Sieve of Eratosthenes optimization

 

    In cybersecurity, ancient algorithms still hold power. The Sieve of Eratosthenes, a prime number finder, underpins modern cryptography. This seemingly simple method, especially with stack optimizations, is fundamental. It acts as a base for complex cryptographic algorithms like Euler's theorem (a^φ(n)≡1(modn)) .

    Prime numbers are vital in public-key encryption. Eratosthenes' Sieve aids in generating primes for systems like RSA. Euler's function, key in cryptography, relies on prime factorization, where the Sieve is crucial.

    Understanding these basics is essential in cybersecurity. This simple algorithm reveals how math grounds our security.

#include <iostream>

using namespace std;

bool vec[ 1000001], m=0;

int n, X=0, i;

int main()

{

    cin>>n;

    i=2;

    while(i*i<n-X+1)

    {

        if(vec[i]==0)

        {

            if(m==0)

            {    m=1;

                  X=i;

             }

            for(int j=i*i; j<=n-X+1; j=j+i)

                vec[j]=1;

        }

        i++;

    }

    for(int i=2; i<n; i++)

        if(vec[i]==0)

            cout<<i<<" ";

    return 0;

}

This version was written in C/C++ , using the IDE Codeblocks 20.3.