* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
**********************************************************************/
-#ifndef _SECP256K1_FIELD_
-#define _SECP256K1_FIELD_
+#ifndef SECP256K1_FIELD_H
+#define SECP256K1_FIELD_H
/** Field element module.
*
* Field elements can be represented in several ways, but code accessing
- * it (and implementations) need to take certain properaties into account:
+ * it (and implementations) need to take certain properties into account:
* - Each field element can be normalized or not.
* - Each field element has a magnitude, which represents how far away
* its representation is away from normalization. Normalized elements
#include "libsecp256k1-config.h"
#endif
-#if defined(USE_FIELD_GMP)
-#include "field_gmp.h"
-#elif defined(USE_FIELD_10X26)
-#include "field_10x26.h"
-#elif defined(USE_FIELD_5X52)
+#include "util.h"
+
+#if defined(SECP256K1_WIDEMUL_INT128)
#include "field_5x52.h"
+#elif defined(SECP256K1_WIDEMUL_INT64)
+#include "field_10x26.h"
#else
-#error "Please select field implementation"
+#error "Please select wide multiplication implementation"
#endif
-typedef struct {
-#ifndef USE_NUM_NONE
- secp256k1_num_t p;
-#endif
- secp256k1_fe_t order;
-} secp256k1_fe_consts_t;
+/** Normalize a field element. This brings the field element to a canonical representation, reduces
+ * its magnitude to 1, and reduces it modulo field size `p`.
+ */
+static void secp256k1_fe_normalize(secp256k1_fe *r);
-static const secp256k1_fe_consts_t *secp256k1_fe_consts = NULL;
+/** Weakly normalize a field element: reduce its magnitude to 1, but don't fully normalize. */
+static void secp256k1_fe_normalize_weak(secp256k1_fe *r);
-/** Initialize field element precomputation data. */
-static void secp256k1_fe_start(void);
+/** Normalize a field element, without constant-time guarantee. */
+static void secp256k1_fe_normalize_var(secp256k1_fe *r);
-/** Unload field element precomputation data. */
-static void secp256k1_fe_stop(void);
+/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
+ * implementation may optionally normalize the input, but this should not be relied upon. */
+static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r);
-/** Normalize a field element. */
-static void secp256k1_fe_normalize(secp256k1_fe_t *r);
+/** Verify whether a field element represents zero i.e. would normalize to a zero value. The field
+ * implementation may optionally normalize the input, but this should not be relied upon. */
+static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r);
/** Set a field element equal to a small integer. Resulting field element is normalized. */
-static void secp256k1_fe_set_int(secp256k1_fe_t *r, int a);
+static void secp256k1_fe_set_int(secp256k1_fe *r, int a);
+
+/** Sets a field element equal to zero, initializing all fields. */
+static void secp256k1_fe_clear(secp256k1_fe *a);
/** Verify whether a field element is zero. Requires the input to be normalized. */
-static int secp256k1_fe_is_zero(const secp256k1_fe_t *a);
+static int secp256k1_fe_is_zero(const secp256k1_fe *a);
/** Check the "oddness" of a field element. Requires the input to be normalized. */
-static int secp256k1_fe_is_odd(const secp256k1_fe_t *a);
+static int secp256k1_fe_is_odd(const secp256k1_fe *a);
-/** Compare two field elements. Requires both inputs to be normalized */
-static int secp256k1_fe_equal(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
+/** 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 */
-static int secp256k1_fe_cmp_var(const secp256k1_fe_t *a, const secp256k1_fe_t *b);
+static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b);
-/** Set a field element equal to 32-byte big endian value. If succesful, the resulting field element is normalized. */
-static int secp256k1_fe_set_b32(secp256k1_fe_t *r, const unsigned char *a);
+/** Set a field element equal to 32-byte big endian value. If successful, the resulting field element is normalized. */
+static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a);
/** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */
-static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a);
/** Set a field element equal to the additive inverse of another. Takes a maximum magnitude of the input
* as an argument. The magnitude of the output is one higher. */
-static void secp256k1_fe_negate(secp256k1_fe_t *r, const secp256k1_fe_t *a, int m);
+static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m);
/** Multiplies the passed field element with a small integer constant. Multiplies the magnitude by that
* small integer. */
-static void secp256k1_fe_mul_int(secp256k1_fe_t *r, int a);
+static void secp256k1_fe_mul_int(secp256k1_fe *r, int a);
/** Adds a field element to another. The result has the sum of the inputs' magnitudes as magnitude. */
-static void secp256k1_fe_add(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a);
/** Sets a field element to be the product of two others. Requires the inputs' magnitudes to be at most 8.
* The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_mul(secp256k1_fe_t *r, const secp256k1_fe_t *a, const secp256k1_fe_t * SECP256K1_RESTRICT b);
+static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b);
/** Sets a field element to be the square of another. Requires the input's magnitude to be at most 8.
* The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_sqr(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a);
-/** Sets a field element to be the (modular) square root (if any exist) of another. Requires the
- * input's magnitude to be at most 8. The output magnitude is 1 (but not guaranteed to be
- * normalized). Return value indicates whether a square root was found. */
-static int secp256k1_fe_sqrt(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+/** If a has a square root, it is computed in r and 1 is returned. If a does not
+ * have a square root, the root of its negation is computed and 0 is returned.
+ * 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(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);
/** Sets a field element to be the (modular) inverse of another. Requires the input's magnitude to be
* at most 8. The output magnitude is 1 (but not guaranteed to be normalized). */
-static void secp256k1_fe_inv(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_inv(secp256k1_fe *r, const secp256k1_fe *a);
/** Potentially faster version of secp256k1_fe_inv, without constant-time guarantee. */
-static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a);
+static void secp256k1_fe_inv_var(secp256k1_fe *r, const secp256k1_fe *a);
/** Calculate the (modular) inverses of a batch of field elements. Requires the inputs' magnitudes to be
* at most 8. The output magnitudes are 1 (but not guaranteed to be normalized). The inputs and
* outputs must not overlap in memory. */
-static void secp256k1_fe_inv_all(size_t len, secp256k1_fe_t r[len], const secp256k1_fe_t a[len]);
+static void secp256k1_fe_inv_all_var(secp256k1_fe *r, const secp256k1_fe *a, size_t len);
-/** Potentially faster version of secp256k1_fe_inv_all, without constant-time guarantee. */
-static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t r[len], const secp256k1_fe_t a[len]);
+/** Convert a field element to the storage type. */
+static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a);
-/** Convert a field element to a hexadecimal string. */
-static void secp256k1_fe_get_hex(char *r, int *rlen, const secp256k1_fe_t *a);
+/** Convert a field element back from the storage type. */
+static void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a);
-/** Convert a hexadecimal string to a field element. */
-static int secp256k1_fe_set_hex(secp256k1_fe_t *r, const char *a, int alen);
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/
+static void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag);
-/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. */
-static void secp256k1_fe_cmov(secp256k1_fe_t *r, const secp256k1_fe_t *a, int flag);
+/** If flag is true, set *r equal to *a; otherwise leave it. Constant-time. Both *r and *a must be initialized.*/
+static void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag);
-#endif
+#endif /* SECP256K1_FIELD_H */