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/*
* (C) 2009,2010,2015 Jack Lloyd
*
* Botan is released under the Simplified BSD License (see license.txt)
*/
#include "cli.h"
#if defined(BOTAN_HAS_NUMBERTHEORY)
#include <botan/reducer.h>
#include <botan/numthry.h>
#include <iterator>
namespace Botan_CLI {
class Modular_Inverse final : public Command
{
public:
Modular_Inverse() : Command("mod_inverse n mod") {}
std::string group() const override
{
return "numtheory";
}
std::string description() const override
{
return "Calculates a modular inverse";
}
void go() override
{
const Botan::BigInt n(get_arg("n"));
const Botan::BigInt mod(get_arg("mod"));
output() << Botan::inverse_mod(n, mod) << "\n";
}
};
BOTAN_REGISTER_COMMAND("mod_inverse", Modular_Inverse);
class Gen_Prime final : public Command
{
public:
Gen_Prime() : Command("gen_prime --count=1 bits") {}
std::string group() const override
{
return "numtheory";
}
std::string description() const override
{
return "Samples one or more primes";
}
void go() override
{
const size_t bits = get_arg_sz("bits");
const size_t cnt = get_arg_sz("count");
for(size_t i = 0; i != cnt; ++i)
{
const Botan::BigInt p = Botan::random_prime(rng(), bits);
output() << p << "\n";
}
}
};
BOTAN_REGISTER_COMMAND("gen_prime", Gen_Prime);
class Is_Prime final : public Command
{
public:
Is_Prime() : Command("is_prime --prob=56 n") {}
std::string group() const override
{
return "numtheory";
}
std::string description() const override
{
return "Test if the integer n is composite or prime";
}
void go() override
{
Botan::BigInt n(get_arg("n"));
const size_t prob = get_arg_sz("prob");
const bool prime = Botan::is_prime(n, rng(), prob);
output() << n << " is " << (prime ? "probably prime" : "composite") << "\n";
}
};
BOTAN_REGISTER_COMMAND("is_prime", Is_Prime);
/*
* Factor integers using a combination of trial division by small
* primes, and Pollard's Rho algorithm
*/
class Factor final : public Command
{
public:
Factor() : Command("factor n") {}
std::string group() const override
{
return "numtheory";
}
std::string description() const override
{
return "Factor a given integer";
}
void go() override
{
Botan::BigInt n(get_arg("n"));
std::vector<Botan::BigInt> factors = factorize(n, rng());
std::sort(factors.begin(), factors.end());
output() << n << ": ";
std::copy(factors.begin(), factors.end(), std::ostream_iterator<Botan::BigInt>(output(), " "));
output() << std::endl;
}
private:
std::vector<Botan::BigInt> factorize(const Botan::BigInt& n_in,
Botan::RandomNumberGenerator& rng)
{
Botan::BigInt n = n_in;
std::vector<Botan::BigInt> factors = remove_small_factors(n);
while(n != 1)
{
if(Botan::is_prime(n, rng))
{
factors.push_back(n);
break;
}
Botan::BigInt a_factor = 0;
while(a_factor == 0)
{
a_factor = rho(n, rng);
}
std::vector<Botan::BigInt> rho_factored = factorize(a_factor, rng);
for(size_t j = 0; j != rho_factored.size(); j++)
{
factors.push_back(rho_factored[j]);
}
n /= a_factor;
}
return factors;
}
/*
* Pollard's Rho algorithm, as described in the MIT algorithms book. We
* use (x^2+x) mod n instead of (x*2-1) mod n as the random function,
* it _seems_ to lead to faster factorization for the values I tried.
*/
Botan::BigInt rho(const Botan::BigInt& n, Botan::RandomNumberGenerator& rng)
{
Botan::BigInt x = Botan::BigInt::random_integer(rng, 0, n - 1);
Botan::BigInt y = x;
Botan::BigInt d = 0;
Botan::Modular_Reducer mod_n(n);
size_t i = 1, k = 2;
while(true)
{
i++;
if(i == 0) // overflow, bail out
{
break;
}
x = mod_n.multiply((x + 1), x);
d = Botan::gcd(y - x, n);
if(d != 1 && d != n)
{
return d;
}
if(i == k)
{
y = x;
k = 2 * k;
}
}
return 0;
}
// Remove (and return) any small (< 2^16) factors
std::vector<Botan::BigInt> remove_small_factors(Botan::BigInt& n)
{
std::vector<Botan::BigInt> factors;
while(n.is_even())
{
factors.push_back(2);
n /= 2;
}
for(size_t j = 0; j != Botan::PRIME_TABLE_SIZE; j++)
{
uint16_t prime = Botan::PRIMES[j];
if(n < prime)
{
break;
}
Botan::BigInt x = Botan::gcd(n, prime);
if(x != 1)
{
n /= x;
while(x != 1)
{
x /= prime;
factors.push_back(prime);
}
}
}
return factors;
}
};
BOTAN_REGISTER_COMMAND("factor", Factor);
}
#endif
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