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329 lines
10 KiB
C++
329 lines
10 KiB
C++
/*
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* Copyright (c) 2020, Ali Mohammad Pur <ali.mpfard@gmail.com>
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions are met:
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*
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* 1. Redistributions of source code must retain the above copyright notice, this
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* list of conditions and the following disclaimer.
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*
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* 2. Redistributions in binary form must reproduce the above copyright notice,
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* this list of conditions and the following disclaimer in the documentation
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* and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
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* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
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* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
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* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
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* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
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* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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#pragma once
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#include <LibCrypto/BigInt/UnsignedBigInteger.h>
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//#define NT_DEBUG
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namespace Crypto {
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namespace NumberTheory {
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static auto ModularInverse(const UnsignedBigInteger& a_, const UnsignedBigInteger& b) -> UnsignedBigInteger
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{
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if (b == 1)
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return { 1 };
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UnsignedBigInteger one { 1 };
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UnsignedBigInteger temp_1;
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UnsignedBigInteger temp_2;
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UnsignedBigInteger temp_3;
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UnsignedBigInteger temp_4;
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UnsignedBigInteger temp_plus;
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UnsignedBigInteger temp_minus;
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UnsignedBigInteger temp_quotient;
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UnsignedBigInteger temp_remainder;
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UnsignedBigInteger d;
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auto a = a_;
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auto u = a;
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if (a.words()[0] % 2 == 0) {
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// u += b
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UnsignedBigInteger::add_without_allocation(u, b, temp_plus);
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u.set_to(temp_plus);
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}
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auto v = b;
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UnsignedBigInteger x { 0 };
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// d = b - 1
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UnsignedBigInteger::subtract_without_allocation(b, one, d);
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while (!(v == 1)) {
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while (v < u) {
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// u -= v
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UnsignedBigInteger::subtract_without_allocation(u, v, temp_minus);
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u.set_to(temp_minus);
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// d += x
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UnsignedBigInteger::add_without_allocation(d, x, temp_plus);
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d.set_to(temp_plus);
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while (u.words()[0] % 2 == 0) {
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if (d.words()[0] % 2 == 1) {
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// d += b
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UnsignedBigInteger::add_without_allocation(d, b, temp_plus);
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d.set_to(temp_plus);
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}
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// u /= 2
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UnsignedBigInteger::divide_u16_without_allocation(u, 2, temp_quotient, temp_remainder);
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u.set_to(temp_quotient);
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// d /= 2
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UnsignedBigInteger::divide_u16_without_allocation(d, 2, temp_quotient, temp_remainder);
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d.set_to(temp_quotient);
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}
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}
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// v -= u
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UnsignedBigInteger::subtract_without_allocation(v, u, temp_minus);
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v.set_to(temp_minus);
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// x += d
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UnsignedBigInteger::add_without_allocation(x, d, temp_plus);
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x.set_to(temp_plus);
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while (v.words()[0] % 2 == 0) {
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if (x.words()[0] % 2 == 1) {
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// x += b
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UnsignedBigInteger::add_without_allocation(x, b, temp_plus);
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x.set_to(temp_plus);
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}
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// v /= 2
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UnsignedBigInteger::divide_u16_without_allocation(v, 2, temp_quotient, temp_remainder);
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v.set_to(temp_quotient);
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// x /= 2
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UnsignedBigInteger::divide_u16_without_allocation(x, 2, temp_quotient, temp_remainder);
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x.set_to(temp_quotient);
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}
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}
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// x % b
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UnsignedBigInteger::divide_without_allocation(x, b, temp_1, temp_2, temp_3, temp_4, temp_quotient, temp_remainder);
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return temp_remainder;
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}
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static auto ModularPower(const UnsignedBigInteger& b, const UnsignedBigInteger& e, const UnsignedBigInteger& m) -> UnsignedBigInteger
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{
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if (m == 1)
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return 0;
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UnsignedBigInteger ep { e };
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UnsignedBigInteger base { b };
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UnsignedBigInteger exp { 1 };
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UnsignedBigInteger temp_1;
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UnsignedBigInteger temp_2;
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UnsignedBigInteger temp_3;
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UnsignedBigInteger temp_4;
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UnsignedBigInteger temp_multiply;
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UnsignedBigInteger temp_quotient;
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UnsignedBigInteger temp_remainder;
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while (!(ep < 1)) {
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#ifdef NT_DEBUG
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dbg() << ep.to_base10();
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#endif
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if (ep.words()[0] % 2 == 1) {
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// exp = (exp * base) % m;
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UnsignedBigInteger::multiply_without_allocation(exp, base, temp_1, temp_2, temp_3, temp_4, temp_multiply);
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UnsignedBigInteger::divide_without_allocation(temp_multiply, m, temp_1, temp_2, temp_3, temp_4, temp_quotient, temp_remainder);
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exp.set_to(temp_remainder);
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}
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// ep = ep / 2;
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UnsignedBigInteger::divide_u16_without_allocation(ep, 2, temp_quotient, temp_remainder);
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ep.set_to(temp_quotient);
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// base = (base * base) % m;
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UnsignedBigInteger::multiply_without_allocation(base, base, temp_1, temp_2, temp_3, temp_4, temp_multiply);
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UnsignedBigInteger::divide_without_allocation(temp_multiply, m, temp_1, temp_2, temp_3, temp_4, temp_quotient, temp_remainder);
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base.set_to(temp_remainder);
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}
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return exp;
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}
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static void GCD_without_allocation(
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const UnsignedBigInteger& a,
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const UnsignedBigInteger& b,
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UnsignedBigInteger& temp_a,
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UnsignedBigInteger& temp_b,
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UnsignedBigInteger& temp_1,
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UnsignedBigInteger& temp_2,
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UnsignedBigInteger& temp_3,
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UnsignedBigInteger& temp_4,
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UnsignedBigInteger& temp_quotient,
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UnsignedBigInteger& temp_remainder,
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UnsignedBigInteger& output)
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{
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temp_a.set_to(a);
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temp_b.set_to(b);
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for (;;) {
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if (temp_a == 0) {
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output.set_to(temp_b);
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return;
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}
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// temp_b %= temp_a
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UnsignedBigInteger::divide_without_allocation(temp_b, temp_a, temp_1, temp_2, temp_3, temp_4, temp_quotient, temp_remainder);
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temp_b.set_to(temp_remainder);
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if (temp_b == 0) {
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output.set_to(temp_a);
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return;
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}
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// temp_a %= temp_b
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UnsignedBigInteger::divide_without_allocation(temp_a, temp_b, temp_1, temp_2, temp_3, temp_4, temp_quotient, temp_remainder);
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temp_a.set_to(temp_remainder);
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}
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}
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static UnsignedBigInteger GCD(const UnsignedBigInteger& a, const UnsignedBigInteger& b)
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{
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UnsignedBigInteger temp_a;
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UnsignedBigInteger temp_b;
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UnsignedBigInteger temp_1;
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UnsignedBigInteger temp_2;
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UnsignedBigInteger temp_3;
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UnsignedBigInteger temp_4;
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UnsignedBigInteger temp_quotient;
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UnsignedBigInteger temp_remainder;
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UnsignedBigInteger output;
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GCD_without_allocation(a, b, temp_a, temp_b, temp_1, temp_2, temp_3, temp_4, temp_quotient, temp_remainder, output);
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return output;
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}
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static auto LCM(const UnsignedBigInteger& a, const UnsignedBigInteger& b) -> UnsignedBigInteger
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{
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UnsignedBigInteger temp_a;
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UnsignedBigInteger temp_b;
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UnsignedBigInteger temp_1;
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UnsignedBigInteger temp_2;
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UnsignedBigInteger temp_3;
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UnsignedBigInteger temp_4;
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UnsignedBigInteger temp_quotient;
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UnsignedBigInteger temp_remainder;
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UnsignedBigInteger gcd_output;
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UnsignedBigInteger output { 0 };
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GCD_without_allocation(a, b, temp_a, temp_b, temp_1, temp_2, temp_3, temp_4, temp_quotient, temp_remainder, gcd_output);
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if (gcd_output == 0) {
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#ifdef NT_DEBUG
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dbg() << "GCD is zero";
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#endif
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return output;
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}
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// output = (a / gcd_output) * b
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UnsignedBigInteger::divide_without_allocation(a, gcd_output, temp_1, temp_2, temp_3, temp_4, temp_quotient, temp_remainder);
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UnsignedBigInteger::multiply_without_allocation(temp_quotient, b, temp_1, temp_2, temp_3, temp_4, output);
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#ifdef NT_DEBUG
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dbg() << "quot: " << temp_quotient << " rem: " << temp_remainder << " out: " << output;
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#endif
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return output;
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}
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template<size_t test_count>
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static bool MR_primality_test(UnsignedBigInteger n, const Vector<UnsignedBigInteger, test_count>& tests)
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{
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auto prev = n.minus({ 1 });
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auto b = prev;
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auto r = 0;
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auto div_result = b.divided_by(2);
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while (div_result.quotient == 0) {
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div_result = b.divided_by(2);
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b = div_result.quotient;
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++r;
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}
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for (size_t i = 0; i < tests.size(); ++i) {
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auto return_ = true;
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if (n < tests[i])
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continue;
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auto x = ModularPower(tests[i], b, n);
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if (x == 1 || x == prev)
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continue;
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for (auto d = r - 1; d != 0; --d) {
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x = ModularPower(x, 2, n);
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if (x == 1)
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return false;
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if (x == prev) {
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return_ = false;
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break;
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}
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}
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if (return_)
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return false;
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}
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return true;
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}
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static UnsignedBigInteger random_number(const UnsignedBigInteger& min, const UnsignedBigInteger& max)
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{
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ASSERT(min < max);
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auto range = max.minus(min);
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UnsignedBigInteger base;
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// FIXME: Need a cryptographically secure rng
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auto size = range.trimmed_length() * sizeof(u32);
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u8 buf[size];
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arc4random_buf(buf, size);
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Vector<u32> vec;
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for (size_t i = 0; i < size / sizeof(u32); ++i) {
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vec.append(*(u32*)buf + i);
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}
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UnsignedBigInteger offset { move(vec) };
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return offset.plus(min);
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}
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static bool is_probably_prime(const UnsignedBigInteger& p)
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{
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if (p == 2 || p == 3 || p == 5)
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return true;
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if (p < 49)
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return true;
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Vector<UnsignedBigInteger, 256> tests;
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UnsignedBigInteger seven { 7 };
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for (size_t i = 0; i < tests.size(); ++i)
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tests.append(random_number(seven, p.minus(2)));
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return MR_primality_test(p, tests);
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}
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static UnsignedBigInteger random_big_prime(size_t bits)
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{
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ASSERT(bits >= 33);
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UnsignedBigInteger min = UnsignedBigInteger::from_base10("6074001000").shift_left(bits - 33);
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UnsignedBigInteger max = UnsignedBigInteger { 1 }.shift_left(bits).minus(1);
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for (;;) {
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auto p = random_number(min, max);
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if (is_probably_prime(p))
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return p;
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}
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}
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}
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}
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