[email protected] writes:
> GOST curves will require different "fixups" for fast (mul X mod p)
> operations. Move these operations to ecc_modulo structure and call them
> via function pointer.
Can you explain what methods you intend to use? I had a quick look at
the prime definitions in the next patch,
+ else if (!strcmp (curve, "gc256b"))
+ {
+ ecc_curve_init_str (ecc, ECC_TYPE_WEIERSTRASS,
+ "ffffffffffffffffffffffffffffffff"
+ "fffffffffffffffffffffffffffffd97",
Should work fine with the current functions.
+ else if (!strcmp (curve, "gc256c"))
+ {
+ ecc_curve_init_str (ecc, ECC_TYPE_WEIERSTRASS,
+ "80000000000000000000000000000000"
+ "00000000000000000000000000000c99",
Could use special tricks. Structure is similar to the q for curve25519.
+ else if (!strcmp (curve, "gc256d"))
+ {
+ ecc_curve_init_str (ecc, ECC_TYPE_WEIERSTRASS,
+ "9b9f605f5a858107ab1ec85e6b41c8aa"
+ "cf846e86789051d37998f7b9022d759b",
This has no visible structure. One could maybe use some variant of the
3/2 division in https://gmplib.org/~tege/division-paper.pdf to find a
good enough quotient, and divide without any bignum adjustment step. The
result should then be a non-canonical remainder, in the range 0 <= r <
2^256. Everything needs to be side-channel silent.
Another option is to premultiply, and do computations mod k p for some
smallish k. With k = 0x1a51f176161f1d734 (same as the 3/2 reciprocal, I
think),
k p =
ffffffffffffffffd8e5627c0706fb8dc4f73162b7fca65ab59cdb66ec652b2787ac757f10ec107c
with friendly structure (but one word larger). I think this trick is
known as Svoboda division. But for the main operations, it is likely
more efficient to use plain unstructured redc, precomputing p^{-1} mod B
(where B is word size, 2^32 or 2^64 depending on architecture).
Regards,
/Niels
--
Niels Möller. PGP-encrypted email is preferred. Keyid 368C6677.
Internet email is subject to wholesale government surveillance.
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