Commit a067a870 authored by Billy Brumley's avatar Billy Brumley Committed by Matt Caswell
Browse files

ladder description: why it works 



Reviewed-by: default avatarAndy Polyakov <appro@openssl.org>
Reviewed-by: default avatarMatt Caswell <matt@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/6009)
parent 36bed230

crypto/ec/ec_mult.c

+60 −0
Original line number Diff line number Diff line
@@ -111,6 +111,8 @@ void EC_ec_pre_comp_free(EC_PRE_COMP *pre) 
 * This functions computes (in constant time) a point multiplication over the

 * EC group.

 *

 * At a high level, it is Montgomery ladder with conditional swaps.

 *

 * It performs either a fixed scalar point multiplication

 *          (scalar * generator)

 * when point is NULL, or a generic scalar point multiplication
@@ -232,6 +234,64 @@ static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r, const BIGNUM *sc 
        (b)->Z_is_one ^= (t);                      \

} while(0)



    /*

     * The ladder step, with branches, is

     *

     * k[i] == 0: S = add(R, S), R = dbl(R)

     * k[i] == 1: R = add(S, R), S = dbl(S)

     *

     * Swapping R, S conditionally on k[i] leaves you with state

     *

     * k[i] == 0: T, U = R, S

     * k[i] == 1: T, U = S, R

     *

     * Then perform the ECC ops.

     *

     * U = add(T, U)

     * T = dbl(T)

     *

     * Which leaves you with state

     *

     * k[i] == 0: U = add(R, S), T = dbl(R)

     * k[i] == 1: U = add(S, R), T = dbl(S)

     *

     * Swapping T, U conditionally on k[i] leaves you with state

     *

     * k[i] == 0: R, S = T, U

     * k[i] == 1: R, S = U, T

     *

     * Which leaves you with state

     *

     * k[i] == 0: S = add(R, S), R = dbl(R)

     * k[i] == 1: R = add(S, R), S = dbl(S)

     *

     * So we get the same logic, but instead of a branch it's a

     * conditional swap, followed by ECC ops, then another conditional swap.

     *

     * Optimization: The end of iteration i and start of i-1 looks like

     *

     * ...

     * CSWAP(k[i], R, S)

     * ECC

     * CSWAP(k[i], R, S)

     * (next iteration)

     * CSWAP(k[i-1], R, S)

     * ECC

     * CSWAP(k[i-1], R, S)

     * ...

     *

     * So instead of two contiguous swaps, you can merge the condition

     * bits and do a single swap.

     *

     * k[i]    k[i-1]    Outcome

     * 0       0         No Swap

     * 0       1         Swap

     * 1       0         Swap

     * 1       1         No Swap

     *

     * This is XOR. pbit tracks the previous bit of k.

     */



    for (i = order_bits - 1; i >= 0; i--) {

        kbit = BN_is_bit_set(k, i) ^ pbit;

        EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);