Native jacobi symbol algorithm
This introduces variants of the divsteps-based GCD algorithm used for modular inverses to compute Jacobi symbols. Changes compared to the normal vartime divsteps: * Only positive matrices are used, guaranteeing that f and g remain positive. * An additional jac variable is updated to track sign changes during matrix computation. * There is (so far) no proof that this algorithm terminates within reasonable amount of time for every input, but experimentally it appears to almost always need less than 900 iterations. To account for that, only a bounded number of iterations is performed (1500), after which failure is returned. In VERIFY mode a lower iteration count is used to make sure that callers exercise their fallback. * The algorithm converges to f=g=gcd(f0,g0) rather than g=0. To keep this test simple, the end condition is f=1, which won't be reached if started with non-coprime or g=0 inputs. Because of that we only support coprime non-zero inputs.
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@@ -39,4 +39,9 @@ static void secp256k1_modinv64_var(secp256k1_modinv64_signed62 *x, const secp256
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/* Same as secp256k1_modinv64_var, but constant time in x (not in the modulus). */
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static void secp256k1_modinv64(secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo);
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/* Compute the Jacobi symbol for (x | modinfo->modulus). x must be coprime with modulus (and thus
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* cannot be 0, as modulus >= 3). All limbs of x must be non-negative. Returns 0 if the result
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* cannot be computed. */
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static int secp256k1_jacobi64_maybe_var(const secp256k1_modinv64_signed62 *x, const secp256k1_modinv64_modinfo *modinfo);
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#endif /* SECP256K1_MODINV64_H */
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