Daiki Ueno ueno@gnu.org writes:
Thank you. By the way, one thing I realized in my past rebase attempts is that, this commit doing the final reduction of a value by mod q seems to be incorrect for curve448 and should probably be reverted:
commit 6cf6abd68eb3d6c8c8e5ab217be734f9c537037f Author: Daiki Ueno dueno@redhat.com Date: Sat Aug 5 09:43:47 2017 +0200
ecc-eh-to-a, eddsa-sign: Parameterize hard-coded value This allows the same code to be reused in curve448 and Ed448. Signed-off-by: Daiki Ueno <dueno@redhat.com>
shift = 252 - GMP_NUMB_BITS * (ecc->p.size - 1);
shift = ecc->q.bit_size - 1 - GMP_NUMB_BITS * (ecc->p.size - 1); cy = mpn_submul_1 (r, ecc->q.m, ecc->p.size, r[ecc->p.size-1] >> shift);For curve25519, q is defined as:
2^252 + 0x14def9dea2f79cd65812631a5cf5d3ed
whose bit pattern starts with 0x1000, so r - q * (r>>252) should work.
On the other hand, for curve448, q is defined as:
2^446 - 0x8335dc163bb124b65129c96fde933d8d723a70aadc873d6d54a7bb0d
whose bit pattern starts with 0xFFFF. In that case the formula (r - q * (r>>445)) could be incorrect due to the accumulated errors by multiplication (i.e. q * 0x7FFF...).
Good catch! Right, this needs a bit more analysis. Fur curve25519, the subtraction can underflow (unlikely), which is addressed with the conditional addition a few lines down.
Therefore, I suggest using r - q * (r>>446) instead, though it would introduce another hard-coded value.
But for curve448, that subtraction will never underflow, instead it will sometimes produce a non-canonical result, r >= q. So correcting the shift isn't enough.
On the other hand, this code should perhaps be deleted altogether, I think h_to_a with flags == 2 is used only for ecdsa. It might make sense to instead add a function pointer to struct ecc_modulo to do canonical reduction; that's needed in a few different places, not only here.
Regards, /Niels