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[crypto/ec] for ECC parameters with NULL or zero cofactor, compute it

The cofactor argument to EC_GROUP_set_generator is optional, and SCA
mitigations for ECC currently use it. So the library currently falls
back to very old SCA-vulnerable code if the cofactor is not present.

This PR allows EC_GROUP_set_generator to compute the cofactor for all
curves of cryptographic interest. Steering scalar multiplication to more
SCA-robust code.

This issue affects persisted private keys in explicit parameter form,
where the (optional) cofactor field is zero or absent.

It also affects curves not built-in to the library, but constructed
programatically with explicit parameters, then calling
EC_GROUP_set_generator with a nonsensical value (NULL, zero).

The very old scalar multiplication code is known to be vulnerable to
local uarch attacks, outside of the OpenSSL threat model. New results
suggest the code path is also vulnerable to traditional wall clock
timing attacks.

CVE-2019-1547

Reviewed-by: Nicola Tuveri <nic.tuv@gmail.com>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from #9795)
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bbbrumley authored and romen committed Sep 6, 2019
1 parent 207a564 commit 7c1709c2da5414f5b6133d00a03fc8c5bf996c7a
Showing with 105 additions and 8 deletions.
  1. +7 −1 CHANGES
  2. +1 −0 crypto/ec/ec_err.c
  3. +96 −7 crypto/ec/ec_lib.c
  4. +1 −0 include/openssl/ec.h
@@ -9,14 +9,20 @@

Changes between 1.1.0k and 1.1.0l [xx XXX xxxx]

*) Compute ECC cofactors if not provided during EC_GROUP construction. Before
this change, EC_GROUP_set_generator would accept order and/or cofactor as
NULL. After this change, only the cofactor parameter can be NULL. It also
does some minimal sanity checks on the passed order.
(CVE-2019-1547)
[Billy Bob Brumley]

*) Use Windows installation paths in the mingw builds

Mingw isn't a POSIX environment per se, which means that Windows
paths should be used for installation.
(CVE-2019-1552)
[Richard Levitte]


Changes between 1.1.0j and 1.1.0k [28 May 2019]

*) Change the default RSA, DSA and DH size to 2048 bit instead of 1024.
@@ -273,6 +273,7 @@ static ERR_STRING_DATA EC_str_reasons[] = {
{ERR_REASON(EC_R_SLOT_FULL), "slot full"},
{ERR_REASON(EC_R_UNDEFINED_GENERATOR), "undefined generator"},
{ERR_REASON(EC_R_UNDEFINED_ORDER), "undefined order"},
{ERR_REASON(EC_R_UNKNOWN_COFACTOR), "unknown cofactor"},
{ERR_REASON(EC_R_UNKNOWN_GROUP), "unknown group"},
{ERR_REASON(EC_R_UNKNOWN_ORDER), "unknown order"},
{ERR_REASON(EC_R_UNSUPPORTED_FIELD), "unsupported field"},
@@ -257,6 +257,67 @@ int EC_METHOD_get_field_type(const EC_METHOD *meth)
return meth->field_type;
}

/*-
* Try computing cofactor from the generator order (n) and field cardinality (q).
* This works for all curves of cryptographic interest.
*
* Hasse thm: q + 1 - 2*sqrt(q) <= n*h <= q + 1 + 2*sqrt(q)
* h_min = (q + 1 - 2*sqrt(q))/n
* h_max = (q + 1 + 2*sqrt(q))/n
* h_max - h_min = 4*sqrt(q)/n
* So if n > 4*sqrt(q) holds, there is only one possible value for h:
* h = \lfloor (h_min + h_max)/2 \rceil = \lfloor (q + 1)/n \rceil
*
* Otherwise, zero cofactor and return success.
*/
static int ec_guess_cofactor(EC_GROUP *group) {
int ret = 0;
BN_CTX *ctx = NULL;
BIGNUM *q = NULL;

/*-
* If the cofactor is too large, we cannot guess it.
* The RHS of below is a strict overestimate of lg(4 * sqrt(q))
*/
if (BN_num_bits(group->order) <= (BN_num_bits(group->field) + 1) / 2 + 3) {
/* default to 0 */
BN_zero(group->cofactor);
/* return success */
return 1;
}

if ((ctx = BN_CTX_new()) == NULL)
return 0;

BN_CTX_start(ctx);
if ((q = BN_CTX_get(ctx)) == NULL)
goto err;

/* set q = 2**m for binary fields; q = p otherwise */
if (group->meth->field_type == NID_X9_62_characteristic_two_field) {
BN_zero(q);
if (!BN_set_bit(q, BN_num_bits(group->field) - 1))
goto err;
} else {
if (!BN_copy(q, group->field))
goto err;
}

/* compute h = \lfloor (q + 1)/n \rceil = \lfloor (q + 1 + n/2)/n \rfloor */
if (!BN_rshift1(group->cofactor, group->order) /* n/2 */
|| !BN_add(group->cofactor, group->cofactor, q) /* q + n/2 */
/* q + 1 + n/2 */
|| !BN_add(group->cofactor, group->cofactor, BN_value_one())
/* (q + 1 + n/2)/n */
|| !BN_div(group->cofactor, NULL, group->cofactor, group->order, ctx))
goto err;
ret = 1;
err:
BN_CTX_end(ctx);
BN_CTX_free(ctx);
return ret;
}

int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
const BIGNUM *order, const BIGNUM *cofactor)
{
@@ -265,6 +326,34 @@ int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
return 0;
}

/* require group->field >= 1 */
if (group->field == NULL || BN_is_zero(group->field)
|| BN_is_negative(group->field)) {
ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_FIELD);
return 0;
}

/*-
* - require order >= 1
* - enforce upper bound due to Hasse thm: order can be no more than one bit
* longer than field cardinality
*/
if (order == NULL || BN_is_zero(order) || BN_is_negative(order)
|| BN_num_bits(order) > BN_num_bits(group->field) + 1) {
ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_INVALID_GROUP_ORDER);
return 0;
}

/*-
* Unfortunately the cofactor is an optional field in many standards.
* Internally, the lib uses 0 cofactor as a marker for "unknown cofactor".
* So accept cofactor == NULL or cofactor >= 0.
*/
if (cofactor != NULL && BN_is_negative(cofactor)) {
ECerr(EC_F_EC_GROUP_SET_GENERATOR, EC_R_UNKNOWN_COFACTOR);
return 0;
}

if (group->generator == NULL) {
group->generator = EC_POINT_new(group);
if (group->generator == NULL)
@@ -273,17 +362,17 @@ int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
if (!EC_POINT_copy(group->generator, generator))
return 0;

if (order != NULL) {
if (!BN_copy(group->order, order))
return 0;
} else
BN_zero(group->order);
if (!BN_copy(group->order, order))
return 0;

if (cofactor != NULL) {
/* Either take the provided positive cofactor, or try to compute it */
if (cofactor != NULL && !BN_is_zero(cofactor)) {
if (!BN_copy(group->cofactor, cofactor))
return 0;
} else
} else if (!ec_guess_cofactor(group)) {
BN_zero(group->cofactor);
return 0;
}

/*
* Some groups have an order with
@@ -1568,6 +1568,7 @@ int ERR_load_EC_strings(void);
# define EC_R_SLOT_FULL 108
# define EC_R_UNDEFINED_GENERATOR 113
# define EC_R_UNDEFINED_ORDER 128
# define EC_R_UNKNOWN_COFACTOR 164
# define EC_R_UNKNOWN_GROUP 129
# define EC_R_UNKNOWN_ORDER 114
# define EC_R_UNSUPPORTED_FIELD 131

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