Alien-libsecp256k1
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libsecp256k1/doc/safegcd_implementation.md view on Meta::CPAN
# always odd, so its inverse modulo a power of two always exists.
w = (g * NEGINV16[(f & 15) // 2]) % (2**limit)
# As w = -g/f mod (2**limit), g+w*f mod 2**limit = 0 mod 2**limit.
g += w * f
assert g % (2**limit) == 0
# The next iteration will now shift out at least limit bottom zero bits from g.
```
By using a bigger table more bits can be cancelled at once. The table can also be implemented
as a formula. Several formulas are known for computing modular inverses modulo powers of two;
some can be found in Hacker's Delight second edition by Henry S. Warren, Jr. pages 245-247.
Here we need the negated modular inverse, which is a simple transformation of those:
- Instead of a 3-bit table:
- *-f* or *f ^ 6*
- Instead of a 4-bit table:
- *1 - f(f + 1)*
- *-(f + (((f + 1) & 4) << 1))*
- For larger tables the following technique can be used: if *w=-1/f mod 2<sup>L</sup>*, then *w(w f+2)* is
*-1/f mod 2<sup>2L</sup>*. This allows extending the previous formulas (or tables). In particular we
have this 6-bit function (based on the 3-bit function above):
libsecp256k1/src/tests.c view on Meta::CPAN
memcpy(msg, "msg", 3);
CHECK(secp256k1_tagged_sha256(CTX, hash32, tag, 3, msg, 3) == 1);
CHECK(secp256k1_memcmp_var(hash32, hash_expected, sizeof(hash32)) == 0);
}
/***** MODINV TESTS *****/
/* Compute the modular inverse of (odd) x mod 2^64. */
static uint64_t modinv2p64(uint64_t x) {
/* If w = 1/x mod 2^(2^L), then w*(2 - w*x) = 1/x mod 2^(2^(L+1)). See
* Hacker's Delight second edition, Henry S. Warren, Jr., pages 245-247 for
* why. Start with L=0, for which it is true for every odd x that
* 1/x=1 mod 2. Iterating 6 times gives us 1/x mod 2^64. */
int l;
uint64_t w = 1;
CHECK(x & 1);
for (l = 0; l < 6; ++l) w *= (2 - w*x);
return w;
}
libsecp256k1/src/wycheproof/WYCHEPROOF_COPYING view on Meta::CPAN
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libsecp256k1/src/wycheproof/ecdsa_secp256k1_sha256_bitcoin_test.h view on Meta::CPAN
/* Note: this file was autogenerated using tests_wycheproof_generate.py. Do not edit. */
#define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS (463)
typedef struct {
size_t pk_offset;
size_t msg_offset;
size_t msg_len;
size_t sig_offset;
size_t sig_len;
int expected_verify;
} wycheproof_ecdsa_testvector;
libsecp256k1/tools/tests_wycheproof_generate.py view on Meta::CPAN
size_t pk_offset;
size_t msg_offset;
size_t msg_len;
size_t sig_offset;
size_t sig_len;
int expected_verify;
} wycheproof_ecdsa_testvector;
"""
print("/* Note: this file was autogenerated using tests_wycheproof_generate.py. Do not edit. */")
print(f"#define SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS ({num_vectors})")
print(struct_definition)
print("static const unsigned char wycheproof_ecdsa_messages[] = { " + messages + "};\n")
print("static const unsigned char wycheproof_ecdsa_public_keys[] = { " + public_keys + "};\n")
print("static const unsigned char wycheproof_ecdsa_signatures[] = { " + signatures + "};\n")
print("static const wycheproof_ecdsa_testvector testvectors[SECP256K1_ECDSA_WYCHEPROOF_NUMBER_TESTVECTORS] = {")
print(out)
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