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Elliptic curve scalar multiplication with timing attack defenses

Co-authored-by: Nicola Tuveri <nic.tuv@gmail.com>
Co-authored-by: Cesar Pereida Garcia <cesar.pereidagarcia@tut.fi>
Co-authored-by: Sohaib ul Hassan <soh.19.hassan@gmail.com>

Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from #6009)

(cherry picked from commit 40e48e5)
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bbbrumley authored and mattcaswell committed Apr 19, 2018
1 parent aab39f6 commit aab7c770353b1dc4ba045938c8fb446dd1c4531e
Showing with 195 additions and 0 deletions.
  1. +13 −0 crypto/bn/bn_lib.c
  2. +182 −0 crypto/ec/ec_mult.c
@@ -824,6 +824,19 @@ void BN_consttime_swap(BN_ULONG condition, BIGNUM *a, BIGNUM *b, int nwords)
a->top ^= t;
b->top ^= t;
t = (a->neg ^ b->neg) & condition;
a->neg ^= t;
b->neg ^= t;
/*
* cannot just arbitrarily swap flags.
* The way a->d is allocated etc.
* BN_FLG_MALLOCED, BN_FLG_STATIC_DATA, ...
*/
t = (a->flags ^ b->flags) & condition & BN_FLG_CONSTTIME;
a->flags ^= t;
b->flags ^= t;
#define BN_CONSTTIME_SWAP(ind) \
do { \
t = (a->d[ind] ^ b->d[ind]) & condition; \
@@ -105,6 +105,166 @@ void EC_ec_pre_comp_free(EC_PRE_COMP *pre)
OPENSSL_free(pre);
}
#define EC_POINT_set_flags(P, flags) do { \
BN_set_flags((P)->X, (flags)); \
BN_set_flags((P)->Y, (flags)); \
BN_set_flags((P)->Z, (flags)); \
} while(0)
/*
* This functions computes (in constant time) a point multiplication over the
* EC group.
*
* It performs either a fixed scalar point multiplication
* (scalar * generator)
* when point is NULL, or a generic scalar point multiplication
* (scalar * point)
* when point is not NULL.
*
* scalar should be in the range [0,n) otherwise all constant time bets are off.
*
* NB: This says nothing about EC_POINT_add and EC_POINT_dbl,
* which of course are not constant time themselves.
*
* The product is stored in r.
*
* Returns 1 on success, 0 otherwise.
*/
static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
const EC_POINT *point, BN_CTX *ctx)
{
int i, order_bits, group_top, kbit, pbit, Z_is_one, ret;
ret = 0;
EC_POINT *s = NULL;
BIGNUM *k = NULL;
BIGNUM *lambda = NULL;
BN_CTX *new_ctx = NULL;
if (ctx == NULL)
if ((ctx = new_ctx = BN_CTX_secure_new()) == NULL)
return 0;
if ((group->order == NULL) || (group->field == NULL))
goto err;
order_bits = BN_num_bits(group->order);
s = EC_POINT_new(group);
if (s == NULL)
goto err;
if (point == NULL) {
if (group->generator == NULL)
goto err;
if (!EC_POINT_copy(s, group->generator))
goto err;
} else {
if (!EC_POINT_copy(s, point))
goto err;
}
EC_POINT_set_flags(s, BN_FLG_CONSTTIME);
BN_CTX_start(ctx);
lambda = BN_CTX_get(ctx);
k = BN_CTX_get(ctx);
if (k == NULL)
goto err;
/*
* Group orders are often on a word boundary.
* So when we pad the scalar, some timing diff might
* pop if it needs to be expanded due to carries.
* So expand ahead of time.
*/
group_top = bn_get_top(group->order);
if ((bn_wexpand(k, group_top + 1) == NULL)
|| (bn_wexpand(lambda, group_top + 1) == NULL))
goto err;
if (!BN_copy(k, scalar))
goto err;
BN_set_flags(k, BN_FLG_CONSTTIME);
if ((BN_num_bits(k) > order_bits) || (BN_is_negative(k))) {
/*
* this is an unusual input, and we don't guarantee
* constant-timeness
*/
if(!BN_nnmod(k, k, group->order, ctx))
goto err;
}
if (!BN_add(lambda, k, group->order))
goto err;
BN_set_flags(lambda, BN_FLG_CONSTTIME);
if (!BN_add(k, lambda, group->order))
goto err;
/*
* lambda := scalar + order
* k := scalar + 2*order
*/
kbit = BN_is_bit_set(lambda, order_bits);
BN_consttime_swap(kbit, k, lambda, group_top + 1);
group_top = bn_get_top(group->field);
if ((bn_wexpand(s->X, group_top) == NULL)
|| (bn_wexpand(s->Y, group_top) == NULL)
|| (bn_wexpand(s->Z, group_top) == NULL)
|| (bn_wexpand(r->X, group_top) == NULL)
|| (bn_wexpand(r->Y, group_top) == NULL)
|| (bn_wexpand(r->Z, group_top) == NULL))
goto err;
/* top bit is a 1, in a fixed pos */
if (!EC_POINT_copy(r, s))
goto err;
EC_POINT_set_flags(r, BN_FLG_CONSTTIME);
if (!EC_POINT_dbl(group, s, s, ctx))
goto err;
pbit = 0;
#define EC_POINT_CSWAP(c, a, b, w, t) do { \
BN_consttime_swap(c, (a)->X, (b)->X, w); \
BN_consttime_swap(c, (a)->Y, (b)->Y, w); \
BN_consttime_swap(c, (a)->Z, (b)->Z, w); \
t = ((a)->Z_is_one ^ (b)->Z_is_one) & (c); \
(a)->Z_is_one ^= (t); \
(b)->Z_is_one ^= (t); \
} while(0)
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);
if (!EC_POINT_add(group, s, r, s, ctx))
goto err;
if (!EC_POINT_dbl(group, r, r, ctx))
goto err;
/*
* pbit logic merges this cswap with that of the
* next iteration
*/
pbit ^= kbit;
}
/* one final cswap to move the right value into r */
EC_POINT_CSWAP(pbit, r, s, group_top, Z_is_one);
#undef EC_POINT_CSWAP
ret = 1;
err:
EC_POINT_free(s);
BN_CTX_end(ctx);
BN_CTX_free(new_ctx);
return ret;
}
#undef EC_POINT_set_flags
/*
* TODO: table should be optimised for the wNAF-based implementation,
* sometimes smaller windows will give better performance (thus the
@@ -130,6 +290,28 @@ int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
size_t num, const EC_POINT *points[], const BIGNUM *scalars[],
BN_CTX *ctx)
{
if ((scalar != NULL) && (num == 0)) {
/* In this case we want to compute scalar * GeneratorPoint:
* this codepath is reached most prominently by (ephemeral) key
* generation of EC cryptosystems (i.e. ECDSA keygen and sign setup,
* ECDH keygen/first half), where the scalar is always secret.
* This is why we ignore if BN_FLG_CONSTTIME is actually set and we
* always call the constant time version.
*/
return ec_mul_consttime(group, r, scalar, NULL, ctx);
}
if ((scalar == NULL) && (num == 1)) {
/* In this case we want to compute scalar * GenericPoint:
* this codepath is reached most prominently by the second half of
* ECDH, where the secret scalar is multiplied by the peer's public
* point.
* To protect the secret scalar, we ignore if BN_FLG_CONSTTIME is
* actually set and we always call the constant time version.
*/
return ec_mul_consttime(group, r, scalars[0], points[0], ctx);
}
BN_CTX *new_ctx = NULL;
const EC_POINT *generator = NULL;
EC_POINT *tmp = NULL;

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