knf approximation

1 files changed, 213 insertions, 161 deletions

diff --git a/src/lib/libcrypto/ec/ec2_mult.c b/src/lib/libcrypto/ec/ec2_mult.c
index 1c575dc47a..040d7bb278 100644
--- a/src/lib/libcrypto/ec/ec2_mult.c
+++ b/src/lib/libcrypto/ec/ec2_mult.c
@@ -21,7 +21,7 @@
  * are met:
  *
  * 1. Redistributions of source code must retain the above copyright
- *    notice, this list of conditions and the following disclaimer. 
+ *    notice, this list of conditions and the following disclaimer.
  *
  * 2. Redistributions in binary form must reproduce the above copyright
  *    notice, this list of conditions and the following disclaimer in
@@ -74,178 +74,215 @@
 #ifndef OPENSSL_NO_EC2M
 
 
-/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective 
+/* Compute the x-coordinate x/z for the point 2*(x/z) in Montgomery projective
  * coordinates.
- * Uses algorithm Mdouble in appendix of 
- *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over 
+ * Uses algorithm Mdouble in appendix of
+ *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
  *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  * modified to not require precomputation of c=b^{2^{m-1}}.
  */
-static int gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
-        {
+static int 
+gf2m_Mdouble(const EC_GROUP *group, BIGNUM *x, BIGNUM *z, BN_CTX *ctx)
+{
         BIGNUM *t1;
         int ret = 0;
-        
+
         /* Since Mdouble is static we can guarantee that ctx != NULL. */
         BN_CTX_start(ctx);
         t1 = BN_CTX_get(ctx);
-        if (t1 == NULL) goto err;
+        if (t1 == NULL)
+                goto err;
 
-        if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
-        if (!group->meth->field_sqr(group, t1, z, ctx)) goto err;
-        if (!group->meth->field_mul(group, z, x, t1, ctx)) goto err;
-        if (!group->meth->field_sqr(group, x, x, ctx)) goto err;
-        if (!group->meth->field_sqr(group, t1, t1, ctx)) goto err;
-        if (!group->meth->field_mul(group, t1, &group->b, t1, ctx)) goto err;
-        if (!BN_GF2m_add(x, x, t1)) goto err;
+        if (!group->meth->field_sqr(group, x, x, ctx))
+                goto err;
+        if (!group->meth->field_sqr(group, t1, z, ctx))
+                goto err;
+        if (!group->meth->field_mul(group, z, x, t1, ctx))
+                goto err;
+        if (!group->meth->field_sqr(group, x, x, ctx))
+                goto err;
+        if (!group->meth->field_sqr(group, t1, t1, ctx))
+                goto err;
+        if (!group->meth->field_mul(group, t1, &group->b, t1, ctx))
+                goto err;
+        if (!BN_GF2m_add(x, x, t1))
+                goto err;
 
         ret = 1;
 
- err:
+err:
         BN_CTX_end(ctx);
         return ret;
-        }
+}
 
-/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery 
+/* Compute the x-coordinate x1/z1 for the point (x1/z1)+(x2/x2) in Montgomery
  * projective coordinates.
- * Uses algorithm Madd in appendix of 
- *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over 
+ * Uses algorithm Madd in appendix of
+ *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
  *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  */
-static int gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1, 
-        const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
-        {
+static int 
+gf2m_Madd(const EC_GROUP *group, const BIGNUM *x, BIGNUM *x1, BIGNUM *z1,
+    const BIGNUM *x2, const BIGNUM *z2, BN_CTX *ctx)
+{
         BIGNUM *t1, *t2;
         int ret = 0;
-        
+
         /* Since Madd is static we can guarantee that ctx != NULL. */
         BN_CTX_start(ctx);
         t1 = BN_CTX_get(ctx);
         t2 = BN_CTX_get(ctx);
-        if (t2 == NULL) goto err;
+        if (t2 == NULL)
+                goto err;
 
-        if (!BN_copy(t1, x)) goto err;
-        if (!group->meth->field_mul(group, x1, x1, z2, ctx)) goto err;
-        if (!group->meth->field_mul(group, z1, z1, x2, ctx)) goto err;
-        if (!group->meth->field_mul(group, t2, x1, z1, ctx)) goto err;
-        if (!BN_GF2m_add(z1, z1, x1)) goto err;
-        if (!group->meth->field_sqr(group, z1, z1, ctx)) goto err;
-        if (!group->meth->field_mul(group, x1, z1, t1, ctx)) goto err;
-        if (!BN_GF2m_add(x1, x1, t2)) goto err;
+        if (!BN_copy(t1, x))
+                goto err;
+        if (!group->meth->field_mul(group, x1, x1, z2, ctx))
+                goto err;
+        if (!group->meth->field_mul(group, z1, z1, x2, ctx))
+                goto err;
+        if (!group->meth->field_mul(group, t2, x1, z1, ctx))
+                goto err;
+        if (!BN_GF2m_add(z1, z1, x1))
+                goto err;
+        if (!group->meth->field_sqr(group, z1, z1, ctx))
+                goto err;
+        if (!group->meth->field_mul(group, x1, z1, t1, ctx))
+                goto err;
+        if (!BN_GF2m_add(x1, x1, t2))
+                goto err;
 
         ret = 1;
 
- err:
+err:
         BN_CTX_end(ctx);
         return ret;
-        }
+}
 
-/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2) 
- * using Montgomery point multiplication algorithm Mxy() in appendix of 
- *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over 
+/* Compute the x, y affine coordinates from the point (x1, z1) (x2, z2)
+ * using Montgomery point multiplication algorithm Mxy() in appendix of
+ *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
  *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  * Returns:
  *     0 on error
  *     1 if return value should be the point at infinity
  *     2 otherwise
  */
-static int gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1, 
-        BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
-        {
+static int 
+gf2m_Mxy(const EC_GROUP *group, const BIGNUM *x, const BIGNUM *y, BIGNUM *x1,
+    BIGNUM *z1, BIGNUM *x2, BIGNUM *z2, BN_CTX *ctx)
+{
         BIGNUM *t3, *t4, *t5;
         int ret = 0;
-        
-        if (BN_is_zero(z1))
-                {
+
+        if (BN_is_zero(z1)) {
                 BN_zero(x2);
                 BN_zero(z2);
                 return 1;
-                }
-        
-        if (BN_is_zero(z2))
-                {
-                if (!BN_copy(x2, x)) return 0;
-                if (!BN_GF2m_add(z2, x, y)) return 0;
+        }
+        if (BN_is_zero(z2)) {
+                if (!BN_copy(x2, x))
+                        return 0;
+                if (!BN_GF2m_add(z2, x, y))
+                        return 0;
                 return 2;
-                }
-                
+        }
         /* Since Mxy is static we can guarantee that ctx != NULL. */
         BN_CTX_start(ctx);
         t3 = BN_CTX_get(ctx);
         t4 = BN_CTX_get(ctx);
         t5 = BN_CTX_get(ctx);
-        if (t5 == NULL) goto err;
+        if (t5 == NULL)
+                goto err;
 
-        if (!BN_one(t5)) goto err;
+        if (!BN_one(t5))
+                goto err;
 
-        if (!group->meth->field_mul(group, t3, z1, z2, ctx)) goto err;
+        if (!group->meth->field_mul(group, t3, z1, z2, ctx))
+                goto err;
 
-        if (!group->meth->field_mul(group, z1, z1, x, ctx)) goto err;
-        if (!BN_GF2m_add(z1, z1, x1)) goto err;
-        if (!group->meth->field_mul(group, z2, z2, x, ctx)) goto err;
-        if (!group->meth->field_mul(group, x1, z2, x1, ctx)) goto err;
-        if (!BN_GF2m_add(z2, z2, x2)) goto err;
+        if (!group->meth->field_mul(group, z1, z1, x, ctx))
+                goto err;
+        if (!BN_GF2m_add(z1, z1, x1))
+                goto err;
+        if (!group->meth->field_mul(group, z2, z2, x, ctx))
+                goto err;
+        if (!group->meth->field_mul(group, x1, z2, x1, ctx))
+                goto err;
+        if (!BN_GF2m_add(z2, z2, x2))
+                goto err;
 
-        if (!group->meth->field_mul(group, z2, z2, z1, ctx)) goto err;
-        if (!group->meth->field_sqr(group, t4, x, ctx)) goto err;
-        if (!BN_GF2m_add(t4, t4, y)) goto err;
-        if (!group->meth->field_mul(group, t4, t4, t3, ctx)) goto err;
-        if (!BN_GF2m_add(t4, t4, z2)) goto err;
+        if (!group->meth->field_mul(group, z2, z2, z1, ctx))
+                goto err;
+        if (!group->meth->field_sqr(group, t4, x, ctx))
+                goto err;
+        if (!BN_GF2m_add(t4, t4, y))
+                goto err;
+        if (!group->meth->field_mul(group, t4, t4, t3, ctx))
+                goto err;
+        if (!BN_GF2m_add(t4, t4, z2))
+                goto err;
 
-        if (!group->meth->field_mul(group, t3, t3, x, ctx)) goto err;
-        if (!group->meth->field_div(group, t3, t5, t3, ctx)) goto err;
-        if (!group->meth->field_mul(group, t4, t3, t4, ctx)) goto err;
-        if (!group->meth->field_mul(group, x2, x1, t3, ctx)) goto err;
-        if (!BN_GF2m_add(z2, x2, x)) goto err;
+        if (!group->meth->field_mul(group, t3, t3, x, ctx))
+                goto err;
+        if (!group->meth->field_div(group, t3, t5, t3, ctx))
+                goto err;
+        if (!group->meth->field_mul(group, t4, t3, t4, ctx))
+                goto err;
+        if (!group->meth->field_mul(group, x2, x1, t3, ctx))
+                goto err;
+        if (!BN_GF2m_add(z2, x2, x))
+                goto err;
 
-        if (!group->meth->field_mul(group, z2, z2, t4, ctx)) goto err;
-        if (!BN_GF2m_add(z2, z2, y)) goto err;
+        if (!group->meth->field_mul(group, z2, z2, t4, ctx))
+                goto err;
+        if (!BN_GF2m_add(z2, z2, y))
+                goto err;
 
         ret = 2;
 
- err:
+err:
         BN_CTX_end(ctx);
         return ret;
-        }
+}
 
 
 /* Computes scalar*point and stores the result in r.
  * point can not equal r.
  * Uses a modified algorithm 2P of
- *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over 
+ *     Lopez, J. and Dahab, R.  "Fast multiplication on elliptic curves over
  *     GF(2^m) without precomputation" (CHES '99, LNCS 1717).
  *
  * To protect against side-channel attack the function uses constant time swap,
  * avoiding conditional branches.
  */
-static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
-        const EC_POINT *point, BN_CTX *ctx)
-        {
+static int 
+ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
+    const BIGNUM *scalar, const EC_POINT *point, BN_CTX *ctx)
+{
         BIGNUM *x1, *x2, *z1, *z2;
         int ret = 0, i;
-        BN_ULONG mask,word;
+        BN_ULONG mask, word;
 
-        if (r == point)
-                {
+        if (r == point) {
                 ECerr(EC_F_EC_GF2M_MONTGOMERY_POINT_MULTIPLY, EC_R_INVALID_ARGUMENT);
                 return 0;
-                }
-        
+        }
         /* if result should be point at infinity */
-        if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) || 
-                EC_POINT_is_at_infinity(group, point))
-                {
+        if ((scalar == NULL) || BN_is_zero(scalar) || (point == NULL) ||
+            EC_POINT_is_at_infinity(group, point)) {
                 return EC_POINT_set_to_infinity(group, r);
-                }
-
+        }
         /* only support affine coordinates */
-        if (!point->Z_is_one) return 0;
+        if (!point->Z_is_one)
+                return 0;
 
         /* Since point_multiply is static we can guarantee that ctx != NULL. */
         BN_CTX_start(ctx);
         x1 = BN_CTX_get(ctx);
         z1 = BN_CTX_get(ctx);
-        if (z1 == NULL) goto err;
+        if (z1 == NULL)
+                goto err;
 
         x2 = &r->X;
         z2 = &r->Y;
@@ -255,53 +292,57 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
         bn_wexpand(x2, group->field.top);
         bn_wexpand(z2, group->field.top);
 
-        if (!BN_GF2m_mod_arr(x1, &point->X, group->poly)) goto err; /* x1 = x */
-        if (!BN_one(z1)) goto err; /* z1 = 1 */
-        if (!group->meth->field_sqr(group, z2, x1, ctx)) goto err; /* z2 = x1^2 = x^2 */
-        if (!group->meth->field_sqr(group, x2, z2, ctx)) goto err;
-        if (!BN_GF2m_add(x2, x2, &group->b)) goto err; /* x2 = x^4 + b */
+        if (!BN_GF2m_mod_arr(x1, &point->X, group->poly))
+                goto err;       /* x1 = x */
+        if (!BN_one(z1))
+                goto err;       /* z1 = 1 */
+        if (!group->meth->field_sqr(group, z2, x1, ctx))
+                goto err;       /* z2 = x1^2 = x^2 */
+        if (!group->meth->field_sqr(group, x2, z2, ctx))
+                goto err;
+        if (!BN_GF2m_add(x2, x2, &group->b))
+                goto err;       /* x2 = x^4 + b */
 
         /* find top most bit and go one past it */
         i = scalar->top - 1;
         mask = BN_TBIT;
         word = scalar->d[i];
-        while (!(word & mask)) mask >>= 1;
+        while (!(word & mask))
+                mask >>= 1;
         mask >>= 1;
         /* if top most bit was at word break, go to next word */
-        if (!mask) 
-                {
+        if (!mask) {
                 i--;
                 mask = BN_TBIT;
-                }
-
-        for (; i >= 0; i--)
-                {
+        }
+        for (; i >= 0; i--) {
                 word = scalar->d[i];
-                while (mask)
-                        {
+                while (mask) {
                         BN_consttime_swap(word & mask, x1, x2, group->field.top);
                         BN_consttime_swap(word & mask, z1, z2, group->field.top);
-                        if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx)) goto err;
-                        if (!gf2m_Mdouble(group, x1, z1, ctx)) goto err;
+                        if (!gf2m_Madd(group, &point->X, x2, z2, x1, z1, ctx))
+                                goto err;
+                        if (!gf2m_Mdouble(group, x1, z1, ctx))
+                                goto err;
                         BN_consttime_swap(word & mask, x1, x2, group->field.top);
                         BN_consttime_swap(word & mask, z1, z2, group->field.top);
                         mask >>= 1;
-                        }
-                mask = BN_TBIT;
                 }
+                mask = BN_TBIT;
+        }
 
         /* convert out of "projective" coordinates */
         i = gf2m_Mxy(group, &point->X, &point->Y, x1, z1, x2, z2, ctx);
-        if (i == 0) goto err;
-        else if (i == 1) 
-                {
-                if (!EC_POINT_set_to_infinity(group, r)) goto err;
-                }
-        else
-                {
-                if (!BN_one(&r->Z)) goto err;
+        if (i == 0)
+                goto err;
+        else if (i == 1) {
+                if (!EC_POINT_set_to_infinity(group, r))
+                        goto err;
+        } else {
+                if (!BN_one(&r->Z))
+                        goto err;
                 r->Z_is_one = 1;
-                }
+        }
 
         /* GF(2^m) field elements should always have BIGNUM::neg = 0 */
         BN_set_negative(&r->X, 0);
@@ -309,87 +350,98 @@ static int ec_GF2m_montgomery_point_multiply(const EC_GROUP *group, EC_POINT *r,
 
         ret = 1;
 
- err:
+err:
         BN_CTX_end(ctx);
         return ret;
-        }
+}
 
 
 /* Computes the sum
  *     scalar*group->generator + scalars[0]*points[0] + ... + scalars[num-1]*points[num-1]
  * gracefully ignoring NULL scalar values.
  */
-int ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
-        size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
-        {
+int 
+ec_GF2m_simple_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+    size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx)
+{
         BN_CTX *new_ctx = NULL;
         int ret = 0;
         size_t i;
-        EC_POINT *p=NULL;
+        EC_POINT *p = NULL;
         EC_POINT *acc = NULL;
 
-        if (ctx == NULL)
-                {
+        if (ctx == NULL) {
                 ctx = new_ctx = BN_CTX_new();
                 if (ctx == NULL)
                         return 0;
-                }
-
-        /* This implementation is more efficient than the wNAF implementation for 2
-         * or fewer points.  Use the ec_wNAF_mul implementation for 3 or more points,
-         * or if we can perform a fast multiplication based on precomputation.
+        }
+        /*
+         * This implementation is more efficient than the wNAF implementation
+         * for 2 or fewer points.  Use the ec_wNAF_mul implementation for 3
+         * or more points, or if we can perform a fast multiplication based
+         * on precomputation.
          */
-        if ((scalar && (num > 1)) || (num > 2) || (num == 0 && EC_GROUP_have_precompute_mult(group)))
-                {
+        if ((scalar && (num > 1)) || (num > 2) ||
+            (num == 0 && EC_GROUP_have_precompute_mult(group))) {
                 ret = ec_wNAF_mul(group, r, scalar, num, points, scalars, ctx);
                 goto err;
-                }
-
-        if ((p = EC_POINT_new(group)) == NULL) goto err;
-        if ((acc = EC_POINT_new(group)) == NULL) goto err;
+        }
+        if ((p = EC_POINT_new(group)) == NULL)
+                goto err;
+        if ((acc = EC_POINT_new(group)) == NULL)
+                goto err;
 
-        if (!EC_POINT_set_to_infinity(group, acc)) goto err;
+        if (!EC_POINT_set_to_infinity(group, acc))
+                goto err;
 
-        if (scalar)
-                {
-                if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx)) goto err;
+        if (scalar) {
+                if (!ec_GF2m_montgomery_point_multiply(group, p, scalar, group->generator, ctx))
+                        goto err;
                 if (BN_is_negative(scalar))
-                        if (!group->meth->invert(group, p, ctx)) goto err;
-                if (!group->meth->add(group, acc, acc, p, ctx)) goto err;
-                }
-
-        for (i = 0; i < num; i++)
-                {
-                if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx)) goto err;
+                        if (!group->meth->invert(group, p, ctx))
+                                goto err;
+                if (!group->meth->add(group, acc, acc, p, ctx))
+                        goto err;
+        }
+        for (i = 0; i < num; i++) {
+                if (!ec_GF2m_montgomery_point_multiply(group, p, scalars[i], points[i], ctx))
+                        goto err;
                 if (BN_is_negative(scalars[i]))
-                        if (!group->meth->invert(group, p, ctx)) goto err;
-                if (!group->meth->add(group, acc, acc, p, ctx)) goto err;
-                }
+                        if (!group->meth->invert(group, p, ctx))
+                                goto err;
+                if (!group->meth->add(group, acc, acc, p, ctx))
+                        goto err;
+        }
 
-        if (!EC_POINT_copy(r, acc)) goto err;
+        if (!EC_POINT_copy(r, acc))
+                goto err;
 
         ret = 1;
 
-  err:
-        if (p) EC_POINT_free(p);
-        if (acc) EC_POINT_free(acc);
+err:
+        if (p)
+                EC_POINT_free(p);
+        if (acc)
+                EC_POINT_free(acc);
         if (new_ctx != NULL)
                 BN_CTX_free(new_ctx);
         return ret;
-        }
+}
 
 
 /* Precomputation for point multiplication: fall back to wNAF methods
  * because ec_GF2m_simple_mul() uses ec_wNAF_mul() if appropriate */
 
-int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx)
-        {
+int 
+ec_GF2m_precompute_mult(EC_GROUP * group, BN_CTX * ctx)
+{
         return ec_wNAF_precompute_mult(group, ctx);
-        }
+}
 
-int ec_GF2m_have_precompute_mult(const EC_GROUP *group)
-        {
+int 
+ec_GF2m_have_precompute_mult(const EC_GROUP * group)
+{
         return ec_wNAF_have_precompute_mult(group);
-        }
+}
 
 #endif