[PATCH v6 04/13] crypto: ecdsa - Extend res.x mod n calculation for NIST P521

Stefan Berger
2024-03-12T18:37:40Z

From: Stefan Berger <stefanb@linux.ibm.com>

res.x has been calculated by ecc_point_mult_shamir, which uses
'mod curve_prime'. The curve_prime 'p' is typically larger than the
curve_order 'n' and therefore it is possible that 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 n > res.x. 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 => true for the NIST curves

Signed-off-by: Stefan Berger <stefanb@linux.ibm.com>
Tested-by: Lukas Wunner <lukas@wunner.de>
---
crypto/ecdsa.c | 2 +-
1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/crypto/ecdsa.c b/crypto/ecdsa.c
index 64e1e69d53ba..1814f009f971 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