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Atmosphere/libraries/libvapours/source/crypto/impl/crypto_bignum_operations.cpp

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/*
* Copyright (c) Atmosphère-NX
*
* This program is free software; you can redistribute it and/or modify it
* under the terms and conditions of the GNU General Public License,
* version 2, as published by the Free Software Foundation.
*
* This program is distributed in the hope it will be useful, but WITHOUT
* ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
* FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for
* more details.
*
* You should have received a copy of the GNU General Public License
* along with this program. If not, see <http://www.gnu.org/licenses/>.
*/
#include <vapours.hpp>
namespace ams::crypto::impl {
namespace {
constexpr ALWAYS_INLINE BigNum::Word GetTop2Bits(BigNum::Word w) {
return (w >> (BigNum::BitsPerWord - 2)) & 0x3u;
}
constexpr ALWAYS_INLINE void MultWord(BigNum::Word *dst, BigNum::Word lhs, BigNum::Word rhs) {
static_assert(sizeof(BigNum::DoubleWord) == sizeof(BigNum::Word) * 2);
BigNum::DoubleWord result = static_cast<BigNum::DoubleWord>(lhs) * static_cast<BigNum::DoubleWord>(rhs);
dst[0] = static_cast<BigNum::Word>(result & ~BigNum::Word());
dst[1] = static_cast<BigNum::Word>(result >> BITSIZEOF(BigNum::Word));
}
constexpr ALWAYS_INLINE BigNum::HalfWord GetUpperHalf(BigNum::Word word) {
static_assert(sizeof(BigNum::Word) == sizeof(BigNum::HalfWord) * 2);
return static_cast<BigNum::HalfWord>((word >> BITSIZEOF(BigNum::HalfWord)) & ~BigNum::HalfWord());
}
constexpr ALWAYS_INLINE BigNum::HalfWord GetLowerHalf(BigNum::Word word) {
static_assert(sizeof(BigNum::Word) == sizeof(BigNum::HalfWord) * 2);
return static_cast<BigNum::HalfWord>(word & ~BigNum::HalfWord());
}
constexpr ALWAYS_INLINE BigNum::Word ToUpperHalf(BigNum::HalfWord half) {
static_assert(sizeof(BigNum::Word) == sizeof(BigNum::HalfWord) * 2);
return static_cast<BigNum::Word>(half) << BITSIZEOF(BigNum::HalfWord);
}
constexpr ALWAYS_INLINE BigNum::Word ToLowerHalf(BigNum::HalfWord half) {
static_assert(sizeof(BigNum::Word) == sizeof(BigNum::HalfWord) * 2);
return static_cast<BigNum::Word>(half);
}
constexpr ALWAYS_INLINE BigNum::Word DivWord(const BigNum::Word *w, BigNum::Word div) {
using Word = BigNum::Word;
using HalfWord = BigNum::HalfWord;
Word work[2] = { w[0], w[1] };
HalfWord r_hi = 0, r_lo = 0;
HalfWord d_hi = GetUpperHalf(div);
HalfWord d_lo = GetLowerHalf(div);
if (d_hi == BigNum::MaxHalfWord) {
r_hi = GetUpperHalf(work[1]);
} else {
r_hi = GetLowerHalf(work[1] / (d_hi + 1));
}
{
const Word hh = static_cast<Word>(r_hi) * static_cast<Word>(d_hi);
const Word hl = static_cast<Word>(r_hi) * static_cast<Word>(d_lo);
const Word uhl = ToUpperHalf(static_cast<HalfWord>(hl));
if ((work[0] -= uhl) > (BigNum::MaxWord - uhl)) {
work[1]--;
}
work[1] -= GetUpperHalf(hl);
work[1] -= hh;
const Word udl = ToUpperHalf(d_lo);
while (work[1] > d_hi || (work[1] == d_hi && work[0] >= udl)) {
if ((work[0] -= udl) > (BigNum::MaxWord - udl)) {
work[1]--;
}
work[1] -= d_hi;
r_hi++;
}
}
if (d_hi == BigNum::MaxHalfWord) {
r_lo = GetLowerHalf(work[1]);
} else {
r_lo = GetLowerHalf((ToUpperHalf(static_cast<HalfWord>(work[1])) + GetUpperHalf(work[0])) / (d_hi + 1));
}
{
const Word ll = static_cast<Word>(r_lo) * static_cast<Word>(d_lo);
const Word lh = static_cast<Word>(r_lo) * static_cast<Word>(d_hi);
if ((work[0] -= ll) > (BigNum::MaxWord - ll)) {
work[1]--;
}
const Word ulh = ToUpperHalf(static_cast<HalfWord>(lh));
if ((work[0] -= ulh) > (BigNum::MaxWord - ulh)) {
work[1]--;
}
work[1] -= GetUpperHalf(lh);
while ((work[1] > 0) || (work[1] == 0 && work[0] >= div)) {
if ((work[0] -= div) > (BigNum::MaxWord - div)) {
work[1]--;
}
r_lo++;
}
}
return ToUpperHalf(r_hi) + r_lo;
}
}
bool BigNum::IsZero(const Word *w, size_t num_words) {
for (size_t i = 0; i < num_words; i++) {
if (w[i]) {
return false;
}
}
return true;
}
int BigNum::Compare(const Word *lhs, const Word *rhs, size_t num_words) {
for (s32 i = static_cast<s32>(num_words) - 1; i >= 0; i--) {
if (lhs[i] > rhs[i]) {
return 1;
} else if (lhs[i] < rhs[i]) {
return -1;
}
}
return 0;
}
size_t BigNum::CountWords(const Word *w, size_t num_words) {
s32 i = static_cast<s32>(num_words) - 1;
while (i >= 0 && !w[i]) {
i--;
}
return i + 1;
}
size_t BigNum::CountSignificantBits(Word w) {
size_t i;
for (i = 0; i < BitsPerWord && w != 0; i++) {
w >>= 1;
}
return i;
}
void BigNum::ClearToZero(Word *w, size_t num_words) {
for (size_t i = 0; i < num_words; i++) {
w[i] = 0;
}
}
void BigNum::SetToWord(Word *w, size_t num_words, Word v) {
ClearToZero(w, num_words);
w[0] = v;
}
void BigNum::Copy(Word *dst, const Word *src, size_t num_words) {
for (size_t i = 0; i < num_words; i++) {
dst[i] = src[i];
}
}
BigNum::Word BigNum::LeftShift(Word *dst, const Word *w, size_t num_words, const size_t shift) {
if (shift >= BitsPerWord) {
return 0;
}
const size_t invshift = BitsPerWord - shift;
Word carry = 0;
for (size_t i = 0; i < num_words; i++) {
const Word cur = w[i];
dst[i] = (cur << shift) | carry;
carry = shift ? (cur >> invshift) : 0;
}
return carry;
}
BigNum::Word BigNum::RightShift(Word *dst, const Word *w, size_t num_words, const size_t shift) {
if (shift >= BitsPerWord) {
return 0;
}
const size_t invshift = BitsPerWord - shift;
Word carry = 0;
for (s32 i = static_cast<s32>(num_words) - 1; i >= 0; i--) {
const Word cur = w[i];
dst[i] = (cur >> shift) | carry;
carry = shift ? (cur << invshift) : 0;
}
return carry;
}
BigNum::Word BigNum::MultSub(Word *dst, const Word *w, const Word *v, size_t num_words, Word mult) {
/* If multiplying by zero, nothing to do. */
if (mult == 0) {
return 0;
}
Word borrow = 0, work[2];
for (size_t i = 0; i < num_words; i++) {
/* Multiply, calculate borrow for next. */
MultWord(work, mult, v[i]);
if ((dst[i] = (w[i] - borrow)) > (MaxWord - borrow)) {
borrow = 1;
} else {
borrow = 0;
}
if ((dst[i] -= work[0]) > (MaxWord - work[0])) {
borrow++;
}
borrow += work[1];
}
return borrow;
}
bool BigNum::ExpMod(Word *dst, const Word *src, const Word *exp, size_t exp_words, const Word *mod, size_t mod_words, WordAllocator *allocator) {
/* Nintendo uses an algorithm that relies on powers of exp. */
bool needs_exp[4] = {};
if (exp_words > 1) {
needs_exp[2] = true;
needs_exp[3] = true;
} else {
Word exp_w = exp[0];
for (size_t i = 0; i < BitsPerWord / 2; i++) {
/* Nintendo at each step determines needed exponent from a pair of two bits. */
needs_exp[exp_w & 0x3u] = true;
exp_w >>= 2;
}
if (needs_exp[3]) {
needs_exp[2] = true;
}
}
/* Allocate space for powers 1, 2, 3. */
auto power_1 = allocator->Allocate(mod_words);
auto power_2 = allocator->Allocate(mod_words);
auto power_3 = allocator->Allocate(mod_words);
if (!(power_1.IsValid() && power_2.IsValid() && power_3.IsValid())) {
return false;
}
decltype(power_1)* powers[3] = { std::addressof(power_1), std::addressof(power_2), std::addressof(power_3) };
/* Set the powers of src. */
Copy(power_1.GetBuffer(), src, mod_words);
if (needs_exp[2]) {
if (!MultMod(power_2.GetBuffer(), power_1.GetBuffer(), src, mod, mod_words, allocator)) {
return false;
}
}
if (needs_exp[3]) {
if (!MultMod(power_3.GetBuffer(), power_2.GetBuffer(), src, mod, mod_words, allocator)) {
return false;
}
}
/* Allocate space to work. */
auto work = allocator->Allocate(mod_words);
if (!work.IsValid()) {
return false;
}
SetToWord(work.GetBuffer(), work.GetCount(), 1);
/* Ensure we're working with the correct exponent word count. */
exp_words = CountWords(exp, exp_words);
for (s32 i = static_cast<s32>(exp_words - 1); i >= 0; i--) {
Word cur_word = exp[i];
size_t cur_bits = BitsPerWord;
/* Remove leading zeroes in first word. */
if (i == static_cast<s32>(exp_words - 1)) {
while (!GetTop2Bits(cur_word)) {
cur_word <<= 2;
cur_bits -= 2;
}
}
/* Compute current modular multiplicative step. */
for (size_t j = 0; j < cur_bits; j += 2, cur_word <<= 2) {
/* Exponentiate current work to the 4th power. */
if (!MultMod(work.GetBuffer(), work.GetBuffer(), work.GetBuffer(), mod, mod_words, allocator)) {
return false;
}
if (!MultMod(work.GetBuffer(), work.GetBuffer(), work.GetBuffer(), mod, mod_words, allocator)) {
return false;
}
if (const Word top = GetTop2Bits(cur_word)) {
if (!MultMod(work.GetBuffer(), work.GetBuffer(), powers[top - 1]->GetBuffer(), mod, mod_words, allocator)) {
return false;
}
}
}
}
/* Copy work to output. */
Copy(dst, work.GetBuffer(), mod_words);
return true;
}
bool BigNum::MultMod(Word *dst, const Word *src, const Word *mult, const Word *mod, size_t num_words, WordAllocator *allocator) {
/* Allocate work. */
auto work = allocator->Allocate(2 * num_words);
if (!work.IsValid()) {
return false;
}
/* Multiply. */
if (!Mult(work.GetBuffer(), src, mult, num_words, allocator)) {
return false;
}
/* Mod. */
if (!Mod(dst, work.GetBuffer(), 2 * num_words, mod, num_words, allocator)) {
return false;
}
return true;
}
bool BigNum::Mod(Word *dst, const Word *src, size_t src_words, const Word *mod, size_t mod_words, WordAllocator *allocator) {
/* Allocate work. */
auto work = allocator->Allocate(src_words);
if (!work.IsValid()) {
return false;
}
if (!DivMod(work.GetBuffer(), dst, src, src_words, mod, mod_words, allocator)) {
return false;
}
return true;
}
bool BigNum::DivMod(Word *quot, Word *rem, const Word *top, size_t top_words, const Word *bot, size_t bot_words, WordAllocator *allocator) {
/* Allocate work. */
auto top_work = allocator->Allocate(top_words + 1);
auto bot_work = allocator->Allocate(bot_words);
if (!(top_work.IsValid() && bot_work.IsValid())) {
return false;
}
/* Prevent division by zero. */
size_t bot_work_words = CountWords(bot, bot_words);
if (bot_work_words == 0) {
return false;
}
ClearToZero(quot, top_words);
ClearToZero(top_work.GetBuffer(), bot_work_words);
/* Align to edges. */
const size_t shift = BitsPerWord - CountSignificantBits(bot[bot_work_words - 1]);
top_work.GetBuffer()[top_words] = LeftShift(top_work.GetBuffer(), top, top_words, shift);
LeftShift(bot_work.GetBuffer(), bot, bot_work_words, shift);
const Word tb = bot_work.GetBuffer()[bot_work_words - 1];
/* Repeatedly div + sub. */
for (s32 i = (top_words - bot_work_words); i >= 0; i--) {
Word cur_word;
if (tb == MaxWord) {
cur_word = top_work.GetBuffer()[i + bot_work_words];
} else {
cur_word = DivWord(top_work.GetBuffer() + i + bot_work_words - 1, tb + 1);
}
top_work.GetBuffer()[i + bot_work_words] -= MultSub(top_work.GetBuffer() + i, top_work.GetBuffer() + i, bot_work.GetBuffer(), bot_work_words, cur_word);
while (top_work.GetBuffer()[i + bot_work_words] || Compare(top_work.GetBuffer() + i, bot_work.GetBuffer(), bot_work_words) >= 0) {
cur_word++;
top_work.GetBuffer()[i + bot_work_words] -= Sub(top_work.GetBuffer() + i, top_work.GetBuffer() + i, bot_work.GetBuffer(), bot_work_words);
}
quot[i] = cur_word;
}
/* Calculate remainder. */
ClearToZero(rem, bot_words);
RightShift(rem, top_work.GetBuffer(), bot_work_words, shift);
return true;
}
bool BigNum::Mult(Word *dst, const Word *lhs, const Word *rhs, size_t num_words, WordAllocator *allocator) {
/* Allocate work. */
auto work = allocator->Allocate(2 * num_words);
if (!work.IsValid()) {
return false;
}
ClearToZero(work.GetBuffer(), work.GetCount());
/* Repeatedly add and multiply. */
const size_t lhs_words = CountWords(lhs, num_words);
const size_t rhs_words = CountWords(rhs, num_words);
for (size_t i = 0; i < lhs_words; i++) {
work.GetBuffer()[i + rhs_words] += MultAdd(work.GetBuffer() + i, rhs, rhs_words, lhs[i]);
}
/* Copy to output. */
Copy(dst, work.GetBuffer(), work.GetCount());
return true;
}
}
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