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110 lines
2.4 KiB
C++
110 lines
2.4 KiB
C++
/*
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* C++ Program to Implement Solovay-Strassen Primality Test
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*/
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#include <cstring>
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#include <iostream>
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#include <cstdlib>
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#define ll long long
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using namespace std;
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/*
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* modular exponentiation
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*/
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ll modulo(ll base, ll exponent, ll mod)
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{
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ll x = 1;
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ll y = base;
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while (exponent > 0)
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{
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if (exponent % 2 == 1)
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x = (x * y) % mod;
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y = (y * y) % mod;
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exponent = exponent / 2;
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}
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return x % mod;
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}
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/*
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* calculates Jacobian(a/n) n>0 and n is odd
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*/
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int calculateJacobian(ll a,ll n)
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{
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if (!a)
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return 0;
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int ans = 1;
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ll temp;
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if (a < 0)
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{
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a = -a;
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if (n % 4 == 3)
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ans=-ans;
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}
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if (a == 1)
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return ans;
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while (a)
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{
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if (a < 0)
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{
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a = -a;
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if (n % 4 == 3)
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ans = -ans;
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}
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while (a % 2 == 0)
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{
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a = a / 2;
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if (n % 8 == 3 || n % 8 == 5)
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ans = -ans;
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}
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swap(a, n);
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if (a % 4 == 3 && n % 4 == 3)
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ans = -ans;
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a = a % n;
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if (a > n / 2)
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a = a - n;
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}
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if (n == 1)
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return ans;
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return 0;
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}
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/*
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* Solovay-Strassen Primality Test
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* Iterations determine the accuracy of the test
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*/
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bool Solovoy(ll p, int iteration)
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{
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if (p < 2)
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return false;
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if (p != 2 && p % 2 == 0)
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return false;
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for (int i = 0; i < iteration; i++)
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{
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ll a = rand() % (p - 1) + 1;
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ll jacobian = (p + calculateJacobian(a, p)) % p;
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ll mod = modulo(a, (p - 1) / 2, p);
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if (!jacobian || mod != jacobian)
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{
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return false;
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}
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}
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return true;
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}
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//Main
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int main()
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{
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int iteration = 50;
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ll num;
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cout<<"Enter integr to test primality: ";
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cin>>num;
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if (Solovoy(num, iteration))
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cout<<num<<" is prime"<<endl;
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else
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cout<<num<<" is not prime"<<endl;
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return 0;
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}
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/*
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Enter integr to test primality: 219891801103773
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219891801103773 is not prime
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------------------
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(program exited with code: 1)
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Press return to continue
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