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LibCrypto: Fix random generation and primality tests

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It was quite silly that LibCrypto thought that 30! is a prime number! :P
This commit is contained in:
Ben Wiederhake 2020-08-15 22:57:01 +02:00 committed by Andreas Kling
parent 67b24cb3a6
commit bbed5b99fd
Notes: sideshowbarker 2024-07-19 03:34:00 +09:00 
Author: https://github.com/BenWiederhake
Commit: https://github.com/SerenityOS/serenity/commit/bbed5b99fd9
Pull-request: https://github.com/SerenityOS/serenity/pull/3168
Reviewed-by: https://github.com/alimpfard
1 changed files with 60 additions and 28 deletions
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88
Libraries/LibCrypto/NumberTheory/ModularFunctions.h
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@ -272,38 +272,47 @@ inline UnsignedBigInteger LCM(const UnsignedBigInteger& a, const UnsignedBigInte
template<size_t test_count>
static bool MR_primality_test(UnsignedBigInteger n, const Vector<UnsignedBigInteger, test_count>& tests)
{
auto prev = n.minus({ 1 });
auto b = prev;
auto r = 0;
// Written using Wikipedia:
// https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test#Miller%E2%80%93Rabin_test
ASSERT(!(n < 4));
auto predecessor = n.minus({ 1 });
auto d = predecessor;
size_t r = 0;
auto div_result = b.divided_by(2);
while (div_result.quotient == 0) {
div_result = b.divided_by(2);
b = div_result.quotient;
++r;
{
auto div_result = d.divided_by(2);
while (div_result.remainder == 0) {
d = div_result.quotient;
div_result = d.divided_by(2);
++r;
}
}
if (r == 0) {
// n - 1 is odd, so n was even. But there is only one even prime:
return n == 2;
}
for (size_t i = 0; i < tests.size(); ++i) {
auto return_ = true;
if (n < tests[i])
for (auto a : tests) {
// Technically: ASSERT(2 <= a && a <= n - 2)
ASSERT(a < n);
auto x = ModularPower(a, d, n);
if (x == 1 || x == predecessor)
continue;
auto x = ModularPower(tests[i], b, n);
if (x == 1 || x == prev)
continue;
for (auto d = r - 1; d != 0; --d) {
bool skip_this_witness = false;
// r − 1 iterations.
for (size_t i = 0; i < r - 1; ++i) {
x = ModularPower(x, 2, n);
if (x == 1)
return false;
if (x == prev) {
return_ = false;
if (x == predecessor) {
skip_this_witness = true;
break;
}
}
if (return_)
return false;
if (skip_this_witness)
continue;
return false; // "composite"
}
return true;
return true; // "probably prime"
}
static UnsignedBigInteger random_number(const UnsignedBigInteger& min, const UnsignedBigInteger& max_excluded)
@ -329,15 +338,34 @@ static UnsignedBigInteger random_number(const UnsignedBigInteger& min, const Uns
static bool is_probably_prime(const UnsignedBigInteger& p)
{
if (p == 2 || p == 3 || p == 5)
return true;
if (p < 49)
// Is it a small number?
if (p < 49) {
u32 p_value = p.words()[0];
// Is it a very small prime?
if (p_value == 2 || p_value == 3 || p_value == 5 || p_value == 7)
return true;
// Is it the multiple of a very small prime?
if (p_value % 2 == 0 || p_value % 3 == 0 || p_value % 5 == 0 || p_value % 7 == 0)
return false;
// Then it must be a prime, but not a very small prime, like 37.
return true;
}
Vector<UnsignedBigInteger, 256> tests;
UnsignedBigInteger seven { 7 };
for (size_t i = 0; i < tests.size(); ++i)
tests.append(random_number(seven, p.minus(2)));
// Make some good initial guesses that are guaranteed to find all primes < 2^64.
tests.append(UnsignedBigInteger(2));
tests.append(UnsignedBigInteger(3));
tests.append(UnsignedBigInteger(5));
tests.append(UnsignedBigInteger(7));
tests.append(UnsignedBigInteger(11));
tests.append(UnsignedBigInteger(13));
UnsignedBigInteger seventeen { 17 };
for (size_t i = tests.size(); i < 256; ++i) {
tests.append(random_number(seventeen, p.minus(2)));
}
// Miller-Rabin's "error" is 8^-k. In adversarial cases, it's 4^-k.
// With 200 random numbers, this would mean an error of about 2^-400.
// So we don't need to worry too much about the quality of the random numbers.
return MR_primality_test(p, tests);
}
@ -349,6 +377,10 @@ inline static UnsignedBigInteger random_big_prime(size_t bits)
UnsignedBigInteger max = UnsignedBigInteger { 1 }.shift_left(bits).minus(1);
for (;;) {
auto p = random_number(min, max);
if ((p.words()[0] & 1) == 0) {
// An even number is definitely not a large prime.
continue;
}
if (is_probably_prime(p))
return p;
}