/* crypto/ec/ec_lcl.h */
+/*
+ * Originally written by Bodo Moeller for the OpenSSL project.
+ */
/* ====================================================================
- * Copyright (c) 1998-2001 The OpenSSL Project. All rights reserved.
+ * Copyright (c) 1998-2003 The OpenSSL Project. All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* Hudson (tjh@cryptsoft.com).
*
*/
+/* ====================================================================
+ * Copyright 2002 Sun Microsystems, Inc. ALL RIGHTS RESERVED.
+ *
+ * Portions of the attached software ("Contribution") are developed by
+ * SUN MICROSYSTEMS, INC., and are contributed to the OpenSSL project.
+ *
+ * The Contribution is licensed pursuant to the OpenSSL open source
+ * license provided above.
+ *
+ * The elliptic curve binary polynomial software is originally written by
+ * Sheueling Chang Shantz and Douglas Stebila of Sun Microsystems Laboratories.
+ *
+ */
#include <stdlib.h>
+#include <openssl/obj_mac.h>
#include <openssl/ec.h>
+#if defined(__SUNPRO_C)
+# if __SUNPRO_C >= 0x520
+# pragma error_messages (off,E_ARRAY_OF_INCOMPLETE_NONAME,E_ARRAY_OF_INCOMPLETE)
+# endif
+#endif
/* Structure details are not part of the exported interface,
* so all this may change in future versions. */
struct ec_method_st {
- /* used by EC_GROUP_new, EC_GROUP_set_curve_GFp, EC_GROUP_free, EC_GROUP_copy: */
+ /* used by EC_METHOD_get_field_type: */
+ int field_type; /* a NID */
+
+ /* used by EC_GROUP_new, EC_GROUP_free, EC_GROUP_clear_free, EC_GROUP_copy: */
int (*group_init)(EC_GROUP *);
- /* int (*group_set)(EC_GROUP *, .....); */
- int (*group_set_curve_GFp)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
void (*group_finish)(EC_GROUP *);
void (*group_clear_finish)(EC_GROUP *);
int (*group_copy)(EC_GROUP *, const EC_GROUP *);
- /* used by EC_GROUP_set_generator: */
- int (*group_set_generator)(EC_GROUP *, const EC_POINT *generator,
- const BIGNUM *order, const BIGNUM *cofactor);
-
- /* TODO: 'set' and 'get' functions for EC_GROUPs */
+ /* used by EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, */
+ /* EC_GROUP_set_curve_GF2m, and EC_GROUP_get_curve_GF2m: */
+ int (*group_set_curve)(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+ int (*group_get_curve)(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
+
+ /* used by EC_GROUP_get_degree: */
+ int (*group_get_degree)(const EC_GROUP *);
+ /* used by EC_GROUP_check: */
+ int (*group_check_discriminant)(const EC_GROUP *, BN_CTX *);
- /* used by EC_POINT_new, EC_POINT_free, EC_POINT_copy: */
+ /* used by EC_POINT_new, EC_POINT_free, EC_POINT_clear_free, EC_POINT_copy: */
int (*point_init)(EC_POINT *);
void (*point_finish)(EC_POINT *);
void (*point_clear_finish)(EC_POINT *);
int (*point_copy)(EC_POINT *, const EC_POINT *);
- /* TODO: 'set' and 'get' functions for EC_POINTs */
+ /* used by EC_POINT_set_to_infinity,
+ * EC_POINT_set_Jprojective_coordinates_GFp,
+ * EC_POINT_get_Jprojective_coordinates_GFp,
+ * EC_POINT_set_affine_coordinates_GFp, ..._GF2m,
+ * EC_POINT_get_affine_coordinates_GFp, ..._GF2m,
+ * EC_POINT_set_compressed_coordinates_GFp, ..._GF2m:
+ */
+ int (*point_set_to_infinity)(const EC_GROUP *, EC_POINT *);
+ int (*point_set_Jprojective_coordinates_GFp)(const EC_GROUP *, EC_POINT *,
+ const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
+ int (*point_get_Jprojective_coordinates_GFp)(const EC_GROUP *, const EC_POINT *,
+ BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
+ int (*point_set_affine_coordinates)(const EC_GROUP *, EC_POINT *,
+ const BIGNUM *x, const BIGNUM *y, BN_CTX *);
+ int (*point_get_affine_coordinates)(const EC_GROUP *, const EC_POINT *,
+ BIGNUM *x, BIGNUM *y, BN_CTX *);
+ int (*point_set_compressed_coordinates)(const EC_GROUP *, EC_POINT *,
+ const BIGNUM *x, int y_bit, BN_CTX *);
/* used by EC_POINT_point2oct, EC_POINT_oct2point: */
size_t (*point2oct)(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
int (*oct2point)(const EC_GROUP *, EC_POINT *,
const unsigned char *buf, size_t len, BN_CTX *);
- /* used by EC_POINT_add, EC_POINT_dbl: */
+ /* used by EC_POINT_add, EC_POINT_dbl, ECP_POINT_invert: */
int (*add)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
int (*dbl)(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
+ int (*invert)(const EC_GROUP *, EC_POINT *, BN_CTX *);
- /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_make_affine */
+ /* used by EC_POINT_is_at_infinity, EC_POINT_is_on_curve, EC_POINT_cmp: */
int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
int (*is_on_curve)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
- int (*make_affine)(const EC_GROUP *, const EC_POINT *, BN_CTX *);
+ int (*point_cmp)(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
+
+ /* used by EC_POINT_make_affine, EC_POINTs_make_affine: */
+ int (*make_affine)(const EC_GROUP *, EC_POINT *, BN_CTX *);
+ int (*points_make_affine)(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
+
+ /* used by EC_POINTs_mul, EC_POINT_mul, EC_POINT_precompute_mult, EC_POINT_have_precompute_mult
+ * (default implementations are used if the 'mul' pointer is 0): */
+ int (*mul)(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+ size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
+ int (*precompute_mult)(EC_GROUP *group, BN_CTX *);
+ int (*have_precompute_mult)(const EC_GROUP *group);
/* internal functions */
- /* 'field_mult' and 'field_sqr' can be used by 'add' and 'dbl' so that
+ /* 'field_mul', 'field_sqr', and 'field_div' can be used by 'add' and 'dbl' so that
* the same implementations of point operations can be used with different
* optimized implementations of expensive field operations: */
- int (*field_mult)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+ int (*field_mul)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int (*field_sqr)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
+ int (*field_div)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int (*field_encode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. to Montgomery */
int (*field_decode)(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *); /* e.g. from Montgomery */
+ int (*field_set_to_one)(const EC_GROUP *, BIGNUM *r, BN_CTX *);
} /* EC_METHOD */;
+typedef struct ec_extra_data_st {
+ struct ec_extra_data_st *next;
+ void *data;
+ void *(*dup_func)(void *);
+ void (*free_func)(void *);
+ void (*clear_free_func)(void *);
+} EC_EXTRA_DATA; /* used in EC_GROUP */
struct ec_group_st {
const EC_METHOD *meth;
- void *extra_data;
- void *(*extra_data_dup_func)(void *);
- void (*extra_data_free_func)(void *);
- void (*extra_data_clear_free_func)(void *);
+ EC_POINT *generator; /* optional */
+ BIGNUM order, cofactor;
+
+ int curve_name;/* optional NID for named curve */
+ int asn1_flag; /* flag to control the asn1 encoding */
+ point_conversion_form_t asn1_form;
- /* All members except 'meth' and 'extra_data...' are handled by
- * the method functions, even if they appear generic */
+ unsigned char *seed; /* optional seed for parameters (appears in ASN1) */
+ size_t seed_len;
+
+ EC_EXTRA_DATA *extra_data; /* linked list */
+
+ /* The following members are handled by the method functions,
+ * even if they appear generic */
BIGNUM field; /* Field specification.
- * For curves over GF(p), this is the modulus. */
- void *field_data; /* method-specific (e.g., Montgomery structure) */
+ * For curves over GF(p), this is the modulus;
+ * for curves over GF(2^m), this is the
+ * irreducible polynomial defining the field.
+ */
+
+ unsigned int poly[5]; /* Field specification for curves over GF(2^m).
+ * The irreducible f(t) is then of the form:
+ * t^poly[0] + t^poly[1] + ... + t^poly[k]
+ * where m = poly[0] > poly[1] > ... > poly[k] = 0.
+ */
BIGNUM a, b; /* Curve coefficients.
* (Here the assumption is that BIGNUMs can be used
* or abused for all kinds of fields, not just GF(p).)
* For characteristic > 3, the curve is defined
* by a Weierstrass equation of the form
- * Y^2 = X^3 + a*X + b.
+ * y^2 = x^3 + a*x + b.
+ * For characteristic 2, the curve is defined by
+ * an equation of the form
+ * y^2 + x*y = x^3 + a*x^2 + b.
*/
+
int a_is_minus3; /* enable optimized point arithmetics for special case */
- EC_POINT *generator; /* optional */
- BIGNUM order, cofactor;
+ void *field_data1; /* method-specific (e.g., Montgomery structure) */
+ void *field_data2; /* method-specific */
+ int (*field_mod_func)(BIGNUM *, const BIGNUM *, const BIGNUM *, BN_CTX *); /* method-specific */
} /* EC_GROUP */;
* (with visibility limited to 'package' level for now).
* We use the function pointers as index for retrieval; this obviates
* global ex_data-style index tables.
- * (Currently, we have one slot only, but is is possible to extend this
- * if necessary.) */
-int EC_GROUP_set_extra_data(EC_GROUP *, void *extra_data, void *(*extra_data_dup_func)(void *),
- void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
-void *EC_GROUP_get_extra_data(EC_GROUP *, void *(*extra_data_dup_func)(void *),
- void (*extra_data_free_func)(void *), void (*extra_data_clear_free_func)(void *));
-void EC_GROUP_free_extra_data(EC_GROUP *);
-void EC_GROUP_clear_free_extra_data(EC_GROUP *);
+ */
+int EC_GROUP_set_extra_data(EC_GROUP *, void *data,
+ void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
+void *EC_GROUP_get_extra_data(const EC_GROUP *,
+ void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
+void EC_GROUP_free_extra_data(EC_GROUP*,
+ void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
+void EC_GROUP_clear_free_extra_data(EC_GROUP*,
+ void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
+void EC_GROUP_free_all_extra_data(EC_GROUP *);
+void EC_GROUP_clear_free_all_extra_data(EC_GROUP *);
+/* method functions in ec_mult.c
+ * (ec_lib.c uses these as defaults if group->method->mul is 0) */
+int ec_wNAF_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar,
+ size_t num, const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *);
+int ec_wNAF_precompute_mult(EC_GROUP *group, BN_CTX *);
+int ec_wNAF_have_precompute_mult(const EC_GROUP *group);
+
+
/* method functions in ecp_smpl.c */
int ec_GFp_simple_group_init(EC_GROUP *);
-int ec_GFp_simple_group_set_curve_GFp(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
void ec_GFp_simple_group_finish(EC_GROUP *);
void ec_GFp_simple_group_clear_finish(EC_GROUP *);
int ec_GFp_simple_group_copy(EC_GROUP *, const EC_GROUP *);
-int ec_GFp_simple_group_set_generator(EC_GROUP *, const EC_POINT *generator,
- const BIGNUM *order, const BIGNUM *cofactor);
-/* TODO: 'set' and 'get' functions for EC_GROUPs */
+int ec_GFp_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
+int ec_GFp_simple_group_get_degree(const EC_GROUP *);
+int ec_GFp_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
int ec_GFp_simple_point_init(EC_POINT *);
void ec_GFp_simple_point_finish(EC_POINT *);
void ec_GFp_simple_point_clear_finish(EC_POINT *);
int ec_GFp_simple_point_copy(EC_POINT *, const EC_POINT *);
-/* TODO: 'set' and 'get' functions for EC_POINTs */
+int ec_GFp_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
+int ec_GFp_simple_set_Jprojective_coordinates_GFp(const EC_GROUP *, EC_POINT *,
+ const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *);
+int ec_GFp_simple_get_Jprojective_coordinates_GFp(const EC_GROUP *, const EC_POINT *,
+ BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *);
+int ec_GFp_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
+ const BIGNUM *x, const BIGNUM *y, BN_CTX *);
+int ec_GFp_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
+ BIGNUM *x, BIGNUM *y, BN_CTX *);
+int ec_GFp_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
+ const BIGNUM *x, int y_bit, BN_CTX *);
size_t ec_GFp_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
unsigned char *buf, size_t len, BN_CTX *);
int ec_GFp_simple_oct2point(const EC_GROUP *, EC_POINT *,
const unsigned char *buf, size_t len, BN_CTX *);
int ec_GFp_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
int ec_GFp_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
+int ec_GFp_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
int ec_GFp_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
int ec_GFp_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
-int ec_GFp_simple_make_affine(const EC_GROUP *, const EC_POINT *, BN_CTX *);
-int ec_GFp_simple_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
+int ec_GFp_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
+int ec_GFp_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
+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 *);
/* method functions in ecp_mont.c */
-int ec_GFp_mont_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_mont_group_init(EC_GROUP *);
+int ec_GFp_mont_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+void ec_GFp_mont_group_finish(EC_GROUP *);
+void ec_GFp_mont_group_clear_finish(EC_GROUP *);
+int ec_GFp_mont_group_copy(EC_GROUP *, const EC_GROUP *);
+int ec_GFp_mont_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_mont_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int ec_GFp_mont_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
int ec_GFp_mont_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
+int ec_GFp_mont_field_set_to_one(const EC_GROUP *, BIGNUM *r, BN_CTX *);
/* method functions in ecp_recp.c */
-int ec_GFp_recp_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_recp_group_init(EC_GROUP *);
+int ec_GFp_recp_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+void ec_GFp_recp_group_finish(EC_GROUP *);
+void ec_GFp_recp_group_clear_finish(EC_GROUP *);
+int ec_GFp_recp_group_copy(EC_GROUP *, const EC_GROUP *);
+int ec_GFp_recp_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_recp_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
-int ec_GFp_recp_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
-int ec_GFp_recp_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
/* method functions in ecp_nist.c */
-int ec_GFp_nist_field_mult(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_nist_group_copy(EC_GROUP *dest, const EC_GROUP *src);
+int ec_GFp_nist_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GFp_nist_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
int ec_GFp_nist_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
-int ec_GFp_nist_field_encode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
-int ec_GFp_nist_field_decode(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
+
+
+/* method functions in ec2_smpl.c */
+int ec_GF2m_simple_group_init(EC_GROUP *);
+void ec_GF2m_simple_group_finish(EC_GROUP *);
+void ec_GF2m_simple_group_clear_finish(EC_GROUP *);
+int ec_GF2m_simple_group_copy(EC_GROUP *, const EC_GROUP *);
+int ec_GF2m_simple_group_set_curve(EC_GROUP *, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GF2m_simple_group_get_curve(const EC_GROUP *, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *);
+int ec_GF2m_simple_group_get_degree(const EC_GROUP *);
+int ec_GF2m_simple_group_check_discriminant(const EC_GROUP *, BN_CTX *);
+int ec_GF2m_simple_point_init(EC_POINT *);
+void ec_GF2m_simple_point_finish(EC_POINT *);
+void ec_GF2m_simple_point_clear_finish(EC_POINT *);
+int ec_GF2m_simple_point_copy(EC_POINT *, const EC_POINT *);
+int ec_GF2m_simple_point_set_to_infinity(const EC_GROUP *, EC_POINT *);
+int ec_GF2m_simple_point_set_affine_coordinates(const EC_GROUP *, EC_POINT *,
+ const BIGNUM *x, const BIGNUM *y, BN_CTX *);
+int ec_GF2m_simple_point_get_affine_coordinates(const EC_GROUP *, const EC_POINT *,
+ BIGNUM *x, BIGNUM *y, BN_CTX *);
+int ec_GF2m_simple_set_compressed_coordinates(const EC_GROUP *, EC_POINT *,
+ const BIGNUM *x, int y_bit, BN_CTX *);
+size_t ec_GF2m_simple_point2oct(const EC_GROUP *, const EC_POINT *, point_conversion_form_t form,
+ unsigned char *buf, size_t len, BN_CTX *);
+int ec_GF2m_simple_oct2point(const EC_GROUP *, EC_POINT *,
+ const unsigned char *buf, size_t len, BN_CTX *);
+int ec_GF2m_simple_add(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
+int ec_GF2m_simple_dbl(const EC_GROUP *, EC_POINT *r, const EC_POINT *a, BN_CTX *);
+int ec_GF2m_simple_invert(const EC_GROUP *, EC_POINT *, BN_CTX *);
+int ec_GF2m_simple_is_at_infinity(const EC_GROUP *, const EC_POINT *);
+int ec_GF2m_simple_is_on_curve(const EC_GROUP *, const EC_POINT *, BN_CTX *);
+int ec_GF2m_simple_cmp(const EC_GROUP *, const EC_POINT *a, const EC_POINT *b, BN_CTX *);
+int ec_GF2m_simple_make_affine(const EC_GROUP *, EC_POINT *, BN_CTX *);
+int ec_GF2m_simple_points_make_affine(const EC_GROUP *, size_t num, EC_POINT *[], BN_CTX *);
+int ec_GF2m_simple_field_mul(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+int ec_GF2m_simple_field_sqr(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, BN_CTX *);
+int ec_GF2m_simple_field_div(const EC_GROUP *, BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *);
+
+
+/* method functions in ec2_mult.c */
+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 *);
+int ec_GF2m_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
+int ec_GF2m_have_precompute_mult(const EC_GROUP *group);
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