-/* TODO */
/* 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>
+#include <openssl/bn.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_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 *);
+ void (*group_finish)(EC_GROUP *);
+ void (*group_clear_finish)(EC_GROUP *);
+ int (*group_copy)(EC_GROUP *, const EC_GROUP *);
+
+ /* 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_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 *);
+
+ /* 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,
+ unsigned char *buf, size_t len, BN_CTX *);
+ int (*oct2point)(const EC_GROUP *, EC_POINT *,
+ const unsigned char *buf, size_t len, BN_CTX *);
+
+ /* 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_cmp: */
+ int (*is_at_infinity)(const EC_GROUP *, const EC_POINT *);
+ int (*is_on_curve)(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_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_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;
+
+ 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;
+
+ 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;
+ * for curves over GF(2^m), this is the
+ * irreducible polynomial defining the field.
+ */
+
+ int poly[6]; /* 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.
+ * The array is terminated with poly[k+1]=-1.
+ * All elliptic curve irreducibles have at most 5
+ * non-zero terms.
+ */
+
+ 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.
+ * 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 */
+
+ 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 */;
+
+struct ec_key_st {
+ int version;
+
+ EC_GROUP *group;
+
+ EC_POINT *pub_key;
+ BIGNUM *priv_key;
+
+ unsigned int enc_flag;
+ point_conversion_form_t conv_form;
+
+ int references;
+
+ EC_EXTRA_DATA *method_data;
+} /* EC_KEY */;
+
+/* Basically a 'mixin' for extra data, but available for EC_GROUPs/EC_KEYs only
+ * (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.
+ */
+int EC_EX_DATA_set_data(EC_EXTRA_DATA **, void *data,
+ void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
+void *EC_EX_DATA_get_data(const EC_EXTRA_DATA *,
+ void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
+void EC_EX_DATA_free_data(EC_EXTRA_DATA **,
+ void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
+void EC_EX_DATA_clear_free_data(EC_EXTRA_DATA **,
+ void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
+void EC_EX_DATA_free_all_data(EC_EXTRA_DATA **);
+void EC_EX_DATA_clear_free_all_data(EC_EXTRA_DATA **);
+
+
+
+struct ec_point_st {
+ const EC_METHOD *meth;
+
+ /* All members except 'meth' are handled by the method functions,
+ * even if they appear generic */
+
+ BIGNUM X;
+ BIGNUM Y;
+ BIGNUM Z; /* Jacobian projective coordinates:
+ * (X, Y, Z) represents (X/Z^2, Y/Z^3) if Z != 0 */
+ int Z_is_one; /* enable optimized point arithmetics for special case */
+} /* EC_POINT */;
+
+
+
+/* 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 *);
+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_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 *);
+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_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_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_nist.c */
+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 *);
+
+
+/* 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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