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+/**********************************************************************
+ * Copyright (c) 2013, 2014 Pieter Wuille                             *
+ * Distributed under the MIT software license, see the accompanying   *
+ * file COPYING or http://www.opensource.org/licenses/mit-license.php.*
+ **********************************************************************/
+
+#ifndef _SECP256K1_GROUP_
+#define _SECP256K1_GROUP_
+
+#include "num.h"
+#include "field.h"
+
+/** A group element of the secp256k1 curve, in affine coordinates. */
+typedef struct {
+    secp256k1_fe_t x;
+    secp256k1_fe_t y;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_ge_t;
+
+/** A group element of the secp256k1 curve, in jacobian coordinates. */
+typedef struct {
+    secp256k1_fe_t x; /* actual X: x/z^2 */
+    secp256k1_fe_t y; /* actual Y: y/z^3 */
+    secp256k1_fe_t z;
+    int infinity; /* whether this represents the point at infinity */
+} secp256k1_gej_t;
+
+/** Global constants related to the group */
+typedef struct {
+    secp256k1_num_t order; /* the order of the curve (= order of its generator) */
+    secp256k1_num_t half_order; /* half the order of the curve (= order of its generator) */
+    secp256k1_ge_t g; /* the generator point */
+
+#ifdef USE_ENDOMORPHISM
+    /* constants related to secp256k1's efficiently computable endomorphism */
+    secp256k1_fe_t beta;
+    secp256k1_num_t lambda, a1b2, b1, a2;
+#endif
+} secp256k1_ge_consts_t;
+
+static const secp256k1_ge_consts_t *secp256k1_ge_consts = NULL;
+
+/** Initialize the group module. */
+static void secp256k1_ge_start(void);
+
+/** De-initialize the group module. */
+static void secp256k1_ge_stop(void);
+
+/** Set a group element equal to the point at infinity */
+static void secp256k1_ge_set_infinity(secp256k1_ge_t *r);
+
+/** Set a group element equal to the point with given X and Y coordinates */
+static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
+
+/** 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. */
+static int secp256k1_ge_set_xo(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a);
+
+/** Check whether a group element is valid (i.e., on the curve). */
+static int secp256k1_ge_is_valid(const secp256k1_ge_t *a);
+
+static void secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a);
+
+/** Get a hex representation of a point. *rlen will be overwritten with the real length. */
+static void secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a);
+
+/** Set a group element equal to another which is given in jacobian coordinates */
+static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a);
+
+/** Set a batch of group elements equal to the inputs given in jacobian coordinates */
+static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t r[len], const secp256k1_gej_t a[len]);
+
+
+/** Set a group element (jacobian) equal to the point at infinity. */
+static void secp256k1_gej_set_infinity(secp256k1_gej_t *r);
+
+/** Set a group element (jacobian) equal to the point with given X and Y coordinates. */
+static void secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y);
+
+/** Set a group element (jacobian) equal to another which is given in affine coordinates. */
+static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a);
+
+/** Get the X coordinate of a group element (jacobian). */
+static void secp256k1_gej_get_x_var(secp256k1_fe_t *r, const secp256k1_gej_t *a);
+
+/** Set r equal to the inverse of a (i.e., mirrored around the X axis) */
+static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+
+/** Check whether a group element is the point at infinity. */
+static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a);
+
+/** Set r equal to the double of a. */
+static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+
+/** Set r equal to the sum of a and b. */
+static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates, and not infinity). */
+static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
+
+/** Set r equal to the sum of a and b (with b given in affine coordinates). This is more efficient
+    than secp256k1_gej_add_var. It is identical to secp256k1_gej_add_ge but without constant-time
+    guarantee, and b is allowed to be infinity. */
+static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b);
+
+/** Get a hex representation of a point. *rlen will be overwritten with the real length. */
+static void secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a);
+
+#ifdef USE_ENDOMORPHISM
+/** Set r to be equal to lambda times a, where lambda is chosen in a way such that this is very fast. */
+static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a);
+
+/** Find r1 and r2 such that r1+r2*lambda = a, and r1 and r2 are maximum 128 bits long (given that a is
+    not more than 256 bits). */
+static void secp256k1_gej_split_exp_var(secp256k1_num_t *r1, secp256k1_num_t *r2, const secp256k1_num_t *a);
+#endif
+
+/** Clear a secp256k1_gej_t to prevent leaking sensitive information. */
+static void secp256k1_gej_clear(secp256k1_gej_t *r);
+
+/** Clear a secp256k1_ge_t to prevent leaking sensitive information. */
+static void secp256k1_ge_clear(secp256k1_ge_t *r);
+
+
+#endif