Implement coordinate blinding for EC_POINT

This commit implements coordinate blinding, i.e., it randomizes the
representative of an elliptic curve point in its equivalence class, for
prime curves implemented through EC_GFp_simple_method,
EC_GFp_mont_method, and EC_GFp_nist_method.

This commit is derived from the patch
https://marc.info/?l=openssl-dev&m=131194808413635 by Billy Brumley.

Coordinate blinding is a generally useful side-channel countermeasure
and is (mostly) free. The function itself takes a few field
multiplicationss, but is usually only necessary at the beginning of a
scalar multiplication (as implemented in the patch). When used this way,
it makes the values that variables take (i.e., field elements in an
algorithm state) unpredictable.

For instance, this mitigates chosen EC point side-channel attacks for
settings such as ECDH and EC private key decryption, for the
aforementioned curves.

For EC_METHODs using different coordinate representations this commit
does nothing, but the corresponding coordinate blinding function can be
easily added in the future to extend these changes to such curves.

Co-authored-by: Nicola Tuveri <nic.tuv@gmail.com>
Co-authored-by: Billy Brumley <bbrumley@gmail.com>

Reviewed-by: Andy Polyakov <appro@openssl.org>
Reviewed-by: Matt Caswell <matt@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/6501)

CHANGES

@@ -8,6 +8,11 @@
  release branch.
 
  Changes between 1.1.0h and 1.1.1 [xx XXX xxxx]
+  *) Add coordinate blinding for EC_POINT and implement projective
+     coordinate blinding for generic prime curves as a countermeasure to
+     chosen point SCA attacks.
+     [Sohaib ul Hassan, Nicola Tuveri, Billy Bob Brumley]
+
   *) Add blinding to an ECDSA signature to protect against side channel attacks
      discovered by Keegan Ryan (NCC Group).
      [Matt Caswell]

crypto/ec/ec2_smpl.c

@@ -64,7 +64,9 @@ const EC_METHOD *EC_GF2m_simple_method(void)
         ec_key_simple_generate_public_key,
         0, /* keycopy */
         0, /* keyfinish */
-        ecdh_simple_compute_key
+        ecdh_simple_compute_key,
+        0, /* field_inverse_mod_ord */
+        0  /* blind_coordinates */
     };
 
     return &ret;

crypto/ec/ec_err.c

@@ -116,6 +116,8 @@ static const ERR_STRING_DATA EC_str_functs[] = {
      "ec_GFp_nist_field_sqr"},
     {ERR_PACK(ERR_LIB_EC, EC_F_EC_GFP_NIST_GROUP_SET_CURVE, 0),
      "ec_GFp_nist_group_set_curve"},
+    {ERR_PACK(ERR_LIB_EC, EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, 0),
+     "ec_GFp_simple_blind_coordinates"},
     {ERR_PACK(ERR_LIB_EC, EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT, 0),
      "ec_GFp_simple_group_check_discriminant"},
     {ERR_PACK(ERR_LIB_EC, EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE, 0),

crypto/ec/ec_lcl.h

@@ -176,6 +176,7 @@ struct ec_method_st {
     /* Inverse modulo order */
     int (*field_inverse_mod_ord)(const EC_GROUP *, BIGNUM *r, BIGNUM *x,
                                  BN_CTX *ctx);
+    int (*blind_coordinates)(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);
 };
 
 /*
@@ -382,6 +383,8 @@ int ec_GFp_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
                             const BIGNUM *b, BN_CTX *);
 int ec_GFp_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a,
                             BN_CTX *);
+int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
+                                   BN_CTX *ctx);
 
 /* method functions in ecp_mont.c */
 int ec_GFp_mont_group_init(EC_GROUP *);
@@ -635,3 +638,5 @@ void X25519_public_from_private(uint8_t out_public_value[32],
 
 int EC_GROUP_do_inverse_ord(const EC_GROUP *group, BIGNUM *res,
                             BIGNUM *x, BN_CTX *ctx);
+
+int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx);

crypto/ec/ec_lib.c

@@ -1025,3 +1025,21 @@ int EC_GROUP_do_inverse_ord(const EC_GROUP *group, BIGNUM *res,
     else
         return 0;
 }
+
+/*-
+ * Coordinate blinding for EC_POINT.
+ *
+ * The underlying EC_METHOD can optionally implement this function:
+ * underlying implementations should return 0 on errors, or 1 on
+ * success.
+ *
+ * This wrapper returns 1 in case the underlying EC_METHOD does not
+ * support coordinate blinding.
+ */
+int ec_point_blind_coordinates(const EC_GROUP *group, EC_POINT *p, BN_CTX *ctx)
+{
+    if (group->meth->blind_coordinates == NULL)
+        return 1; /* ignore if not implemented */
+
+    return group->meth->blind_coordinates(group, p, ctx);
+}

crypto/ec/ec_mult.c

@@ -211,6 +211,17 @@ static int ec_mul_consttime(const EC_GROUP *group, EC_POINT *r,
         || (bn_wexpand(r->Z, group_top) == NULL))
         goto err;
 
+    /*-
+     * Apply coordinate blinding for EC_POINT.
+     *
+     * The underlying EC_METHOD can optionally implement this function:
+     * ec_point_blind_coordinates() returns 0 in case of errors or 1 on
+     * success or if coordinate blinding is not implemented for this
+     * group.
+     */
+    if (!ec_point_blind_coordinates(group, s, ctx))
+        goto err;
+
     /* top bit is a 1, in a fixed pos */
     if (!EC_POINT_copy(r, s))
         goto err;

crypto/ec/ecp_mont.c

@@ -61,7 +61,9 @@ const EC_METHOD *EC_GFp_mont_method(void)
         ec_key_simple_generate_public_key,
         0, /* keycopy */
         0, /* keyfinish */
-        ecdh_simple_compute_key
+        ecdh_simple_compute_key,
+        0, /* field_inverse_mod_ord */
+        ec_GFp_simple_blind_coordinates
     };
 
     return &ret;

crypto/ec/ecp_nist.c

@@ -63,7 +63,9 @@ const EC_METHOD *EC_GFp_nist_method(void)
         ec_key_simple_generate_public_key,
         0, /* keycopy */
         0, /* keyfinish */
-        ecdh_simple_compute_key
+        ecdh_simple_compute_key,
+        0, /* field_inverse_mod_ord */
+        ec_GFp_simple_blind_coordinates
     };
 
     return &ret;

crypto/ec/ecp_nistp224.c

@@ -290,7 +290,9 @@ const EC_METHOD *EC_GFp_nistp224_method(void)
         ec_key_simple_generate_public_key,
         0, /* keycopy */
         0, /* keyfinish */
-        ecdh_simple_compute_key
+        ecdh_simple_compute_key,
+        0, /* field_inverse_mod_ord */
+        0  /* blind_coordinates */
     };
 
     return &ret;

crypto/ec/ecp_nistp521.c

@@ -1658,7 +1658,9 @@ const EC_METHOD *EC_GFp_nistp521_method(void)
         ec_key_simple_generate_public_key,
         0, /* keycopy */
         0, /* keyfinish */
-        ecdh_simple_compute_key
+        ecdh_simple_compute_key,
+        0, /* field_inverse_mod_ord */
+        0  /* blind_coordinates */
     };
 
     return &ret;

crypto/ec/ecp_nistz256.c

@@ -1730,7 +1730,8 @@ const EC_METHOD *EC_GFp_nistz256_method(void)
         0, /* keycopy */
         0, /* keyfinish */
         ecdh_simple_compute_key,
-        ecp_nistz256_inv_mod_ord                    /* can be #define-d NULL */
+        ecp_nistz256_inv_mod_ord,                   /* can be #define-d NULL */
+        0                                           /* blind_coordinates */
     };
 
     return &ret;

crypto/ec/ecp_smpl.c

@@ -62,7 +62,9 @@ const EC_METHOD *EC_GFp_simple_method(void)
         ec_key_simple_generate_public_key,
         0, /* keycopy */
         0, /* keyfinish */
-        ecdh_simple_compute_key
+        ecdh_simple_compute_key,
+        0, /* field_inverse_mod_ord */
+        ec_GFp_simple_blind_coordinates
     };
 
     return &ret;
@@ -1363,3 +1365,57 @@ int ec_GFp_simple_field_sqr(const EC_GROUP *group, BIGNUM *r, const BIGNUM *a,
 {
     return BN_mod_sqr(r, a, group->field, ctx);
 }
+
+/*-
+ * Apply randomization of EC point projective coordinates:
+ *
+ *   (X, Y ,Z ) = (lambda^2*X, lambda^3*Y, lambda*Z)
+ *   lambda = [1,group->field)
+ *
+ */
+int ec_GFp_simple_blind_coordinates(const EC_GROUP *group, EC_POINT *p,
+                                    BN_CTX *ctx)
+{
+    int ret = 0;
+    BIGNUM *lambda = NULL;
+    BIGNUM *temp = NULL;
+
+    BN_CTX_start(ctx);
+    lambda = BN_CTX_get(ctx);
+    temp = BN_CTX_get(ctx);
+    if (temp == NULL) {
+        ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_MALLOC_FAILURE);
+        goto err;
+    }
+
+    /* make sure lambda is not zero */
+    do {
+        if (!BN_priv_rand_range(lambda, group->field)) {
+            ECerr(EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES, ERR_R_BN_LIB);
+            goto err;
+        }
+    } while (BN_is_zero(lambda));
+
+    /* if field_encode defined convert between representations */
+    if (group->meth->field_encode != NULL
+        && !group->meth->field_encode(group, lambda, lambda, ctx))
+        goto err;
+    if (!group->meth->field_mul(group, p->Z, p->Z, lambda, ctx))
+        goto err;
+    if (!group->meth->field_sqr(group, temp, lambda, ctx))
+        goto err;
+    if (!group->meth->field_mul(group, p->X, p->X, temp, ctx))
+        goto err;
+    if (!group->meth->field_mul(group, temp, temp, lambda, ctx))
+        goto err;
+    if (!group->meth->field_mul(group, p->Y, p->Y, temp, ctx))
+        goto err;
+    p->Z_is_one = 0;
+
+    ret = 1;
+
+ err:
+     BN_CTX_end(ctx);
+     return ret;
+}
+

crypto/err/openssl.txt

@@ -550,6 +550,7 @@ EC_F_EC_GFP_NISTP521_POINT_GET_AFFINE_COORDINATES:235:\
 EC_F_EC_GFP_NIST_FIELD_MUL:200:ec_GFp_nist_field_mul
 EC_F_EC_GFP_NIST_FIELD_SQR:201:ec_GFp_nist_field_sqr
 EC_F_EC_GFP_NIST_GROUP_SET_CURVE:202:ec_GFp_nist_group_set_curve
+EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES:287:ec_GFp_simple_blind_coordinates
 EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT:165:\
 	ec_GFp_simple_group_check_discriminant
 EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE:166:ec_GFp_simple_group_set_curve

include/openssl/ecerr.h

@@ -87,6 +87,7 @@ int ERR_load_EC_strings(void);
 #  define EC_F_EC_GFP_NIST_FIELD_MUL                       200
 #  define EC_F_EC_GFP_NIST_FIELD_SQR                       201
 #  define EC_F_EC_GFP_NIST_GROUP_SET_CURVE                 202
+#  define EC_F_EC_GFP_SIMPLE_BLIND_COORDINATES             287
 #  define EC_F_EC_GFP_SIMPLE_GROUP_CHECK_DISCRIMINANT      165
 #  define EC_F_EC_GFP_SIMPLE_GROUP_SET_CURVE               166
 #  define EC_F_EC_GFP_SIMPLE_MAKE_AFFINE                   102