crypto: ecc - regularize scalar for scalar multiplication

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 <[e-mail]>
Cc: [e-mail]
Signed-off-by: Herbert Xu <[e-mail]>

crypto/ecc.c

···
 
 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);
···
 		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;
···
 		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);