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@@ -3,7 +3,7 @@
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* Originally written by Bodo Moeller and Nils Larsch for the OpenSSL project.
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*/
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/* ====================================================================
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- * Copyright (c) 1998-2007 The OpenSSL Project. All rights reserved.
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+ * Copyright (c) 1998-2018 The OpenSSL Project. All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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@@ -310,6 +310,224 @@ static signed char *compute_wNAF(const BIGNUM *scalar, int w, size_t *ret_len)
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return r;
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}
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+#define EC_POINT_BN_set_flags(P, flags) do { \
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+ BN_set_flags(&(P)->X, (flags)); \
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+ BN_set_flags(&(P)->Y, (flags)); \
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+ BN_set_flags(&(P)->Z, (flags)); \
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+} while(0)
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+
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+/*-
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+ * This functions computes (in constant time) a point multiplication over the
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+ * EC group.
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+ *
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+ * At a high level, it is Montgomery ladder with conditional swaps.
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+ *
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+ * It performs either a fixed scalar point multiplication
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+ * (scalar * generator)
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+ * when point is NULL, or a generic scalar point multiplication
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+ * (scalar * point)
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+ * when point is not NULL.
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+ *
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+ * scalar should be in the range [0,n) otherwise all constant time bets are off.
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+ *
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+ * NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
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+ * which of course are not constant time themselves.
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+ *
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+ * The product is stored in r.
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+ *
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+ * Returns 1 on success, 0 otherwise.
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+ */
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+static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r,
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+ const BIGNUM *scalar, const EC_POINT *point,
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+ BN_CTX *ctx)
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+{
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+ int i, cardinality_bits, group_top, kbit, pbit, Z_is_one;
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+ EC_POINT *s = NULL;
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+ BIGNUM *k = NULL;
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+ BIGNUM *lambda = NULL;
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+ BIGNUM *cardinality = NULL;
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+ BN_CTX *new_ctx = NULL;
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+ int ret = 0;
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+
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+ if (ctx == NULL && (ctx = new_ctx = BN_CTX_new()) == NULL)
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+ return 0;
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+
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+ BN_CTX_start(ctx);
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+
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+ s = EC_POINT_new(group);
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+ if (s == NULL)
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+ goto err;
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+
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+ if (point == NULL) {
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+ if (!EC_POINT_copy(s, group->generator))
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+ goto err;
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+ } else {
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+ if (!EC_POINT_copy(s, point))
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+ goto err;
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+ }
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+
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+ EC_POINT_BN_set_flags(s, BN_FLG_CONSTTIME);
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+
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+ cardinality = BN_CTX_get(ctx);
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+ lambda = BN_CTX_get(ctx);
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+ k = BN_CTX_get(ctx);
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+ if (k == NULL || !BN_mul(cardinality, &group->order, &group->cofactor, ctx))
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+ goto err;
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+
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+ /*
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+ * Group cardinalities are often on a word boundary.
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+ * So when we pad the scalar, some timing diff might
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+ * pop if it needs to be expanded due to carries.
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+ * So expand ahead of time.
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+ */
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+ cardinality_bits = BN_num_bits(cardinality);
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+ group_top = cardinality->top;
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+ if ((bn_wexpand(k, group_top + 2) == NULL)
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+ || (bn_wexpand(lambda, group_top + 2) == NULL))
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+ goto err;
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+
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+ if (!BN_copy(k, scalar))
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+ goto err;
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+
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+ BN_set_flags(k, BN_FLG_CONSTTIME);
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+
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+ if ((BN_num_bits(k) > cardinality_bits) || (BN_is_negative(k))) {
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+ /*-
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+ * this is an unusual input, and we don't guarantee
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+ * constant-timeness
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+ */
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+ if (!BN_nnmod(k, k, cardinality, ctx))
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+ goto err;
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+ }
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+
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+ if (!BN_add(lambda, k, cardinality))
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+ goto err;
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+ BN_set_flags(lambda, BN_FLG_CONSTTIME);
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+ if (!BN_add(k, lambda, cardinality))
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+ goto err;
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+ /*
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+ * lambda := scalar + cardinality
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+ * k := scalar + 2*cardinality
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+ */
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+ kbit = BN_is_bit_set(lambda, cardinality_bits);
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+ BN_consttime_swap(kbit, k, lambda, group_top + 2);
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+
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+ group_top = group->field.top;
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+ if ((bn_wexpand(&s->X, group_top) == NULL)
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+ || (bn_wexpand(&s->Y, group_top) == NULL)
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+ || (bn_wexpand(&s->Z, group_top) == NULL)
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+ || (bn_wexpand(&r->X, group_top) == NULL)
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+ || (bn_wexpand(&r->Y, group_top) == NULL)
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+ || (bn_wexpand(&r->Z, group_top) == NULL))
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+ goto err;
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+
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+ /* top bit is a 1, in a fixed pos */
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+ if (!EC_POINT_copy(r, s))
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+ goto err;
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+
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+ EC_POINT_BN_set_flags(r, BN_FLG_CONSTTIME);
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+
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+ if (!EC_POINT_dbl(group, s, s, ctx))
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+ goto err;
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+
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+ pbit = 0;
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+
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+#define EC_POINT_CSWAP(c, a, b, w, t) do { \
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+ BN_consttime_swap(c, &(a)->X, &(b)->X, w); \
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+ BN_consttime_swap(c, &(a)->Y, &(b)->Y, w); \
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+ BN_consttime_swap(c, &(a)->Z, &(b)->Z, w); \
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+ t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
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+ (a)->Z_is_one ^= (t); \
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+ (b)->Z_is_one ^= (t); \
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+} while(0)
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+
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+ /*-
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+ * The ladder step, with branches, is
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+ *
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+ * k[i] == 0: S = add(R, S), R = dbl(R)
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+ * k[i] == 1: R = add(S, R), S = dbl(S)
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+ *
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+ * Swapping R, S conditionally on k[i] leaves you with state
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+ *
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+ * k[i] == 0: T, U = R, S
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+ * k[i] == 1: T, U = S, R
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+ *
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+ * Then perform the ECC ops.
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+ *
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+ * U = add(T, U)
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+ * T = dbl(T)
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+ *
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+ * Which leaves you with state
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+ *
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+ * k[i] == 0: U = add(R, S), T = dbl(R)
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+ * k[i] == 1: U = add(S, R), T = dbl(S)
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+ *
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+ * Swapping T, U conditionally on k[i] leaves you with state
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+ *
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+ * k[i] == 0: R, S = T, U
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+ * k[i] == 1: R, S = U, T
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+ *
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+ * Which leaves you with state
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+ *
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+ * k[i] == 0: S = add(R, S), R = dbl(R)
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+ * k[i] == 1: R = add(S, R), S = dbl(S)
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+ *
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+ * So we get the same logic, but instead of a branch it's a
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+ * conditional swap, followed by ECC ops, then another conditional swap.
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+ *
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+ * Optimization: The end of iteration i and start of i-1 looks like
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+ *
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+ * ...
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+ * CSWAP(k[i], R, S)
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+ * ECC
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+ * CSWAP(k[i], R, S)
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+ * (next iteration)
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+ * CSWAP(k[i-1], R, S)
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+ * ECC
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+ * CSWAP(k[i-1], R, S)
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+ * ...
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+ *
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+ * So instead of two contiguous swaps, you can merge the condition
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+ * bits and do a single swap.
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+ *
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+ * k[i] k[i-1] Outcome
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+ * 0 0 No Swap
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+ * 0 1 Swap
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+ * 1 0 Swap
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+ * 1 1 No Swap
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+ *
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+ * This is XOR. pbit tracks the previous bit of k.
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+ */
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+
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+ for (i = cardinality_bits - 1; i >= 0; i--) {
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+ kbit = BN_is_bit_set(k, i) ^ pbit;
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+ EC_POINT_CSWAP(kbit, r, s, group_top, Z_is_one);
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+ if (!EC_POINT_add(group, s, r, s, ctx))
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+ goto err;
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+ if (!EC_POINT_dbl(group, r, r, ctx))
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+ goto err;
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+ /*
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+ * pbit logic merges this cswap with that of the
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+ * next iteration
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+ */
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+ pbit ^= kbit;
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+ }
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+ /* one final cswap to move the right value into r */
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+ EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
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+#undef EC_POINT_CSWAP
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+
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+ ret = 1;
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+
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+ err:
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+ EC_POINT_free(s);
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+ BN_CTX_end(ctx);
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+ BN_CTX_free(new_ctx);
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+
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+ return ret;
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+}
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+
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+#undef EC_POINT_BN_set_flags
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+
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/*
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* TODO: table should be optimised for the wNAF-based implementation,
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* sometimes smaller windows will give better performance (thus the
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@@ -369,6 +587,34 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
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return EC_POINT_set_to_infinity(group, r);
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}
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+ if (!BN_is_zero(&group->order) && !BN_is_zero(&group->cofactor)) {
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+ /*-
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+ * Handle the common cases where the scalar is secret, enforcing a constant
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+ * time scalar multiplication algorithm.
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+ */
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+ if ((scalar != NULL) && (num == 0)) {
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+ /*-
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+ * In this case we want to compute scalar * GeneratorPoint: this
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+ * codepath is reached most prominently by (ephemeral) key generation
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+ * of EC cryptosystems (i.e. ECDSA keygen and sign setup, ECDH
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+ * keygen/first half), where the scalar is always secret. This is why
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+ * we ignore if BN_FLG_CONSTTIME is actually set and we always call the
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+ * constant time version.
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+ */
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+ return ec_mul_consttime(group, r, scalar, NULL, ctx);
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+ }
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+ if ((scalar == NULL) && (num == 1)) {
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+ /*-
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+ * In this case we want to compute scalar * GenericPoint: this codepath
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+ * is reached most prominently by the second half of ECDH, where the
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+ * secret scalar is multiplied by the peer's public point. To protect
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+ * the secret scalar, we ignore if BN_FLG_CONSTTIME is actually set and
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+ * we always call the constant time version.
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+ */
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+ return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
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+ }
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+ }
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+
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for (i = 0; i < num; i++) {
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if (group->meth != points[i]->meth) {
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ECerr(EC_F_EC_WNAF_MUL, EC_R_INCOMPATIBLE_OBJECTS);
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