nistp521: add a comment to the P+P exceptional case in point_add.

This change adds a comment to the exceptional case in point_add that
handles the case of a doubling, which explains when this case may occur
during normal processing.

Thanks go to Antonio Sanso for noting this.

Reviewed-by: Emilia Käsper <emilia@openssl.org>
Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Rich Salz <rsalz@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/4424)

1 files changed, 19 insertions, 3 deletions

diff --git a/crypto/ec/ecp_nistp521.c b/crypto/ec/ecp_nistp521.c
index e491fe55c2..d68d60ef32 100644
--- a/crypto/ec/ecp_nistp521.c
+++ b/crypto/ec/ecp_nistp521.c
@@ -1157,9 +1157,9 @@ static void copy_conditional(felem out, const felem in, limb mask)
  * adapted for mixed addition (z2 = 1, or z2 = 0 for the point at infinity).
  *
  * This function includes a branch for checking whether the two input points
- * are equal (while not equal to the point at infinity). This case never
- * happens during single point multiplication, so there is no timing leak for
- * ECDH or ECDSA signing. */
+ * are equal (while not equal to the point at infinity). See comment below
+ * on constant-time.
+ */
 static void point_add(felem x3, felem y3, felem z3,
                       const felem x1, const felem y1, const felem z1,
                       const int mixed, const felem x2, const felem y2,
@@ -1253,6 +1253,22 @@ static void point_add(felem x3, felem y3, felem z3,
     /* ftmp5[i] < 2^61 */
 
     if (x_equal && y_equal && !z1_is_zero && !z2_is_zero) {
+        /*
+         * This is obviously not constant-time but it will almost-never happen
+         * for ECDH / ECDSA. The case where it can happen is during scalar-mult
+         * where the intermediate value gets very close to the group order.
+         * Since |ec_GFp_nistp_recode_scalar_bits| produces signed digits for
+         * the scalar, it's possible for the intermediate value to be a small
+         * negative multiple of the base point, and for the final signed digit
+         * to be the same value. We believe that this only occurs for the scalar
+         * 1fffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
+         * ffffffa51868783bf2f966b7fcc0148f709a5d03bb5c9b8899c47aebb6fb
+         * 71e913863f7, in that case the penultimate intermediate is -9G and
+         * the final digit is also -9G. Since this only happens for a single
+         * scalar, the timing leak is irrelevent. (Any attacker who wanted to
+         * check whether a secret scalar was that exact value, can already do
+         * so.)
+         */
         point_double(x3, y3, z3, x1, y1, z1);
         return;
     }