Remove unused secp256k1_wnaf_const
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@@ -104,83 +104,6 @@ static void secp256k1_ecmult_const_odd_multiples_table_globalz(secp256k1_ge *pre
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secp256k1_fe_cmov(&(r)->y, &neg_y, negative); \
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} while(0)
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/** Convert a number to WNAF notation.
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* The number becomes represented by sum(2^{wi} * wnaf[i], i=0..WNAF_SIZE(w)+1) - return_val.
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* It has the following guarantees:
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* - each wnaf[i] an odd integer between -(1 << w) and (1 << w)
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* - each wnaf[i] is nonzero
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* - the number of words set is always WNAF_SIZE(w) + 1
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*
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* Adapted from `The Width-w NAF Method Provides Small Memory and Fast Elliptic Scalar
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* Multiplications Secure against Side Channel Attacks`, Okeya and Tagaki. M. Joye (Ed.)
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* CT-RSA 2003, LNCS 2612, pp. 328-443, 2003. Springer-Verlag Berlin Heidelberg 2003
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*
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* Numbers reference steps of `Algorithm SPA-resistant Width-w NAF with Odd Scalar` on pp. 335
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*/
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static int secp256k1_wnaf_const(int *wnaf, const secp256k1_scalar *scalar, int w, int size) {
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int global_sign;
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int skew;
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int word = 0;
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/* 1 2 3 */
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int u_last;
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int u;
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int flip;
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secp256k1_scalar s = *scalar;
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VERIFY_CHECK(w > 0);
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VERIFY_CHECK(size > 0);
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/* Note that we cannot handle even numbers by negating them to be odd, as is
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* done in other implementations, since if our scalars were specified to have
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* width < 256 for performance reasons, their negations would have width 256
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* and we'd lose any performance benefit. Instead, we use a variation of a
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* technique from Section 4.2 of the Okeya/Tagaki paper, which is to add 1 to the
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* number we are encoding when it is even, returning a skew value indicating
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* this, and having the caller compensate after doing the multiplication.
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*
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* In fact, we _do_ want to negate numbers to minimize their bit-lengths (and in
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* particular, to ensure that the outputs from the endomorphism-split fit into
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* 128 bits). If we negate, the parity of our number flips, affecting whether
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* we want to add to the scalar to ensure that it's odd. */
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flip = secp256k1_scalar_is_high(&s);
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skew = flip ^ secp256k1_scalar_is_even(&s);
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secp256k1_scalar_cadd_bit(&s, 0, skew);
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global_sign = secp256k1_scalar_cond_negate(&s, flip);
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/* 4 */
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u_last = secp256k1_scalar_shr_int(&s, w);
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do {
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int even;
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/* 4.1 4.4 */
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u = secp256k1_scalar_shr_int(&s, w);
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/* 4.2 */
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even = ((u & 1) == 0);
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/* In contrast to the original algorithm, u_last is always > 0 and
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* therefore we do not need to check its sign. In particular, it's easy
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* to see that u_last is never < 0 because u is never < 0. Moreover,
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* u_last is never = 0 because u is never even after a loop
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* iteration. The same holds analogously for the initial value of
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* u_last (in the first loop iteration). */
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VERIFY_CHECK(u_last > 0);
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VERIFY_CHECK((u_last & 1) == 1);
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u += even;
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u_last -= even * (1 << w);
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/* 4.3, adapted for global sign change */
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wnaf[word++] = u_last * global_sign;
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u_last = u;
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} while (word * w < size);
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wnaf[word] = u * global_sign;
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VERIFY_CHECK(secp256k1_scalar_is_zero(&s));
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VERIFY_CHECK(word == WNAF_SIZE_BITS(size, w));
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return skew;
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}
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/* For K as defined in the comment of secp256k1_ecmult_const, we have several precomputed
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* formulas/constants.
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* - in exhaustive test mode, we give an explicit expression to compute it at compile time: */
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