Make secp256k1_fe_sqrt constant time

src/bench_internal.c

@@ -181,12 +181,12 @@ void bench_field_inverse_var(void* arg) {
     }
 }
 
-void bench_field_sqrt_var(void* arg) {
+void bench_field_sqrt(void* arg) {
     int i;
     bench_inv_t *data = (bench_inv_t*)arg;
 
     for (i = 0; i < 20000; i++) {
-        secp256k1_fe_sqrt_var(&data->fe_x, &data->fe_x);
+        secp256k1_fe_sqrt(&data->fe_x, &data->fe_x);
         secp256k1_fe_add(&data->fe_x, &data->fe_y);
     }
 }
@@ -357,7 +357,7 @@ int main(int argc, char **argv) {
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "mul")) run_benchmark("field_mul", bench_field_mul, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse", bench_field_inverse, bench_setup, NULL, &data, 10, 20000);
     if (have_flag(argc, argv, "field") || have_flag(argc, argv, "inverse")) run_benchmark("field_inverse_var", bench_field_inverse_var, bench_setup, NULL, &data, 10, 20000);
-    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt_var", bench_field_sqrt_var, bench_setup, NULL, &data, 10, 20000);
+    if (have_flag(argc, argv, "field") || have_flag(argc, argv, "sqrt")) run_benchmark("field_sqrt", bench_field_sqrt, bench_setup, NULL, &data, 10, 20000);
 
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "double")) run_benchmark("group_double_var", bench_group_double_var, bench_setup, NULL, &data, 10, 200000);
     if (have_flag(argc, argv, "group") || have_flag(argc, argv, "add")) run_benchmark("group_add_var", bench_group_add_var, bench_setup, NULL, &data, 10, 200000);

src/field.h

@@ -57,6 +57,9 @@ static int secp256k1_fe_is_zero(const secp256k1_fe *a);
 static int secp256k1_fe_is_odd(const secp256k1_fe *a);
 
 /** Compare two field elements. Requires magnitude-1 inputs. */
+static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b);
+
+/** Same as secp256k1_fe_equal, but may be variable time. */
 static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b);
 
 /** Compare two field elements. Requires both inputs to be normalized */
@@ -92,7 +95,7 @@ static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
  *  The input's magnitude can be at most 8. The output magnitude is 1 (but not
  *  guaranteed to be normalized). The result in r will always be a square
  *  itself. */
-static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a);
+static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a);
 
 /** Checks whether a field element is a quadratic residue. */
 static int secp256k1_fe_is_quad_var(const secp256k1_fe *a);

src/field_impl.h

@@ -21,6 +21,13 @@
 #error "Please select field implementation"
 #endif
 
+SECP256K1_INLINE static int secp256k1_fe_equal(const secp256k1_fe *a, const secp256k1_fe *b) {
+    secp256k1_fe na;
+    secp256k1_fe_negate(&na, a, 1);
+    secp256k1_fe_add(&na, b);
+    return secp256k1_fe_normalizes_to_zero(&na);
+}
+
 SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const secp256k1_fe *b) {
     secp256k1_fe na;
     secp256k1_fe_negate(&na, a, 1);
@@ -28,7 +35,7 @@ SECP256K1_INLINE static int secp256k1_fe_equal_var(const secp256k1_fe *a, const
     return secp256k1_fe_normalizes_to_zero_var(&na);
 }
 
-static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a) {
+static int secp256k1_fe_sqrt(secp256k1_fe *r, const secp256k1_fe *a) {
     /** Given that p is congruent to 3 mod 4, we can compute the square root of
      *  a mod p as the (p+1)/4'th power of a.
      *
@@ -123,7 +130,7 @@ static int secp256k1_fe_sqrt_var(secp256k1_fe *r, const secp256k1_fe *a) {
     /* Check that a square root was actually calculated */
 
     secp256k1_fe_sqr(&t1, r);
-    return secp256k1_fe_equal_var(&t1, a);
+    return secp256k1_fe_equal(&t1, a);
 }
 
 static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a) {
@@ -301,7 +308,7 @@ static int secp256k1_fe_is_quad_var(const secp256k1_fe *a) {
     return secp256k1_num_jacobi(&n, &m) >= 0;
 #else
     secp256k1_fe r;
-    return secp256k1_fe_sqrt_var(&r, a) == 1;
+    return secp256k1_fe_sqrt(&r, a);
 #endif
 }
 

src/group.h

@@ -47,7 +47,7 @@ static void secp256k1_ge_set_xy(secp256k1_ge *r, const secp256k1_fe *x, const se
  *  and a Y coordinate that is a quadratic residue modulo p. The return value
  *  is true iff a coordinate with the given X coordinate exists.
  */
-static int secp256k1_ge_set_xquad_var(secp256k1_ge *r, const secp256k1_fe *x);
+static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x);
 
 /** Set a group element (affine) equal to the point with the given X coordinate, and given oddness
  *  for Y. Return value indicates whether the result is valid. */

src/group_impl.h

@@ -163,7 +163,7 @@ static void secp256k1_ge_clear(secp256k1_ge *r) {
     secp256k1_fe_clear(&r->y);
 }
 
-static int secp256k1_ge_set_xquad_var(secp256k1_ge *r, const secp256k1_fe *x) {
+static int secp256k1_ge_set_xquad(secp256k1_ge *r, const secp256k1_fe *x) {
     secp256k1_fe x2, x3, c;
     r->x = *x;
     secp256k1_fe_sqr(&x2, x);
@@ -171,11 +171,11 @@ static int secp256k1_ge_set_xquad_var(secp256k1_ge *r, const secp256k1_fe *x) {
     r->infinity = 0;
     secp256k1_fe_set_int(&c, 7);
     secp256k1_fe_add(&c, &x3);
-    return secp256k1_fe_sqrt_var(&r->y, &c);
+    return secp256k1_fe_sqrt(&r->y, &c);
 }
 
 static int secp256k1_ge_set_xo_var(secp256k1_ge *r, const secp256k1_fe *x, int odd) {
-    if (!secp256k1_ge_set_xquad_var(r, x)) {
+    if (!secp256k1_ge_set_xquad(r, x)) {
         return 0;
     }
     secp256k1_fe_normalize_var(&r->y);

src/tests.c

@@ -1574,7 +1574,7 @@ void random_fe_non_zero(secp256k1_fe *nz) {
 void random_fe_non_square(secp256k1_fe *ns) {
     secp256k1_fe r;
     random_fe_non_zero(ns);
-    if (secp256k1_fe_sqrt_var(&r, ns)) {
+    if (secp256k1_fe_sqrt(&r, ns)) {
         secp256k1_fe_negate(ns, ns, 1);
     }
 }
@@ -1769,7 +1769,7 @@ void run_sqr(void) {
 
 void test_sqrt(const secp256k1_fe *a, const secp256k1_fe *k) {
     secp256k1_fe r1, r2;
-    int v = secp256k1_fe_sqrt_var(&r1, a);
+    int v = secp256k1_fe_sqrt(&r1, a);
     CHECK((v == 0) == (k == NULL));
 
     if (k != NULL) {
@@ -2188,7 +2188,7 @@ void test_group_decompress(const secp256k1_fe* x) {
 
     secp256k1_fe_normalize_var(&fex);
 
-    res_quad = secp256k1_ge_set_xquad_var(&ge_quad, &fex);
+    res_quad = secp256k1_ge_set_xquad(&ge_quad, &fex);
     res_even = secp256k1_ge_set_xo_var(&ge_even, &fex, 0);
     res_odd = secp256k1_ge_set_xo_var(&ge_odd, &fex, 1);