crypto: ecc - regularize scalar for scalar multiplication

[ Upstream commit 3da2c1d ]

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
Signed-off-by: Herbert Xu <herbert@gondor.apana.org.au>
Signed-off-by: Sasha Levin <sashal@kernel.org>

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);