My code is here
//RSA.cpp
#include <iostream>
#include <cstring>
#include <ctime>
#include <random>
#include <vector>
#include <string>
#include "BigNum.hpp"
using namespace std;
BigNum mygcd(BigNum a, BigNum b)
{
while(a != b)
{
if(a>b)
{
a = a - b;
}
else
{
b = b - a;
}
}
return a;
}
BigNum prime(int n)
{
vector<BigNum> ans;
ans.push_back(BigNum(2));
ans.push_back(BigNum(3));
for (int i = 0; i < n; i++)
{
BigNum addend = 1;
for (auto j : ans)
{
addend = addend * j;
}
ans.push_back(addend + 1);
}
return ans[ans.size() - 1];
}
BigNum exgcd(BigNum a, BigNum b, BigNum &x, BigNum &y)
{
if (b == 0)
{
x = 1, y = 0;
return a;
}
BigNum g = exgcd(b, a - (a / b) * b, x, y);
BigNum t;
t = x;
x = y;
y = t - a / b * y;
return g;
}
BigNum niyuan(BigNum a, BigNum b)
{
BigNum x, y;
BigNum aa = exgcd(a, b, x, y);
return (x + b) - ((x + b) / b) * b;
}
vector<BigNum> yinshu(BigNum n)
{
vector<BigNum> ans;
int a = 2;
while (n / 2 > a)
{
if (n % a == 0)
{
ans.push_back(a);
}
a++;
}
return ans;
}
vector<int> ToBit(BigNum obj){
vector<int> r;
while (obj != 0){
r.push_back( (obj - (obj / 2) * 2 == 0) ? 0 : 1 );
obj = obj / 2;
}
return r;
}
BigNum jiami(BigNum e, int i, BigNum n)
{
BigNum addend = i;
BigNum result = 1;
vector<int>bitE = ToBit(e);
int now = 0;
while (now != bitE.size())
{ //将e二进制展开（其实就是使用位运算和右移运算）
if (bitE[now])
{
result = addend * result;
result = result - (result / n) * n;
}
addend = addend * addend;
now = now + 1;
}
return result;
}
BigNum jiemi(BigNum d, BigNum i, BigNum n)
{
BigNum addend = i;
BigNum result = 1;
vector<int>bitD = ToBit(d);
int now = 0;
while (now != bitD.size())
{
if (bitD[now])
{
result = addend * result;
result = result - (result / n) * n;
}
addend = addend * addend;
now = now + 1;
}
return result;
}
int main()
{
srand(time(0));
BigNum p = prime(rand() % 20 + 1);
srand(time(0));
BigNum q = prime(rand() % 20 + 1);
BigNum N = p * q;
BigNum r = (p - 1) * (q - 1);
sss:
srand(time(0));
BigNum e = random() + 2;
if (mygcd(e, r) - BigNum(1) > 0)
goto sss;
vector<BigNum> yinshus = yinshu(r);
BigNum d = BigNum(niyuan(e, r));
cout << "Alice send(" << N << ',' << e << ")to Bob" << endl;
cout << "Please input your massage:";
string m;
cin >> m;
vector<int> message;
for (auto i : m)
{
message.push_back((int)i);
}
vector<BigNum> miwen;
for (auto i : message)
{
miwen.push_back(jiami(e, i, N));
}
cout << "coded text：";
for (auto i : miwen)
{
cout << i << " ";
}
vector<BigNum> minwen;
for (auto i : miwen)
{
minwen.push_back(jiemi(d, i, N));
}
cout << "明文：";
for (auto i : minwen)
{
cout << i << " ";
}
cout << endl;
}
I used a self-defined data structure called BigNum in order to store some large integers without them overflowing.
//BigNum.hpp
#include <iostream>
#include <cstring>
#include <string>
#include <iomanip>
#include <algorithm>
using namespace std;
#define MAXN 9999
#define MAXSIZE 10
#define DLEN 4
class BigNum
{
private:
int a[999]; //可以控制大数的位数
int len; //大数长度
public:
BigNum()
{
len = 1;
memset(a, 0, sizeof(a));
} //构造函数
BigNum(const int); //将一个int类型的变量转化为大数
BigNum(const char *); //将一个字符串类型的变量转化为大数
BigNum(const BigNum &); //拷贝构造函数
BigNum &operator=(const BigNum &); //重载赋值运算符，大数之间进行赋值运算
friend istream &operator>>(istream &, BigNum &); //重载输入运算符
friend ostream &operator<<(ostream &, BigNum &); //重载输出运算符
BigNum operator+(const BigNum &) const; //重载加法运算符，两个大数之间的相加运算
BigNum operator-(const BigNum &) const; //重载减法运算符，两个大数之间的相减运算
BigNum operator*(const BigNum &) const; //重载乘法运算符，两个大数之间的相乘运算
BigNum operator/(const int &) const; //重载除法运算符，大数对一个整数进行相除运算
BigNum operator/(const BigNum &) const;
BigNum operator^(const int &) const; //大数的n次方运算
int operator%(const int &) const; //大数对一个int类型的变量进行取模运算
bool operator>(const BigNum &T) const; //大数和另一个大数的大小比较
bool operator>(const int &t) const; //大数和一个int类型的变量的大小比较
bool operator<(const BigNum &) const;
bool operator<=(const BigNum &) const;
bool operator>=(const BigNum &) const;
bool operator==(const BigNum &) const;
bool operator!=(const BigNum &) const;
void print(); //输出大数
};
BigNum::BigNum(const int b) //将一个int类型的变量转化为大数
{
int c, d = b;
len = 0;
memset(a, 0, sizeof(a));
while (d > MAXN)
{
c = d - (d / (MAXN + 1)) * (MAXN + 1);
d = d / (MAXN + 1);
a[len++] = c;
}
a[len++] = d;
}
BigNum::BigNum(const char *s) //将一个字符串类型的变量转化为大数
{
int t, k, index, l, i;
memset(a, 0, sizeof(a));
l = strlen(s);
len = l / DLEN;
if (l % DLEN)
len++;
index = 0;
for (i = l - 1; i >= 0; i -= DLEN)
{
t = 0;
k = i - DLEN + 1;
if (k < 0)
k = 0;
for (int j = k; j <= i; j++)
t = t * 10 + s[j] - '0';
a[index++] = t;
}
}
BigNum::BigNum(const BigNum &T) : len(T.len) //拷贝构造函数
{
int i;
memset(a, 0, sizeof(a));
for (i = 0; i < len; i++)
a[i] = T.a[i];
}
BigNum &BigNum::operator=(const BigNum &n) //重载赋值运算符，大数之间进行赋值运算
{
int i;
len = n.len;
memset(a, 0, sizeof(a));
for (i = 0; i < len; i++)
a[i] = n.a[i];
return *this;
}
istream &operator>>(istream &in, BigNum &b) //重载输入运算符
{
char ch[MAXSIZE * 4];
int i = -1;
in >> ch;
int l = strlen(ch);
int count = 0, sum = 0;
for (i = l - 1; i >= 0;)
{
sum = 0;
int t = 1;
for (int j = 0; j < 4 && i >= 0; j++, i--, t *= 10)
{
sum += (ch[i] - '0') * t;
}
b.a[count] = sum;
count++;
}
b.len = count++;
return in;
}
ostream &operator<<(ostream &out, BigNum &b) //重载输出运算符
{
int i;
cout << b.a[b.len - 1];
for (i = b.len - 2; i >= 0; i--)
{
cout.width(DLEN);
cout.fill('0');
cout << b.a[i];
}
return out;
}
BigNum BigNum::operator+(const BigNum &T) const //两个大数之间的相加运算
{
BigNum t(*this);
int i, big; //位数
big = T.len > len ? T.len : len;
for (i = 0; i < big; i++)
{
t.a[i] += T.a[i];
if (t.a[i] > MAXN)
{
t.a[i + 1]++;
t.a[i] -= MAXN + 1;
}
}
if (t.a[big] != 0)
t.len = big + 1;
else
t.len = big;
return t;
}
BigNum BigNum::operator-(const BigNum &T) const //两个大数之间的相减运算
{
int i, j, big;
bool flag;
BigNum t1, t2;
if (*this > T)
{
t1 = *this;
t2 = T;
flag = 0;
}
else
{
t1 = T;
t2 = *this;
flag = 1;
}
big = t1.len;
for (i = 0; i < big; i++)
{
if (t1.a[i] < t2.a[i])
{
j = i + 1;
while (t1.a[j] == 0)
j++;
t1.a[j--]--;
while (j > i)
t1.a[j--] += MAXN;
t1.a[i] += MAXN + 1 - t2.a[i];
}
else
t1.a[i] -= t2.a[i];
}
t1.len = big;
while (t1.a[t1.len - 1] == 0 && t1.len > 1)
{
t1.len--;
big--;
}
if (flag)
t1.a[big - 1] = 0 - t1.a[big - 1];
return t1;
}
BigNum BigNum::operator*(const BigNum &T) const //两个大数之间的相乘运算
{
BigNum ret;
int i, j, up;
int temp, temp1;
for (i = 0; i < len; i++)
{
up = 0;
for (j = 0; j < T.len; j++)
{
temp = a[i] * T.a[j] + ret.a[i + j] + up;
if (temp > MAXN)
{
temp1 = temp - temp / (MAXN + 1) * (MAXN + 1);
up = temp / (MAXN + 1);
ret.a[i + j] = temp1;
}
else
{
up = 0;
ret.a[i + j] = temp;
}
}
if (up != 0)
ret.a[i + j] = up;
}
ret.len = i + j;
while (ret.a[ret.len - 1] == 0 && ret.len > 1)
ret.len--;
return ret;
}
BigNum BigNum::operator/(const int &b) const //大数对一个整数进行相除运算
{
BigNum ret;
int i, down = 0;
for (i = len - 1; i >= 0; i--)
{
ret.a[i] = (a[i] + down * (MAXN + 1)) / b;
down = a[i] + down * (MAXN + 1) - ret.a[i] * b;
}
ret.len = len;
while (ret.a[ret.len - 1] == 0 && ret.len > 1)
ret.len--;
return ret;
}
int BigNum::operator%(const int &b) const //大数对一个int类型的变量进行取模运算
{
int i, d = 0;
for (i = len - 1; i >= 0; i--)
{
d = ((d * (MAXN + 1)) % b + a[i]) % b;
}
return d;
}
BigNum BigNum::operator^(const int &n) const //大数的n次方运算
{
BigNum t, ret(1);
int i;
if (n < 0)
exit(-1);
if (n == 0)
return 1;
if (n == 1)
return *this;
int m = n;
while (m > 1)
{
t = *this;
for (i = 1; i << 1 <= m; i <<= 1)
{
t = t * t;
}
m -= i;
ret = ret * t;
if (m == 1)
ret = ret * (*this);
}
return ret;
}
bool BigNum::operator>(const BigNum &T) const //大数和另一个大数的大小比较
{
int ln;
if (len > T.len)
return true;
else if (len == T.len)
{
ln = len - 1;
while (a[ln] == T.a[ln] && ln >= 0)
ln--;
if (ln >= 0 && a[ln] > T.a[ln])
return true;
else
return false;
}
else
return false;
}
bool BigNum::operator>(const int &t) const //大数和一个int类型的变量的大小比较
{
BigNum b(t);
return *this > b;
}
void BigNum::print() //输出大数
{
int i;
cout << a[len - 1];
for (i = len - 2; i >= 0; i--)
{
cout.width(DLEN);
cout.fill('0');
cout << a[i];
}
cout << endl;
}
bool BigNum::operator<(const BigNum &obj) const
{
for (int i = 0; i < len; i++)
{
if (a[i] < obj.a[i])
return true;
if (a[i] > obj.a[i])
return false;
}
return false;
}
bool BigNum::operator<=(const BigNum &obj) const
{
for (int i = 0; i < len; i++)
{
if (a[i] < obj.a[i])
return true;
if (a[i] > obj.a[i])
return false;
}
return true;
}
bool BigNum::operator>=(const BigNum &obj) const
{
for (int i = 0; i < len; i++)
{
if (a[i] > obj.a[i])
return true;
if (a[i] < obj.a[i])
return false;
}
return true;
}
bool BigNum::operator==(const BigNum &obj) const
{
for (int i = 0; i < len; i++)
{
if (a[i] != obj.a[i])
return false;
}
return true;
}
bool BigNum::operator!=(const BigNum &obj) const
{
for (int i = 0; i < len; i++)
{
if (a[i] != obj.a[i])
return true;
}
return false;
}
BigNum BigNum::operator/(const BigNum &op2) const
{
BigNum temp(*this);
if (op2 == 0)
{
cout << "ERROR!!";
for (int i = 0; i < len; i++)
temp.a[i] = 0;
}
else if (*this < op2)
{
for (int i = 0; i < len; i++)
temp.a[i] = 0;
}
else if (*this == op2)
{
temp.a[len - 1] = 1;
}
else if (op2 == 1)
{
temp = *this;
}
else if (op2 == 2)
{
int from = 0;
for (int i = 0; i < len; i++)
{
if (temp.a[i] != 0)
{
from = i;
break;
}
}
int carry = 0;
for (int i = from; i < len; i++)
{
if (temp.a[i] & 1)
{
if (carry == 1)
temp.a[i] = (temp.a[i] + 10) / 2;
else
temp.a[i] = temp.a[i] / 2;
carry = 1;
}
else
{
if (carry == 1)
temp.a[i] = (temp.a[i] + 10) / 2;
else
temp.a[i] = temp.a[i] / 2;
carry = 0;
}
}
}
else
{
BigNum begin(1), end("500000000000000000000000000000"); // 500000000000000000000000000000
while (begin < end)
{
BigNum mid = (begin + end) / 2;
BigNum res = mid * op2;
if (res == 0 || res >= *this)
end = mid;
else
begin = mid + 1;
}
temp = begin;
if (temp == 1)
return 0;
int tmp = len - 1;
while (temp.a[tmp] == 0)
{
temp.a[tmp] = 9;
tmp++;
}
temp.a[tmp]--;
return temp;
}
return temp;
}
When I run it, sometimes I get the error "malloc(): corrupted top size", sometimes it will run and then nothing happens, when I debug it, I find that the problem is in the "mygcd" function, the algorithm I use is too slow for a huge The algorithm I'm using is too slow for the huge number, but I don't know how to change it. I'm not sure where in the two files something is going wrong that I don't know about, and I can't guarantee that all the algorithms I'm using are correct and appropriate. Can anyone help me? Thanks a lot. My system is Ubuntu 22.04.1LTS gcc version 11.2.0
