GabrielTofvesson
6cbecfd2c6
- Changed static "size_t"-type to a define to allow for compiling with different data types - Added modular arithmetic operation to protected section - Added a simplified constructor for supplying literals Probably some other things I didn't think were worth mentioning NOTE: Galois-field code may be unstable!
447 lines
15 KiB
C++
447 lines
15 KiB
C++
#define GALOIS_API
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#include "Galois.h"
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#include <string.h>
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#include <vector>
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namespace CryptoCPP{
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namespace Math{
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size_t _ceil(double d)
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{
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return (size_t)d + (d > (size_t)d ? 1 : 0);
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}
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size_t block_count(size_t bin_block_size, size_t bufs)
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{
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return (bufs * 8 * sizeof(BLOCK)) / bin_block_size;
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}
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void* do_copy(void* v, size_t size)
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{
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char * c = new char[size];
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memcpy(c, v, size);
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return c;
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}
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GALOIS_API Galois::Galois(
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BLOCK characteristic,
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BLOCK * irreducible,
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size_t irreducible_size,
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BLOCK * value,
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size_t value_size
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) :
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characteristic(characteristic),
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irreducible(irreducible),
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irreducible_size(irreducible_size),
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binary_block_size(_ceil(characteristic/2.0)),
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exponent(high_factor(irreducible, irreducible_size, _ceil(characteristic / 2.0), 0)),
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data_size(value_size)
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{
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data = value;
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}
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GALOIS_API Galois::Galois(
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BLOCK characteristic,
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BLOCK irreducible,
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BLOCK value
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) : Galois(characteristic, new BLOCK[1]{ irreducible }, 1, new BLOCK[1]{value}, 1)
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{ }
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GALOIS_API Galois::Galois(const Galois & copy) :
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characteristic(copy.characteristic),
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exponent(copy.exponent),
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irreducible(new BLOCK[copy.irreducible_size]),
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irreducible_size(copy.irreducible_size),
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binary_block_size(copy.binary_block_size),
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data_size(copy.data_size)
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{
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data = new BLOCK[data_size];
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memcpy(irreducible, copy.irreducible, irreducible_size * sizeof(BLOCK));
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memcpy(data, copy.data, data_size * sizeof(BLOCK));
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}
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GALOIS_API Galois::~Galois()
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{
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delete[] irreducible;
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delete[] data;
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}
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GALOIS_API Galois * Galois::add(const Galois * value) const
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{
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bool imSmaller = value->data_size > data_size;
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size_t state_size = imSmaller ? value->data_size : data_size;
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BLOCK * state = new BLOCK[state_size];
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memset(state, 0, state_size * sizeof(BLOCK));
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memcpy(state, imSmaller ? value->data : data, state_size * sizeof(BLOCK));
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iadd(imSmaller ? data : value->data, imSmaller ? data_size : value->data_size, binary_block_size, state, state_size, characteristic);
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return new Galois(characteristic, (BLOCK *)do_copy(irreducible, irreducible_size * sizeof(BLOCK)), irreducible_size, state, state_size);
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}
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GALOIS_API Galois * Galois::sub(const Galois * value) const
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{
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bool imSmaller = value->data_size > data_size;
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size_t state_size = imSmaller ? value->data_size : data_size;
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BLOCK * state = new BLOCK[state_size];
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memset(state, 0, state_size * sizeof(BLOCK));
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memcpy(state, data, data_size * sizeof(BLOCK));
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isub(value->data, value->data_size, binary_block_size, state, state_size, characteristic);
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return new Galois(characteristic, (BLOCK *)do_copy(irreducible, irreducible_size * sizeof(BLOCK)), irreducible_size, state, state_size);
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}
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GALOIS_API Galois * Galois::mul(const Galois * value) const
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{
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bool nb1, nb2;
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size_t
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h1 = high_factor(data, data_size, binary_block_size, &nb1),
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h2 = high_factor(value->data, value->data_size, value->binary_block_size, &nb2),
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h1_idx = h1 / (8 * sizeof(BLOCK)),
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h2_idx = h2 / (8 * sizeof(BLOCK));
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// If one of the values is 0, return a zero-Galois
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if (nb1 || nb2) return new Galois(characteristic, (BLOCK *)do_copy(irreducible, irreducible_size * sizeof(BLOCK)), irreducible_size, (BLOCK*)memset(new BLOCK[1], 0, sizeof(BLOCK)), 1);
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// The product of two values with the same base is represented as the sum of their exponents
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BLOCK * state = new BLOCK[h1_idx + h2_idx + 1];
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memset(state, 0, (h1_idx + h2_idx + 1) * sizeof(BLOCK));
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memcpy(state, this->data, this->data_size);
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BLOCK * cmp_exp = new BLOCK[(exponent/(8 * sizeof(BLOCK))) + 1];
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set_value(exponent, 1, binary_block_size, characteristic, cmp_exp);
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imul(value->data, value->data_size, binary_block_size, &state, h1_idx + h2_idx + 1, characteristic, h1_idx, h2_idx);
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ModResult * res = imod(state, h1_idx + h2_idx + 1, irreducible, irreducible_size, cmp_exp, (exponent / (8 * sizeof(BLOCK))) + 1, characteristic, binary_block_size);
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delete[] state;
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state = res->mod;
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size_t state_size = res->mod_size;
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delete[] res->div;
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delete res;
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return new Galois(characteristic, (BLOCK *)do_copy(irreducible, irreducible_size * sizeof(BLOCK)), irreducible_size, state, state_size);
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}
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GALOIS_API Galois * Galois::inv() const
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{
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struct FactorItem {
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FactorItem(BLOCK * factor, size_t factor_size) { this->factor = factor; this->factor_size = factor_size; }
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BLOCK * factor;
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size_t factor_size;
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};
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size_t exp = ((exponent + 1) / (8 * sizeof(BLOCK))) + 1;
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BLOCK * compute = new BLOCK[exp];
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memset(compute, 0, exp * sizeof(size_t));
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memcpy(compute, irreducible, irreducible_size * sizeof(BLOCK));
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size_t compute_size = exp;
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BLOCK * temp = new BLOCK[exp];
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memset(temp, 0, exp * sizeof(BLOCK));
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memcpy(temp, data, data_size * sizeof(BLOCK));
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size_t temp_size = exp;
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std::vector<FactorItem> factors = std::vector<FactorItem>();
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struct ModResult * m;
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size_t high;
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size_t highest1 = 1, highest2 = 1;
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// TODO: Implement extended Euclidean algorithm
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bool nb;
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volatile bool x = false;
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Loop:
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high_factor(temp, temp_size, binary_block_size, &nb);
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if (nb) goto Next;
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m = //new ModResult(); m->div = new size_t[m->div_size = 1]{(size_t)(change?0:1)}; m->mod = new size_t[m->mod_size = 1]{0};
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imod(compute, compute_size, temp, temp_size, temp, temp_size, characteristic, binary_block_size);
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delete[] compute;
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compute = temp;
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temp = m->mod;
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compute_size = temp_size;
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temp_size = m->mod_size;
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factors.push_back(FactorItem(m->div, m->div_size));
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// Record highest values
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high = high_factor(m->div, m->div_size, binary_block_size, &nb);
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if (high > highest1)
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{
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highest2 = highest1;
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highest1 = high;
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}
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else if (high > highest2) highest2 = high;
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delete m;
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goto Loop;
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Next:
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// Free unneeded resources
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delete[] temp;
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delete[] compute;
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// Remove invalid computation result
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delete[] factors.at(factors.size() - 1).factor;
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factors.pop_back();
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if (factors.size() == 0) factors.push_back(FactorItem(new BLOCK[1]{1}, 1));
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// Initialize left result of the diophantine equation
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compute_size = highest1 * highest2;
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compute = new BLOCK[compute_size];
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memset(compute, 0, compute_size * sizeof(BLOCK));
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memcpy(compute, factors.at(factors.size() - 1).factor, factors.at(factors.size() - 1).factor_size * sizeof(BLOCK));
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delete[] factors.at(factors.size() - 1).factor;
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factors.pop_back();
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// Initialize the right result
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temp_size = compute_size;
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temp = new BLOCK[temp_size];
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memset(temp, 0, compute_size * sizeof(BLOCK));
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temp[0] |= 1;
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BLOCK * cmp = new BLOCK[exp];
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memset(cmp, 0, exp * sizeof(BLOCK));
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cmp[exponent] = 1;
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// Initialize a holder for performing intermediate computations on
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size_t holder_size = compute_size;
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BLOCK * holder = new BLOCK[holder_size];
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BLOCK * transfer;
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size_t transfer_size;
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// Continue computation of both sides
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while (factors.size() > 0)
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{
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FactorItem item = factors.at(factors.size() - 1);
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factors.pop_back();
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memcpy(memset(holder, 0, holder_size), item.factor, item.factor_size * sizeof(size_t));
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size_t f1 = high_factor(temp, temp_size, binary_block_size, 0), f2 = high_factor(holder, holder_size, binary_block_size, 0);
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imul(holder, holder_size, binary_block_size, &temp, temp_size, characteristic, f1 / (8 * sizeof(BLOCK)), f2 / (8 * sizeof(BLOCK)));
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temp_size = (f1 / (8 * sizeof(BLOCK))) + (f2 / (8 * sizeof(BLOCK))) + 1;
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ModResult * result = imod(temp, temp_size, irreducible, irreducible_size, cmp, exp, characteristic, binary_block_size);
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memcpy(memset(temp, 0, temp_size * sizeof(BLOCK)), result->mod, result->mod_size);
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delete[] result->mod;
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delete[] result->div;
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delete result;
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// Do swap
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transfer = compute;
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transfer_size = compute_size;
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compute = temp;
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compute_size = temp_size;
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temp = transfer;
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temp_size = transfer_size;
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}
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size_t result_size = ((high_factor(compute, compute_size, binary_block_size, &nb) + 1) / (8 * sizeof(BLOCK))) + 1;
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BLOCK * result = new BLOCK[result_size];
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memcpy(result, compute, result_size * sizeof(BLOCK));
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delete[] compute;
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delete[] temp;
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delete[] cmp;
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return new Galois(characteristic, (BLOCK*)do_copy(irreducible, irreducible_size * sizeof(BLOCK)), irreducible_size, result, result_size);
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}
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// These internal functions assume that an adequate state size has been chose
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GALOIS_API void Galois::iadd(BLOCK * data, size_t data_size, size_t bin_size, BLOCK * state, size_t state_size, BLOCK characteristic)
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{
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for (size_t t = block_count(bin_size, data_size); t > 0; --t)
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set_value(
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t - 1,
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(
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get_value(t-1, bin_size, state) +
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get_value(t - 1, bin_size, data)
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) % characteristic,
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bin_size,
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characteristic,
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state
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);
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}
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GALOIS_API void Galois::isub(BLOCK * data, size_t data_size, size_t bin_size, BLOCK * state, size_t state_size, BLOCK characteristic)
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{
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for (size_t t = block_count(bin_size, data_size); t > 0; --t)
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set_value(
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t - 1,
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(
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characteristic +
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get_value(t - 1, bin_size, state) -
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get_value(t - 1, bin_size, data)
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) % characteristic,
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bin_size,
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characteristic,
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state
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);
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}
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GALOIS_API void Galois::imul(BLOCK * data, size_t data_size, size_t bin_size, BLOCK ** state, size_t state_size, BLOCK characteristic, size_t high1, size_t high2)
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{
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BLOCK * temp = new BLOCK[high1 + high2 + 1];
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//memset(temp, 0, (high1 + high2 + 1) * sizeof(size_t));
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BLOCK * res = new BLOCK[high1 + high2 + 1];
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memset(res, 0, (high1 + high2 + 1) * sizeof(BLOCK));
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size_t data_blocks = block_count(bin_size, data_size);
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for (size_t t = block_count(bin_size, state_size); t > 0; --t)
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{
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memset(temp, 0, (high1 + high2 + 1) * sizeof(BLOCK));
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//memcpy(temp, data, data_size * sizeof(size_t));
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//ilsh(temp, data_size, bin_size, characteristic, t-1);
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for (size_t tblk = 0; tblk < data_blocks; ++tblk) // Multiply each element
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set_value(tblk + t - 1, get_value(tblk, bin_size, data) * get_value(t - 1, bin_size, *state), bin_size, characteristic, temp);
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// Add shifted and multiplied value to state
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iadd(temp, high1 + high2 + 1, bin_size, res, high1 + high2 + 1, characteristic);
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}
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delete[] *state;
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*state = res;
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}
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GALOIS_API Galois::ModResult* Galois::imod(BLOCK * value, size_t value_size, BLOCK * modulo, size_t modulo_size, BLOCK * cmp, size_t cmp_size, BLOCK characteristic, size_t bin_size)
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{
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bool nb;
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size_t mod_max = high_factor(modulo, modulo_size, bin_size, &nb);
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if (nb) return 0;
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size_t cmp_max = high_factor(cmp, cmp_size, bin_size, &nb);
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if (nb) return 0;
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BLOCK * aligned = 0;
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ModResult * result = new ModResult();
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result->mod = new BLOCK[value_size];
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result->mod_size = value_size;
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memcpy(result->mod, value, value_size * sizeof(BLOCK));
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result->div = 0;
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LoopStart: // Loop start
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// Loop evaluation
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size_t idx = high_factor(result->mod, result->mod_size, bin_size, &nb);
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if (nb || idx < cmp_max || (idx == cmp_max && result->mod[idx / (8 * sizeof(BLOCK))] < cmp[cmp_max / (8 * sizeof(BLOCK))])) goto LoopEnd; // Break
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// Loop body
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if (aligned == 0) {
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aligned = new BLOCK[value_size];
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result->div_size = (((idx - mod_max) * bin_size) / (8 * sizeof(BLOCK))) + 1;
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result->div = new BLOCK[result->div_size];
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memset(result->div, 0, result->div_size * sizeof(BLOCK));
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}
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memcpy(memset(aligned, 0, value_size * sizeof(BLOCK)), modulo, modulo_size * sizeof(BLOCK));
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ilsh(aligned, value_size, bin_size, characteristic, idx - mod_max);
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isub(aligned, value_size, bin_size, result->mod, value_size, characteristic);
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set_value(idx - mod_max, (get_value(idx - mod_max, bin_size, result->div) + 1) % characteristic, bin_size, characteristic, result->div);
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// End of loop body
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goto LoopStart;
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LoopEnd:
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if (result->div == 0) {
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result->div = new BLOCK[1]{0};
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result->div_size = 1;
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}
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delete[] aligned;
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// Stuff after loop
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return result;
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}
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GALOIS_API void Galois::ilsh(BLOCK * state, size_t state_size, size_t bin_size, BLOCK characteristic, size_t shiftc)
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{
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for (size_t t = block_count(bin_size, state_size); t > shiftc; --t)
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set_value(t - 1, get_value(t - 1 - shiftc, bin_size, state), bin_size, characteristic, state);
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for (size_t t = shiftc; t > 0; --t)
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set_value(t - 1, 0, bin_size, characteristic, state);
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}
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GALOIS_API size_t Galois::_mask(size_t bits, bool side)
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{
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size_t result = 0;
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for(size_t t = 0; t<bits; ++t) result = side?(result<<1)|1:(result>>1)|high_bit;
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return result;
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}
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GALOIS_API BLOCK Galois::get_value(size_t index, size_t block_size, BLOCK * from)
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{
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// Compute block/sub-block indexing
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size_t upper_bit_size = ((block_size*index)%(8*sizeof(BLOCK)))% block_size;
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size_t upper_block_index = (index*block_size)/(8 * sizeof(BLOCK));
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size_t lower_block_index = ((index - upper_bit_size)*block_size)/ (8 * sizeof(BLOCK));
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// Boundary disparity check
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if(upper_block_index!=lower_block_index)
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{
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// Get block values
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size_t upper_block = from[upper_block_index] & _mask(upper_bit_size, true);
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size_t lower_block = from[lower_block_index] & _mask(block_size -upper_bit_size, false);
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// Do alignment
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BLOCK block = (upper_block << (block_size - upper_bit_size)) | (lower_block >> ((sizeof(BLOCK)*8)-upper_bit_size));
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return block;
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}
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else
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{
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// Passed: no boundary disparity
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size_t shift = (block_size * index) % (8 * sizeof(BLOCK));
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size_t block_index = (block_size * index) / (8 * sizeof(BLOCK));
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// Get and mask
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return from[block_index] >> shift & _mask(block_size, true);
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}
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}
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GALOIS_API void Galois::set_value(size_t index, BLOCK value, size_t block_size, BLOCK characteristic, BLOCK * to)
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{
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value = value % characteristic;
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// Compute block/sub-block indexing
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size_t upper_bit_size = ((block_size*index)%(8*sizeof(BLOCK)))%block_size;
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size_t upper_block_index = (index*block_size)/8;
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size_t lower_block_index = ((index - upper_bit_size)*block_size)/8;
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// Boundary disparity check
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if(upper_block_index!=lower_block_index)
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{
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// Mask bits
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to[upper_block_index] &= ~_mask(upper_bit_size, true);
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to[lower_block_index] &= ~_mask(block_size - upper_bit_size, false);
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// Get block values
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to[upper_block_index] |= value >> (block_size - upper_bit_size);
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to[lower_block_index] |= (value & _mask(block_size -upper_bit_size, false)) << ((8 * sizeof(BLOCK)) - (block_size - upper_bit_size));
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}
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else
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{
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// Passed: no boundary disparity
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size_t shift = (block_size * index) % (8 * sizeof(BLOCK));
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size_t block_index = (block_size * index) / (8 * sizeof(BLOCK));
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// Mask bits
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to[block_index] &= ~(_mask(block_size, true) << shift);
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// Apply shift
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to[block_index] |= value << shift;
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}
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}
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GALOIS_API size_t Galois::high_factor(BLOCK * state, size_t state_size, size_t bin_size, bool * noBits)
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{
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if(noBits!=0) *noBits = false;
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for (size_t t = block_count(bin_size, state_size); t > 0; --t)
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if (get_value(t - 1, bin_size, state))
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return t - 1;
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if (noBits != 0) *noBits = true;
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return 0;
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}
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}
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}
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