[PATCH v2] crypto: ecc - regularize scalar for scalar multiplication

[Vitaly Chikunov <vt@altlinux.org>]

ecc_point_mult is supposed to be used with a regularized scalar,
otherwise, it's possible to deduce the position of the top bit of the
scalar with timing attack. This is important when the scalar is a
private key.

ecc_point_mult is already using a regular algorithm (i.e. having an
operation flow independent of the input scalar) but regularization step
is not implemented.

Arrange scalar to always have fixed top bit by adding a multiple of the
curve order (n).

References:
The constant time regularization step is based on micro-ecc by Kenneth
MacKay and also referenced in the literature (Bernstein, D. J., & Lange,
T. (2017). Montgomery curves and the Montgomery ladder. (Cryptology
ePrint Archive; Vol. 2017/293). s.l.: IACR. Chapter 4.6.2.)

Signed-off-by: Vitaly Chikunov <vt@altlinux.org>
Cc: kernel-hardening@lists.openwall.com
---

Changes from v1:
- No code changes, only description updates to be more informative.

 crypto/ecc.c | 16 ++++++++++++----
 1 file changed, 12 insertions(+), 4 deletions(-)

diff --git a/crypto/ecc.c b/crypto/ecc.c
index 8facafd67802..adcce310f646 100644
--- a/crypto/ecc.c
+++ b/crypto/ecc.c
@@ -842,15 +842,23 @@ static void xycz_add_c(u64 *x1, u64 *y1, u64 *x2, u64 *y2, u64 *curve_prime,
 
 static void ecc_point_mult(struct ecc_point *result,
 			   const struct ecc_point *point, const u64 *scalar,
-			   u64 *initial_z, u64 *curve_prime,
+			   u64 *initial_z, const struct ecc_curve *curve,
 			   unsigned int ndigits)
 {
 	/* R0 and R1 */
 	u64 rx[2][ECC_MAX_DIGITS];
 	u64 ry[2][ECC_MAX_DIGITS];
 	u64 z[ECC_MAX_DIGITS];
+	u64 sk[2][ECC_MAX_DIGITS];
+	u64 *curve_prime = curve->p;
 	int i, nb;
-	int num_bits = vli_num_bits(scalar, ndigits);
+	int num_bits;
+	int carry;
+
+	carry = vli_add(sk[0], scalar, curve->n, ndigits);
+	vli_add(sk[1], sk[0], curve->n, ndigits);
+	scalar = sk[!carry];
+	num_bits = sizeof(u64) * ndigits * 8 + 1;
 
 	vli_set(rx[1], point->x, ndigits);
 	vli_set(ry[1], point->y, ndigits);
@@ -1004,7 +1012,7 @@ int ecc_make_pub_key(unsigned int curve_id, unsigned int ndigits,
 		goto out;
 	}
 
-	ecc_point_mult(pk, &curve->g, priv, NULL, curve->p, ndigits);
+	ecc_point_mult(pk, &curve->g, priv, NULL, curve, ndigits);
 	if (ecc_point_is_zero(pk)) {
 		ret = -EAGAIN;
 		goto err_free_point;
@@ -1090,7 +1098,7 @@ int crypto_ecdh_shared_secret(unsigned int curve_id, unsigned int ndigits,
 		goto err_alloc_product;
 	}
 
-	ecc_point_mult(product, pk, priv, rand_z, curve->p, ndigits);
+	ecc_point_mult(product, pk, priv, rand_z, curve, ndigits);
 
 	ecc_swap_digits(product->x, secret, ndigits);
 
-- 
2.11.0