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added prime field arithmetic

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Ahmet Inan 2024-03-21 17:16:41 +01:00
commit fbbc655589
2 changed files with 181 additions and 0 deletions
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prime_field.hh Normal file
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/*
Prime field arithmetic
Copyright 2024 Ahmet Inan <inan@aicodix.de>
*/
#pragma once
#include <cassert>
namespace CODE {
template <typename TYPE, TYPE PRIME>
struct PrimeField
{
static_assert(std::is_unsigned<TYPE>::value, "TYPE must be unsigned");
static_assert(std::numeric_limits<TYPE>::max() / (PRIME-1) >= (PRIME-1), "Type not wide enough");
static constexpr TYPE P = PRIME;
TYPE v;
PrimeField() = default;
explicit PrimeField(TYPE v) : v(v)
{
}
PrimeField<TYPE, PRIME> operator *= (PrimeField<TYPE, PRIME> a)
{
return *this = *this * a;
}
PrimeField<TYPE, PRIME> operator /= (PrimeField<TYPE, PRIME> a)
{
return *this = *this / a;
}
PrimeField<TYPE, PRIME> operator += (PrimeField<TYPE, PRIME> a)
{
return *this = *this + a;
}
PrimeField<TYPE, PRIME> operator -= (PrimeField<TYPE, PRIME> a)
{
return *this = *this - a;
}
TYPE operator () ()
{
return v;
}
};
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> reduce(PrimeField<TYPE, PRIME> a)
{
return PrimeField<TYPE, PRIME>(a.v % a.P);
}
template <typename TYPE, TYPE PRIME>
bool operator == (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return a.v == b.v;
}
template <typename TYPE, TYPE PRIME>
bool operator != (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return a.v != b.v;
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> add(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return PrimeField<TYPE, PRIME>(a.v + b.v);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator + (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return reduce(add(a, b));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> sub(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return PrimeField<TYPE, PRIME>(a.v - b.v + a.P);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator - (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return reduce(sub(a, b));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> neg(PrimeField<TYPE, PRIME> a)
{
return PrimeField<TYPE, PRIME>(a.P - a.v);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator - (PrimeField<TYPE, PRIME> a)
{
return reduce(neg(a));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> mul(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return PrimeField<TYPE, PRIME>(a.v * b.v);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator * (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return reduce(mul(a, b));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> rcp(PrimeField<TYPE, PRIME> a)
{
assert(a.v);
if (a.v == 1)
return a;
TYPE t = 0, newt = 1;
TYPE r = a.P, newr = a.v;
while (newr) {
TYPE quotient = r / newr;
t -= quotient * newt;
r -= quotient * newr;
std::swap(newt, t);
std::swap(newr, r);
}
assert(r == 1);
if (t >= a.P)
t += a.P;
return PrimeField<TYPE, PRIME>(t);
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> div(PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return mul(a, rcp(b));
}
template <typename TYPE, TYPE PRIME>
PrimeField<TYPE, PRIME> operator / (PrimeField<TYPE, PRIME> a, PrimeField<TYPE, PRIME> b)
{
return reduce(div(a, b));
}
}

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tests/pf_test.cc Normal file
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/*
Test for the prime field arithmetic
Copyright 2024 Ahmet Inan <inan@aicodix.de>
*/
#include <cstdint>
#include <cassert>
#include <iostream>
#include "prime_field.hh"
template <typename TYPE, TYPE PRIME>
void exhaustive_test()
{
typedef CODE::PrimeField<TYPE, PRIME> PF;
for (TYPE a = 0; a < PRIME; ++a)
for (TYPE b = 0; b < PRIME; ++b)
assert((PF(a) * PF(b))() == (a * b) % PRIME);
for (TYPE a = 1; a < PRIME; ++a)
assert(rcp(PF(a)) * PF(a) == PF(1));
for (TYPE a = 0; a < PRIME; ++a)
for (TYPE b = 0; b < PRIME; ++b)
assert((PF(a) + PF(b))() == (a + b) % PRIME);
for (TYPE a = 0; a < PRIME; ++a)
for (TYPE b = 0; b < PRIME; ++b)
assert((PF(a) - PF(b))() == (a - b + PRIME) % PRIME);
}
int main()
{
exhaustive_test<uint32_t, 257>();
exhaustive_test<uint64_t, 65537>();
std::cerr << "Prime field arithmetic test passed!" << std::endl;
return 0;
}