1EC_GROUP_copy(3) OpenSSL EC_GROUP_copy(3)
2
6 EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of,
7 EC_GROUP_set_generator, EC_GROUP_get0_generator, EC_GROUP_get_order,
8 EC_GROUP_get_cofactor, EC_GROUP_set_curve_name,
9 EC_GROUP_get_curve_name, EC_GROUP_set_asn1_flag,
10 EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form,
11 EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed,
12 EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree,
13 EC_GROUP_check, EC_GROUP_check_discriminant, EC_GROUP_cmp,
14 EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis,
15 EC_GROUP_get_pentanomial_basis - Functions for manipulating EC_GROUP
16 objects.
17
19 #include <openssl/ec.h>
20 #include <openssl/bn.h>
21 int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
23 EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
24 const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
26 int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
28 const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
29 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);
34 int EC_GROUP_get_curve_name(const EC_GROUP *group);
35 void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
37 int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
38 void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
40 point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
41 unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
43 size_t EC_GROUP_get_seed_len(const EC_GROUP *);
44 size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
45 int EC_GROUP_get_degree(const EC_GROUP *group);
47 int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
49 int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
51 int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
53 int EC_GROUP_get_basis_type(const EC_GROUP *);
55 int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
56 int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
57 unsigned int *k2, unsigned int *k3);
58
60 EC_GROUP_copy copies the curve src into dst. Both src and dst must use
61 the same EC_METHOD.
62 EC_GROUP_dup creates a new EC_GROUP object and copies the content from
64 src to the newly created EC_GROUP object.
65 EC_GROUP_method_of obtains the EC_METHOD of group.
67 EC_GROUP_set_generator sets curve paramaters that must be agreed by all
69 participants using the curve. These paramaters include the generator,
70 the order and the cofactor. The generator is a well defined point on
71 the curve chosen for cryptographic operations. Integers used for point
72 multiplications will be between 0 and n-1 where n is the order. The
73 order multipied by the cofactor gives the number of points on the
74 curve.
75 EC_GROUP_get0_generator returns the generator for the identified group.
77 The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the
79 provided order and cofactor parameters with the respective order and
80 cofactors for the group.
81 The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set
83 and get the NID for the curve respectively (see EC_GROUP_new(3)). If a
84 curve does not have a NID associated with it, then
85 EC_GROUP_get_curve_name will return 0.
86 The asn1_flag value on a curve is used to determine whether there is a
88 specific ASN1 OID to describe the curve or not. If the asn1_flag is 1
89 then this is a named curve with an associated ASN1 OID. If not then
90 asn1_flag is 0. The functions EC_GROUP_get_asn1_flag and
91 EC_GROUP_set_asn1_flag get and set the status of the asn1_flag for the
92 curve. If set then the curve_name must also be set.
93 The point_coversion_form for a curve controls how EC_POINT data is
95 encoded as ASN1 as defined in X9.62 (ECDSA). point_conversion_form_t
96 is an enum defined as follows:
97 typedef enum {
99 /** the point is encoded as z||x, where the octet z specifies
100 * which solution of the quadratic equation y is */
101 POINT_CONVERSION_COMPRESSED = 2,
102 /** the point is encoded as z||x||y, where z is the octet 0x02 */
103 POINT_CONVERSION_UNCOMPRESSED = 4,
104 /** the point is encoded as z||x||y, where the octet z specifies
105 * which solution of the quadratic equation y is */
106 POINT_CONVERSION_HYBRID = 6
107 } point_conversion_form_t;
108 For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet
110 signifying the UNCOMPRESSED form has been used followed by the octets
111 for x, followed by the octets for y.
112 For any given x co-ordinate for a point on a curve it is possible to
114 derive two possible y values. For POINT_CONVERSION_COMPRESSED the point
115 is encoded as an octet signifying that the COMPRESSED form has been
116 used AND which of the two possible solutions for y has been used,
117 followed by the octets for x.
118 For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying
120 the HYBRID form has been used AND which of the two possible solutions
121 for y has been used, followed by the octets for x, followed by the
122 octets for y.
123 The functions EC_GROUP_set_point_conversion_form and
125 EC_GROUP_get_point_conversion_form set and get the
126 point_conversion_form for the curve respectively.
127 ANSI X9.62 (ECDSA standard) defines a method of generating the curve
129 parameter b from a random number. This provides advantages in that a
130 parameter obtained in this way is highly unlikely to be susceptible to
131 special purpose attacks, or have any trapdoors in it. If the seed is
132 present for a curve then the b parameter was generated in a verifiable
133 fashion using that seed. The OpenSSL EC library does not use this seed
134 value but does enable you to inspect it using EC_GROUP_get0_seed. This
135 returns a pointer to a memory block containing the seed that was used.
136 The length of the memory block can be obtained using
137 EC_GROUP_get_seed_len. A number of the builtin curves within the
138 library provide seed values that can be obtained. It is also possible
139 to set a custom seed using EC_GROUP_set_seed and passing a pointer to a
140 memory block, along with the length of the seed. Again, the EC library
141 will not use this seed value, although it will be preserved in any ASN1
142 based communications.
143 EC_GROUP_get_degree gets the degree of the field. For Fp fields this
145 will be the number of bits in p. For F2^m fields this will be the
146 value m.
147 The function EC_GROUP_check_discriminant calculates the discriminant
149 for the curve and verifies that it is valid. For a curve defined over
150 Fp the discriminant is given by the formula 4*a^3 + 27*b^2 whilst for
151 F2^m curves the discriminant is simply b. In either case for the curve
152 to be valid the discriminant must be non zero.
153 The function EC_GROUP_check performs a number of checks on a curve to
155 verify that it is valid. Checks performed include verifying that the
156 discriminant is non zero; that a generator has been defined; that the
157 generator is on the curve and has the correct order.
158 EC_GROUP_cmp compares a and b to determine whether they represent the
160 same curve or not.
161 The functions EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis and
163 EC_GROUP_get_pentanomial_basis should only be called for curves defined
164 over an F2^m field. Addition and multiplication operations within an
165 F2^m field are performed using an irreducible polynomial function f(x).
166 This function is either a trinomial of the form:
167 f(x) = x^m + x^k + 1 with m > k >= 1
169 or a pentanomial of the form:
171 f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
173 The function EC_GROUP_get_basis_type returns a NID identifying whether
175 a trinomial or pentanomial is in use for the field. The function
176 EC_GROUP_get_trinomial_basis must only be called where f(x) is of the
177 trinomial form, and returns the value of k. Similary the function
178 EC_GROUP_get_pentanomial_basis must only be called where f(x) is of the
179 pentanomial form, and returns the values of k1, k2 and k3 respectively.
180
182 The following functions return 1 on success or 0 on error:
183 EC_GROUP_copy, EC_GROUP_set_generator, EC_GROUP_check,
184 EC_GROUP_check_discriminant, EC_GROUP_get_trinomial_basis and
185 EC_GROUP_get_pentanomial_basis.
186 EC_GROUP_dup returns a pointer to the duplicated curve, or NULL on
188 error.
189 EC_GROUP_method_of returns the EC_METHOD implementation in use for the
191 given curve or NULL on error.
192 EC_GROUP_get0_generator returns the generator for the given curve or
194 NULL on error.
195 EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_get_curve_name,
197 EC_GROUP_get_asn1_flag, EC_GROUP_get_point_conversion_form and
198 EC_GROUP_get_degree return the order, cofactor, curve name (NID), ASN1
199 flag, point_conversion_form and degree for the specified curve
200 respectively. If there is no curve name associated with a curve then
201 EC_GROUP_get_curve_name will return 0.
202 EC_GROUP_get0_seed returns a pointer to the seed that was used to
204 generate the parameter b, or NULL if the seed is not specified.
205 EC_GROUP_get_seed_len returns the length of the seed or 0 if the seed
206 is not specified.
207 EC_GROUP_set_seed returns the length of the seed that has been set. If
209 the supplied seed is NULL, or the supplied seed length is 0, the return
210 value will be 1. On error 0 is returned.
211 EC_GROUP_cmp returns 0 if the curves are equal, 1 if they are not
213 equal, or -1 on error.
214 EC_GROUP_get_basis_type returns the values NID_X9_62_tpBasis or
216 NID_X9_62_ppBasis (as defined in <openssl/obj_mac.h>) for a trinomial
217 or pentanomial respectively. Alternatively in the event of an error a 0
218 is returned.
219
221 crypto(3), ec(3), EC_GROUP_new(3), EC_POINT_new(3), EC_POINT_add(3),
222 EC_KEY_new(3), EC_GFp_simple_method(3), d2i_ECPKParameters(3)
2231.0.2o 2020-08-01 EC_GROUP_copy(3)