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LibCrypto: Use square-and-multiply loop for modular_inverse

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Instead of using the hand unrolled version of the square-and-multiply
algorithm, we now simply use a loop.
This commit is contained in:
Michiel Visser 2023-11-09 18:51:34 +01:00 • committed by Andrew Kaster
parent 5b658c341c
commit 153cd3ecf0
1 changed files with 7 additions and 37 deletions
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44
Userland/Libraries/LibCrypto/Curves/SECP256r1.cpp
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@ -189,46 +189,16 @@ static constexpr u256 modular_inverse(u256 const& value)
{
// Modular inverse modulo the curve prime can be computed using Fermat's little theorem: a^(p-2) mod p = a^-1 mod p.
// Calculating a^(p-2) mod p can be done using the square-and-multiply exponentiation method, as p-2 is constant.
//
// p-2 = 2^256 - 2^224 + 2^192 + 2^96 - 3, or written as binary:
// 1111111111111111111111111111111100000000000000000000000000000001
// 0000000000000000000000000000000000000000000000000000000000000000
// 0000000000000000000000000000000011111111111111111111111111111111
// 1111111111111111111111111111111111111111111111111111111111111101
u256 base = value;
u256 result = to_montgomery(1u);
u256 prime_minus_2 = PRIME - 2u;
// 1
u256 result = value;
base = modular_square(base);
// 0
base = modular_square(base);
// 94*1
for (auto i = 0; i < 94; i++) {
result = modular_multiply(result, base);
base = modular_square(base);
}
// 96*0
for (auto i = 0; i < 96; i++) {
base = modular_square(base);
}
// 1
result = modular_multiply(result, base);
base = modular_square(base);
// 31*0
for (auto i = 0; i < 31; i++) {
base = modular_square(base);
}
// 32*1
for (auto i = 0; i < 32; i++) {
result = modular_multiply(result, base);
for (size_t i = 0; i < 256; i++) {
if ((prime_minus_2 & 1u) == 1u) {
result = modular_multiply(result, base);
}
base = modular_square(base);
prime_minus_2 >>= 1u;
}
return result;