1ec(3)                               OpenSSL                              ec(3)
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NAME

6       ec - Elliptic Curve functions
7

SYNOPSIS

9        #include <openssl/ec.h>
10        #include <openssl/bn.h>
11
12        const EC_METHOD *EC_GFp_simple_method(void);
13        const EC_METHOD *EC_GFp_mont_method(void);
14        const EC_METHOD *EC_GFp_nist_method(void);
15        const EC_METHOD *EC_GFp_nistp224_method(void);
16        const EC_METHOD *EC_GFp_nistp256_method(void);
17        const EC_METHOD *EC_GFp_nistp521_method(void);
18
19        const EC_METHOD *EC_GF2m_simple_method(void);
20
21        EC_GROUP *EC_GROUP_new(const EC_METHOD *meth);
22        void EC_GROUP_free(EC_GROUP *group);
23        void EC_GROUP_clear_free(EC_GROUP *group);
24        int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
25        EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
26        const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
27        int EC_METHOD_get_field_type(const EC_METHOD *meth);
28        int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
29        const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
30        int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
31        int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
32        void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
33        int EC_GROUP_get_curve_name(const EC_GROUP *group);
34        void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
35        int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
36        void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
37        point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
38        unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
39        size_t EC_GROUP_get_seed_len(const EC_GROUP *);
40        size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
41        int EC_GROUP_set_curve_GFp(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
42        int EC_GROUP_get_curve_GFp(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
43        int EC_GROUP_set_curve_GF2m(EC_GROUP *group, const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
44        int EC_GROUP_get_curve_GF2m(const EC_GROUP *group, BIGNUM *p, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
45        int EC_GROUP_get_degree(const EC_GROUP *group);
46        int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
47        int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
48        int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
49        EC_GROUP *EC_GROUP_new_curve_GFp(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
50        EC_GROUP *EC_GROUP_new_curve_GF2m(const BIGNUM *p, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx);
51        EC_GROUP *EC_GROUP_new_by_curve_name(int nid);
52
53        size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
54
55        EC_POINT *EC_POINT_new(const EC_GROUP *group);
56        void EC_POINT_free(EC_POINT *point);
57        void EC_POINT_clear_free(EC_POINT *point);
58        int EC_POINT_copy(EC_POINT *dst, const EC_POINT *src);
59        EC_POINT *EC_POINT_dup(const EC_POINT *src, const EC_GROUP *group);
60        const EC_METHOD *EC_POINT_method_of(const EC_POINT *point);
61        int EC_POINT_set_to_infinity(const EC_GROUP *group, EC_POINT *point);
62        int EC_POINT_set_Jprojective_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
63               const BIGNUM *x, const BIGNUM *y, const BIGNUM *z, BN_CTX *ctx);
64        int EC_POINT_get_Jprojective_coordinates_GFp(const EC_GROUP *group,
65               const EC_POINT *p, BIGNUM *x, BIGNUM *y, BIGNUM *z, BN_CTX *ctx);
66        int EC_POINT_set_affine_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
67               const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
68        int EC_POINT_get_affine_coordinates_GFp(const EC_GROUP *group,
69               const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
70        int EC_POINT_set_compressed_coordinates_GFp(const EC_GROUP *group, EC_POINT *p,
71               const BIGNUM *x, int y_bit, BN_CTX *ctx);
72        int EC_POINT_set_affine_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
73               const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx);
74        int EC_POINT_get_affine_coordinates_GF2m(const EC_GROUP *group,
75               const EC_POINT *p, BIGNUM *x, BIGNUM *y, BN_CTX *ctx);
76        int EC_POINT_set_compressed_coordinates_GF2m(const EC_GROUP *group, EC_POINT *p,
77               const BIGNUM *x, int y_bit, BN_CTX *ctx);
78        size_t EC_POINT_point2oct(const EC_GROUP *group, const EC_POINT *p,
79               point_conversion_form_t form,
80               unsigned char *buf, size_t len, BN_CTX *ctx);
81        int EC_POINT_oct2point(const EC_GROUP *group, EC_POINT *p,
82               const unsigned char *buf, size_t len, BN_CTX *ctx);
83        BIGNUM *EC_POINT_point2bn(const EC_GROUP *, const EC_POINT *,
84               point_conversion_form_t form, BIGNUM *, BN_CTX *);
85        EC_POINT *EC_POINT_bn2point(const EC_GROUP *, const BIGNUM *,
86               EC_POINT *, BN_CTX *);
87        char *EC_POINT_point2hex(const EC_GROUP *, const EC_POINT *,
88               point_conversion_form_t form, BN_CTX *);
89        EC_POINT *EC_POINT_hex2point(const EC_GROUP *, const char *,
90               EC_POINT *, BN_CTX *);
91
92        int EC_POINT_add(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
93        int EC_POINT_dbl(const EC_GROUP *group, EC_POINT *r, const EC_POINT *a, BN_CTX *ctx);
94        int EC_POINT_invert(const EC_GROUP *group, EC_POINT *a, BN_CTX *ctx);
95        int EC_POINT_is_at_infinity(const EC_GROUP *group, const EC_POINT *p);
96        int EC_POINT_is_on_curve(const EC_GROUP *group, const EC_POINT *point, BN_CTX *ctx);
97        int EC_POINT_cmp(const EC_GROUP *group, const EC_POINT *a, const EC_POINT *b, BN_CTX *ctx);
98        int EC_POINT_make_affine(const EC_GROUP *group, EC_POINT *point, BN_CTX *ctx);
99        int EC_POINTs_make_affine(const EC_GROUP *group, size_t num, EC_POINT *points[], BN_CTX *ctx);
100        int EC_POINTs_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, size_t num, const EC_POINT *p[], const BIGNUM *m[], BN_CTX *ctx);
101        int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *n, const EC_POINT *q, const BIGNUM *m, BN_CTX *ctx);
102        int EC_GROUP_precompute_mult(EC_GROUP *group, BN_CTX *ctx);
103        int EC_GROUP_have_precompute_mult(const EC_GROUP *group);
104
105        int EC_GROUP_get_basis_type(const EC_GROUP *);
106        int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
107        int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
108               unsigned int *k2, unsigned int *k3);
109        EC_GROUP *d2i_ECPKParameters(EC_GROUP **, const unsigned char **in, long len);
110        int i2d_ECPKParameters(const EC_GROUP *, unsigned char **out);
111        #define d2i_ECPKParameters_bio(bp,x) ASN1_d2i_bio_of(EC_GROUP,NULL,d2i_ECPKParameters,bp,x)
112        #define i2d_ECPKParameters_bio(bp,x) ASN1_i2d_bio_of_const(EC_GROUP,i2d_ECPKParameters,bp,x)
113        #define d2i_ECPKParameters_fp(fp,x) (EC_GROUP *)ASN1_d2i_fp(NULL, \
114                       (char *(*)())d2i_ECPKParameters,(fp),(unsigned char **)(x))
115        #define i2d_ECPKParameters_fp(fp,x) ASN1_i2d_fp(i2d_ECPKParameters,(fp), \
116                       (unsigned char *)(x))
117        int     ECPKParameters_print(BIO *bp, const EC_GROUP *x, int off);
118        int     ECPKParameters_print_fp(FILE *fp, const EC_GROUP *x, int off);
119
120        EC_KEY *EC_KEY_new(void);
121        int EC_KEY_get_flags(const EC_KEY *key);
122        void EC_KEY_set_flags(EC_KEY *key, int flags);
123        void EC_KEY_clear_flags(EC_KEY *key, int flags);
124        EC_KEY *EC_KEY_new_by_curve_name(int nid);
125        void EC_KEY_free(EC_KEY *key);
126        EC_KEY *EC_KEY_copy(EC_KEY *dst, const EC_KEY *src);
127        EC_KEY *EC_KEY_dup(const EC_KEY *src);
128        int EC_KEY_up_ref(EC_KEY *key);
129        const EC_GROUP *EC_KEY_get0_group(const EC_KEY *key);
130        int EC_KEY_set_group(EC_KEY *key, const EC_GROUP *group);
131        const BIGNUM *EC_KEY_get0_private_key(const EC_KEY *key);
132        int EC_KEY_set_private_key(EC_KEY *key, const BIGNUM *prv);
133        const EC_POINT *EC_KEY_get0_public_key(const EC_KEY *key);
134        int EC_KEY_set_public_key(EC_KEY *key, const EC_POINT *pub);
135        unsigned EC_KEY_get_enc_flags(const EC_KEY *key);
136        void EC_KEY_set_enc_flags(EC_KEY *eckey, unsigned int flags);
137        point_conversion_form_t EC_KEY_get_conv_form(const EC_KEY *key);
138        void EC_KEY_set_conv_form(EC_KEY *eckey, point_conversion_form_t cform);
139        void *EC_KEY_get_key_method_data(EC_KEY *key,
140               void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
141        void EC_KEY_insert_key_method_data(EC_KEY *key, void *data,
142               void *(*dup_func)(void *), void (*free_func)(void *), void (*clear_free_func)(void *));
143        void EC_KEY_set_asn1_flag(EC_KEY *eckey, int asn1_flag);
144        int EC_KEY_precompute_mult(EC_KEY *key, BN_CTX *ctx);
145        int EC_KEY_generate_key(EC_KEY *key);
146        int EC_KEY_check_key(const EC_KEY *key);
147        int EC_KEY_set_public_key_affine_coordinates(EC_KEY *key, BIGNUM *x, BIGNUM *y);
148
149        EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);
150        int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);
151
152        EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);
153        int i2d_ECParameters(EC_KEY *key, unsigned char **out);
154
155        EC_KEY *o2i_ECPublicKey(EC_KEY **key, const unsigned char **in, long len);
156        int i2o_ECPublicKey(EC_KEY *key, unsigned char **out);
157        int    ECParameters_print(BIO *bp, const EC_KEY *key);
158        int    EC_KEY_print(BIO *bp, const EC_KEY *key, int off);
159        int    ECParameters_print_fp(FILE *fp, const EC_KEY *key);
160        int    EC_KEY_print_fp(FILE *fp, const EC_KEY *key, int off);
161        #define ECParameters_dup(x) ASN1_dup_of(EC_KEY,i2d_ECParameters,d2i_ECParameters,x)
162        #define EVP_PKEY_CTX_set_ec_paramgen_curve_nid(ctx, nid) \
163               EVP_PKEY_CTX_ctrl(ctx, EVP_PKEY_EC, EVP_PKEY_OP_PARAMGEN, \
164                                       EVP_PKEY_CTRL_EC_PARAMGEN_CURVE_NID, nid, NULL)
165

DESCRIPTION

167       This library provides an extensive set of functions for performing
168       operations on elliptic curves over finite fields.  In general an
169       elliptic curve is one with an equation of the form:
170
171       y^2 = x^3 + ax + b
172
173       An EC_GROUP structure is used to represent the definition of an
174       elliptic curve. Points on a curve are stored using an EC_POINT
175       structure. An EC_KEY is used to hold a private/public key pair, where a
176       private key is simply a BIGNUM and a public key is a point on a curve
177       (represented by an EC_POINT).
178
179       The library contains a number of alternative implementations of the
180       different functions. Each implementation is optimised for different
181       scenarios. No matter which implementation is being used, the interface
182       remains the same. The library handles calling the correct
183       implementation when an interface function is invoked. An implementation
184       is represented by an EC_METHOD structure.
185
186       The creation and destruction of EC_GROUP objects is described in
187       EC_GROUP_new(3). Functions for manipulating EC_GROUP objects are
188       described in EC_GROUP_copy(3).
189
190       Functions for creating, destroying and manipulating EC_POINT objects
191       are explained in EC_POINT_new(3), whilst functions for performing
192       mathematical operations and tests on EC_POINTs are coverd in
193       EC_POINT_add(3).
194
195       For working with private and public keys refer to EC_KEY_new(3).
196       Implementations are covered in EC_GFp_simple_method(3).
197
198       For information on encoding and decoding curve parameters to and from
199       ASN1 see d2i_ECPKParameters(3).
200

SEE ALSO

202       crypto(3), EC_GROUP_new(3), EC_GROUP_copy(3), EC_POINT_new(3),
203       EC_POINT_add(3), EC_KEY_new(3), EC_GFp_simple_method(3),
204       d2i_ECPKParameters(3)
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2081.0.2o                            2019-09-10                             ec(3)
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