This commit leverages the Montgomery ladder scaffold introduced in #6690
(alongside a specialized Lopez-Dahab ladder for binary curves) to
provide a specialized differential addition-and-double implementation to
speedup prime curves, while keeping all the features of
`ec_scalar_mul_ladder` against SCA attacks.
The arithmetic in ladder_pre, ladder_step and ladder_post is auto
generated with tooling, from the following formulae:
- `ladder_pre`: Formula 3 for doubling from Izu-Takagi "A fast parallel
elliptic curve multiplication resistant against side channel attacks",
as described at
https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#doubling-dbl-2002-it-2
- `ladder_step`: differential addition-and-doubling Eq. (8) and (10)
from Izu-Takagi "A fast parallel elliptic curve multiplication
resistant against side channel attacks", as described at
https://hyperelliptic.org/EFD/g1p/auto-shortw-xz.html#ladder-ladd-2002-it-3
- `ladder_post`: y-coordinate recovery using Eq. (8) from Brier-Joye
"Weierstrass Elliptic Curves and Side-Channel Attacks", modified to
work in projective coordinates.
Co-authored-by: Nicola Tuveri <nic.tuv@gmail.com>
Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Rich Salz <rsalz@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/6772)
9d91530d2d