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LibCrypto: Fix random generation and primality tests

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

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@ -272,38 +272,47 @@ inline UnsignedBigInteger LCM(const UnsignedBigInteger& a, const UnsignedBigInte
template<size_t test_count> template<size_t test_count>
static bool MR_primality_test(UnsignedBigInteger n, const Vector<UnsignedBigInteger, test_count>& tests) static bool MR_primality_test(UnsignedBigInteger n, const Vector<UnsignedBigInteger, test_count>& tests)
{ {
auto prev = n.minus({ 1 }); // Written using Wikipedia:
auto b = prev; // https://en.wikipedia.org/wiki/Miller%E2%80%93Rabin_primality_test#Miller%E2%80%93Rabin_test
auto r = 0; 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) { auto div_result = d.divided_by(2);
div_result = b.divided_by(2); while (div_result.remainder == 0) {
b = div_result.quotient; d = div_result.quotient;
++r; 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) { for (auto a : tests) {
auto return_ = true; // Technically: ASSERT(2 <= a && a <= n - 2)
if (n < tests[i]) ASSERT(a < n);
auto x = ModularPower(a, d, n);
if (x == 1 || x == predecessor)
continue; continue;
auto x = ModularPower(tests[i], b, n); bool skip_this_witness = false;
if (x == 1 || x == prev) // r 1 iterations.
continue; for (size_t i = 0; i < r - 1; ++i) {
for (auto d = r - 1; d != 0; --d) {
x = ModularPower(x, 2, n); x = ModularPower(x, 2, n);
if (x == 1) if (x == predecessor) {
return false; skip_this_witness = true;
if (x == prev) {
return_ = false;
break; break;
} }
} }
if (return_) if (skip_this_witness)
return false; continue;
return false; // "composite"
} }
return true; return true; // "probably prime"
} }
static UnsignedBigInteger random_number(const UnsignedBigInteger& min, const UnsignedBigInteger& max_excluded) 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) static bool is_probably_prime(const UnsignedBigInteger& p)
{ {
if (p == 2 || p == 3 || p == 5) // Is it a small number?
return true; if (p < 49) {
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; return true;
}
Vector<UnsignedBigInteger, 256> tests; Vector<UnsignedBigInteger, 256> tests;
UnsignedBigInteger seven { 7 }; // Make some good initial guesses that are guaranteed to find all primes < 2^64.
for (size_t i = 0; i < tests.size(); ++i) tests.append(UnsignedBigInteger(2));
tests.append(random_number(seven, p.minus(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); 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); UnsignedBigInteger max = UnsignedBigInteger { 1 }.shift_left(bits).minus(1);
for (;;) { for (;;) {
auto p = random_number(min, max); 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)) if (is_probably_prime(p))
return p; return p;
} }