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Better public key generation.

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GitOrigin-RevId: 1fd0b8e824620c90901168a2d12e97b92b76e37a
This commit is contained in:
levlam 2019-08-25 01:02:39 +03:00
parent eaca53604a
commit 3306c42e89
1 changed files with 36 additions and 9 deletions
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45
td/mtproto/TlsInit.cpp
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@ -295,18 +295,16 @@ class TlsHelloStore {
auto key = dest_.substr(0, 32);
while (true) {
Random::secure_bytes(key);
key[31] = static_cast<char>(key[31] & 127);
BigNum x = BigNum::from_binary(key);
BigNum::mod_mul(x, x, x, mod, big_num_context);
BigNum y = x.clone();
BigNum coef = BigNum::from_decimal("486662").move_as_ok();
BigNum::mod_add(y, y, coef, mod, big_num_context);
BigNum::mod_mul(y, y, x, mod, big_num_context);
BigNum one = BigNum::from_decimal("1").move_as_ok();
BigNum::mod_add(y, y, one, mod, big_num_context);
BigNum::mod_mul(y, y, x, mod, big_num_context);
// y = x^3 + 486662 * x^2 + x
BigNum y = get_y2(x, mod, big_num_context);
if (is_quadratic_residue(y)) {
for (int i = 0; i < 3; i++) {
x = get_double_x(x, mod, big_num_context);
}
key.copy_from(x.to_le_binary(32));
LOG(ERROR) << td::format::as_hex_dump<0>(td::Slice(key));
break;
}
}
@ -352,6 +350,35 @@ class TlsHelloStore {
MutableSlice dest_;
std::vector<size_t> scope_offset_;
static BigNum get_y2(BigNum &x, const BigNum &mod, BigNumContext &big_num_context) {
// returns y = x^3 + 486662 * x^2 + x
BigNum y = x.clone();
BigNum coef = BigNum::from_decimal("486662").move_as_ok();
BigNum::mod_add(y, y, coef, mod, big_num_context);
BigNum::mod_mul(y, y, x, mod, big_num_context);
BigNum one = BigNum::from_decimal("1").move_as_ok();
BigNum::mod_add(y, y, one, mod, big_num_context);
BigNum::mod_mul(y, y, x, mod, big_num_context);
return y;
}
static BigNum get_double_x(BigNum &x, const BigNum &mod, BigNumContext &big_num_context) {
// returns x_2 = (x^2 - 1)^2/(4*y^2)
BigNum denominator = get_y2(x, mod, big_num_context);
BigNum coef = BigNum::from_decimal("4").move_as_ok();
BigNum::mod_mul(denominator, denominator, coef, mod, big_num_context);
BigNum numerator;
BigNum::mod_mul(numerator, x, x, mod, big_num_context);
BigNum one = BigNum::from_decimal("1").move_as_ok();
BigNum::mod_sub(numerator, numerator, one, mod, big_num_context);
BigNum::mod_mul(numerator, numerator, numerator, mod, big_num_context);
BigNum::mod_inverse(denominator, denominator, mod, big_num_context);
BigNum::mod_mul(numerator, numerator, denominator, mod, big_num_context);
return numerator;
}
static bool is_quadratic_residue(const BigNum &a) {
// 2^255 - 19
BigNum mod = BigNum::from_hex("7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed").move_as_ok();