linux-kernel - [PATCH v3 03/10] crypto: ecdsa - Extend res.x mod n calculation for NIST P521

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Date: Fri, 23 Feb 2024 15:41:42 -0500
From: Stefan Berger <stefanb@...ux.ibm.com>
To: keyrings@...r.kernel.org, linux-crypto@...r.kernel.org,
        herbert@...dor.apana.org.au, davem@...emloft.net
Cc: linux-kernel@...r.kernel.org, saulo.alessandre@....jus.br,
        Stefan Berger <stefanb@...ux.ibm.com>
Subject: [PATCH v3 03/10] crypto: ecdsa - Extend res.x mod n calculation for NIST P521

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@...ux.ibm.com>
---
 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