[PATCH v8 04/13] crypto: ecdsa - Extend res.x mod n calculation for NIST P521

[Stefan Berger]

res.x has been calculated by ecc_point_mult_shamir, which uses
'mod curve_prime' on res.x and therefore p > res.x with 'p' being the
curve_prime. Further, it is true that for the NIST curves p > n with 'n'
being the 'curve_order' and therefore the following may be true as well:
p > res.x >= n.

If res.x >= n then res.x mod n can be calculated by iteratively sub-
tracting n from res.x until res.x < n. For NIST P192/256/384 this can be
done in a single subtraction. This can also be done in a single
subtraction for NIST P521.

The mathematical reason why a single subtraction is sufficient is due to
the values of 'p' and 'n' of the NIST curves where the following holds
true:

   note: max(res.x) = p - 1

   max(res.x) - n < n
       p - 1  - n < n
       p - 1      < 2n  => holds true for the NIST curves

Tested-by: Lukas Wunner <lukas@xxxxxxxxx>
Reviewed-by: Jarkko Sakkinen <jarkko@xxxxxxxxxx>
Signed-off-by: Stefan Berger <stefanb@xxxxxxxxxxxxx>
---
 crypto/ecdsa.c | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/crypto/ecdsa.c b/crypto/ecdsa.c
index 9462a4d640a7..9b84ab503276 100644
--- a/crypto/ecdsa.c
+++ b/crypto/ecdsa.c
@@ -122,7 +122,7 @@ static int _ecdsa_verify(struct ecc_ctx *ctx, const u64 *hash, const u64 *r, con
 
 	/* res.x = res.x mod n (if res.x > order) */
 	if (unlikely(vli_cmp(res.x, curve->n, ndigits) == 1))
-		/* faster alternative for NIST p384, p256 & p192 */
+		/* faster alternative for NIST p521, p384, p256 & p192 */
 		vli_sub(res.x, res.x, curve->n, ndigits);
 
 	if (!vli_cmp(res.x, r, ndigits))
-- 
2.43.0