary, 0);

				Binary_2_char(cipher_binary, cipher_text, BINARY_LENGTH + 8);

				for (l = 0; l <= PLAINTEXT_LENGTH; l++)
					fout << cipher_text[l];

				for (l = 0; l <= PLAINTEXT_LENGTH; l++)
					plain_text[l] = '\0';

				i = 0;
			}

			if (fin.eof())
				break;
		}

		fin.close();
		fout.close();

		mp_clear_multi(&n, &public_key, &plain_number, &cipher_number, NULL);
	}
}



// mode 0: for encrypt
// mode 1: for decrypt
void ADD_0(char *binary, int mode)
{
	int i;
	int difference;

	if (0 == mode)
		difference = BINARY_LENGTH + 8 - strlen(binary);
	else if(1 == mode)
		difference = BINARY_LENGTH - strlen(binary);;
	
	for (i = strlen(binary); i >= 0; i--)
		binary[i + difference] = binary[i];
	for (i = 0; i < difference; i++)
		binary[i] = '0';
}



// mode 0: decrypt char*
// mode 1: decrypt file
void rsa_decrypt(char *src, char *dst, char *key_name, int mode)
{
	mp_int n;
	mp_int private_key;
	mp_int plain_number;
	mp_int cipher_number;

	mp_init_size(&n, SUBKEY_LENGTH * 2);
	mp_init_size(&private_key, SUBKEY_LENGTH * 2);
	mp_init_size(&plain_number, SUBKEY_LENGTH * 2);
	mp_init_size(&cipher_number, SUBKEY_LENGTH * 2);

	Get_key_from_file(&private_key, &n, key_name, 1);

	char plain_text[PLAINTEXT_LENGTH + 1];
	char cipher_text[PLAINTEXT_LENGTH + 2];

	char plain_binary[BINARY_LENGTH + 1];
	char cipher_binary[BINARY_LENGTH + 9];

	int j;
	int k;
	int l;

	if (0 == mode)
	{
		k = -1;
		do
		{
			k++;

			for (l = 0; l <= PLAINTEXT_LENGTH; l++)
				plain_text[l] = '\0';

			for (l = 0; l <= BINARY_LENGTH; l++)
				plain_binary[l] = '\0';

			for (l = 0; l <= BINARY_LENGTH + 8; l++)
				cipher_binary[l] = '\0';

			for (j = 0; j <= PLAINTEXT_LENGTH; j++)
				cipher_text[j] = src[k * (PLAINTEXT_LENGTH + 1) + j];

			cipher_text[PLAINTEXT_LENGTH + 1] = '\0';

			Char_2_binary(cipher_text, cipher_binary, PLAINTEXT_LENGTH + 1);

			mp_zero(&cipher_number);

			mp_read_radix(&cipher_number, cipher_binary, 2);

			mp_zero(&plain_number);

			// ----------------------------------------------------------------
			mp_exptmod(&cipher_number, &private_key, &n, &plain_number);

			//quick_pow(&cipher_number, &private_key, &n, &plain_number);
			// ----------------------------------------------------------------

			mp_toradix(&plain_number, plain_binary, 2);

			ADD_0(plain_binary, 1);

			Binary_2_char(plain_binary, plain_text, BINARY_LENGTH);

			for (l = 0; l <= PLAINTEXT_LENGTH - 1; l++) 
				dst[k*PLAINTEXT_LENGTH + l] = plain_text[l];
		
		} while ('\0' != src[(k + 1)*(PLAINTEXT_LENGTH + 1)]);

		dst[(k + 1) * PLAINTEXT_LENGTH] = '\0';
	}
	else if (1 == mode)
	{
		ifstream fin;
		ofstream fout;

		fin.open(src, ios::binary);
		fout.open(dst, ios::binary);

		int i = 0;

		int limit = PLAINTEXT_LENGTH;

		char ch;

		string temp = "";
		while (1)
		{
			fin.get(ch);
			if ('\n' == ch)
				break;
			temp += ch;
		}

		int len = atoi(temp.c_str());

		while (1)
		{
			fin.get(ch);
			cipher_text[i++] = ch;

			if (i == PLAINTEXT_LENGTH + 1)
			{
				if (i == PLAINTEXT_LENGTH + 1) 
					cipher_text[i] = '\0';
				else
					cipher_text[i - 1] = '\0';

				for (l = 0; l <= BINARY_LENGTH + 8; l++)
					cipher_binary[l] = '\0';

				for (l = 0; l <= PLAINTEXT_LENGTH; l++)
					plain_text[l] = '\0';

				for (l = 0; l <= BINARY_LENGTH; l++)
					plain_binary[l] = '\0';

				Char_2_binary(cipher_text, cipher_binary, PLAINTEXT_LENGTH + 1);

				mp_zero(&cipher_number);
				mp_read_radix(&cipher_number, cipher_binary, 2);

				mp_zero(&plain_number);

				// ----------------------------------------------------------------
				mp_exptmod(&cipher_number, &private_key, &n, &plain_number);

				//quick_pow(&cipher_number, &private_key, &n, &plain_number);
				// ----------------------------------------------------------------

				mp_toradix(&plain_number, plain_binary, 2);

				ADD_0(plain_binary, 1);

				Binary_2_char(plain_binary, plain_text, BINARY_LENGTH);
				
				if (fin.peek() == EOF)
					limit = len;

				for (l = 0; l < limit; l++)
					fout << plain_text[l];

				for (l = 0; l <= PLAINTEXT_LENGTH + 1; l++)
					cipher_text[l] = '\0';

				i = 0;
			}
			
			if (fin.eof())
				break;
		}

		fin.close();
		fout.close();
	}

	mp_clear_multi(&n, &private_key, &plain_number, &cipher_number, NULL);
}



// compute d = a ^ b (mod c)
void quick_pow(mp_int *a, mp_int *b, mp_int *c, mp_int *d)
{
	mp_int temp;
	mp_int temp_a;
	mp_int temp_b;

	mp_init_size(&temp, SUBKEY_LENGTH * 2);
	mp_init_size(&temp_a, SUBKEY_LENGTH * 2);
	mp_init_size(&temp_b, SUBKEY_LENGTH * 2);

	mp_copy(a, &temp_a);
	mp_copy(b, &temp_b);

	mp_set_int(d, 1);

	mp_mod(&temp_a, c, &temp_a);

	while (MP_GT == mp_cmp(&temp_b, &zero))
	{
		mp_mod(&temp_b, &two, &temp);
		if (MP_EQ == mp_cmp(&one, &temp))
		{
			mp_mul(d, &temp_a, d);
			mp_mod(d, c, d);
		}

		mp_div_2(&temp_b, &temp_b);

		mp_mul(&temp_a, &temp_a, &temp_a);
		mp_mod(&temp_a, c, &temp_a);
	}

	mp_clear_multi(&temp, &temp_a, &temp_b, NULL);
}

int Get_file_length(char *filename) 
{
	FILE *fp = fopen(filename, "rb");
	if (NULL == fp)
		return -1;

	fseek(fp, 0, SEEK_END);

	int temp = ftell(fp);

	fclose(fp);
	return temp;
}

main.h

#pragma once
#include "rsa.h"

?main.cpp

#include "main.h"


// example
void main()
{
	initial();

	// generate key belong to arg " "
	Generate_key("hello_world");
	

	// ----------------------example: encrypt char* ---------------------------
	char a[200] = "to_be_or_not_to_be_it_is_a_question";
	char b[400];
	char c[200];

	//rsa_encrypt(a, b, "hello_world", 0);
	//rsa_decrypt(b, c, "hello_world", 0);
	
	cout << "c: " << c << endl;
	// ------------------------------------------------------------------------


	// ----------------------example: encrypt file ----------------------------

	rsa_encrypt("d:\\a.gif", "d:\\m", "d:\\public_key_hello_world", 1);

    rsa_decrypt("d:\\m", "D:\\b.gif", "d:\\private_key_hello_world", 1);

	// ------------------------------------------------------------------------

}