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

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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)
This commit is contained in:
Adam Langley 2017-09-26 10:48:55 -07:00 committed by Rich Salz
parent c55b786a89
commit 2dbfa8444b
1 changed files with 19 additions and 3 deletions
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22
crypto/ec/ecp_nistp521.c
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@ -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;
}