f45846f500
This commit uses the new ladder scaffold to implement a specialized ladder step based on differential addition-and-doubling in mixed Lopez-Dahab projective coordinates, modified to independently blind the operands. The arithmetic in `ladder_pre`, `ladder_step` and `ladder_post` is auto generated with tooling: - see, e.g., "Guide to ECC" Alg 3.40 for reference about the `ladder_pre` implementation; - see https://www.hyperelliptic.org/EFD/g12o/auto-code/shortw/xz/ladder/mladd-2003-s.op3 for the differential addition-and-doubling formulas implemented in `ladder_step`; - see, e.g., "Fast Multiplication on Elliptic Curves over GF(2**m) without Precomputation" (Lopez and Dahab, CHES 1999) Appendix Alg Mxy for the `ladder_post` implementation to recover the `(x,y)` result in affine coordinates. Co-authored-by: Billy Brumley <bbrumley@gmail.com> Co-authored-by: Sohaib ul Hassan <soh.19.hassan@gmail.com> Reviewed-by: Andy Polyakov <appro@openssl.org> Reviewed-by: Matt Caswell <matt@openssl.org> (Merged from https://github.com/openssl/openssl/pull/6690) |
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