1ec(3) OpenSSL ec(3)
2
6 ec - Elliptic Curve functions
7
9 #include <openssl/ec.h>
10 #include <openssl/bn.h>
11 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 const EC_METHOD *EC_GF2m_simple_method(void);
20 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 size_t EC_get_builtin_curves(EC_builtin_curve *r, size_t nitems);
54 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 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 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 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 EC_KEY *d2i_ECPrivateKey(EC_KEY **key, const unsigned char **in, long len);
150 int i2d_ECPrivateKey(EC_KEY *key, unsigned char **out);
151 EC_KEY *d2i_ECParameters(EC_KEY **key, const unsigned char **in, long len);
153 int i2d_ECParameters(EC_KEY *key, unsigned char **out);
154 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
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 y^2 = x^3 + ax + b
172 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 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 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 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 For working with private and public keys refer to EC_KEY_new(3).
196 Implementations are covered in EC_GFp_simple_method(3).
197 For information on encoding and decoding curve parameters to and from
199 ASN1 see d2i_ECPKParameters(3).
200
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)
2051.0.2o 2020-01-28 ec(3)