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/*
Factor integers using a combination of trial division by small primes,
and Pollard's Rho algorithm
*/
#include <botan/botan.h>
#include <botan/reducer.h>
#include <botan/numthry.h>
using namespace Botan;
#include <iostream>
BigInt rho(const BigInt& n)
{
BigInt x = random_integer(0, n-1);
BigInt y = x;
BigInt d = 0;
Modular_Reducer mod_n(n);
u32bit i = 1, k = 2;
while(true)
{
i++;
if(i == 0) // fail
break;
x = mod_n.reduce(square(x) - 1);
d = gcd(y - x, n);
if(d != 1 && d != n)
return d;
if(i == k)
{
y = x;
k = 2*k;
}
}
return 0;
}
void concat(std::vector<BigInt>& x, const std::vector<BigInt>& y)
{
for(u32bit j = 0; j != y.size(); j++)
x.push_back(y[j]);
}
std::vector<BigInt> factorize(const BigInt& n)
{
std::vector<BigInt> factors;
if(n <= 1) // no prime factors at all
return factors;
if(is_prime(n)) // just n itself
{
factors.push_back(n);
return factors;
}
if(n.is_even())
{
factors.push_back(2);
concat(factors, factorize(n / 2));
return factors;
}
BigInt factor = 0;
while(factor == 0)
factor = rho(n);
concat(factors, factorize(factor));
concat(factors, factorize(n / factor));
return factors;
}
int main(int argc, char* argv[])
{
if(argc != 2)
{
std::cerr << "Usage: " << argv[0] << " integer\n";
return 1;
}
try
{
LibraryInitializer init;
BigInt n(argv[1]);
std::vector<BigInt> factors = factorize(n);
std::sort(factors.begin(), factors.end());
std::cout << n << ": ";
for(u32bit j = 0; j != factors.size(); j++)
std::cout << factors[j] << " ";
std::cout << "\n";
}
catch(std::exception& e)
{
std::cout << e.what() << std::endl;
return 1;
}
return 0;
}
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