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aafbe1cc MC |
1 | =pod |
2 | ||
3 | =head1 NAME | |
4 | ||
c952780c RS |
5 | EC_GROUP_get0_order, EC_GROUP_order_bits, EC_GROUP_get0_cofactor, |
6 | EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of, EC_GROUP_set_generator, | |
7 | EC_GROUP_get0_generator, EC_GROUP_get_order, EC_GROUP_get_cofactor, | |
8 | EC_GROUP_set_curve_name, EC_GROUP_get_curve_name, EC_GROUP_set_asn1_flag, | |
9 | EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form, | |
10 | EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed, | |
11 | EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree, | |
8402cd5f SL |
12 | EC_GROUP_check, EC_GROUP_check_named_curve, |
13 | EC_GROUP_check_discriminant, EC_GROUP_cmp, | |
c952780c | 14 | EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis, |
fa1f0306 | 15 | EC_GROUP_get_pentanomial_basis, EC_GROUP_get0_field |
c952780c | 16 | - Functions for manipulating EC_GROUP objects |
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17 | |
18 | =head1 SYNOPSIS | |
19 | ||
20 | #include <openssl/ec.h> | |
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21 | |
22 | int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src); | |
23 | EC_GROUP *EC_GROUP_dup(const EC_GROUP *src); | |
24 | ||
25 | const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group); | |
26 | ||
e9b77246 BB |
27 | int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, |
28 | const BIGNUM *order, const BIGNUM *cofactor); | |
aafbe1cc MC |
29 | const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group); |
30 | ||
31 | int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx); | |
be2e334f | 32 | const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group); |
14f46560 | 33 | int EC_GROUP_order_bits(const EC_GROUP *group); |
aafbe1cc | 34 | int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx); |
be2e334f | 35 | const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group); |
fa1f0306 | 36 | const BIGNUM *EC_GROUP_get0_field(const EC_GROUP *group); |
aafbe1cc MC |
37 | |
38 | void EC_GROUP_set_curve_name(EC_GROUP *group, int nid); | |
39 | int EC_GROUP_get_curve_name(const EC_GROUP *group); | |
40 | ||
41 | void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag); | |
42 | int EC_GROUP_get_asn1_flag(const EC_GROUP *group); | |
43 | ||
44 | void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form); | |
df3d1e84 | 45 | point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *group); |
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46 | |
47 | unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x); | |
48 | size_t EC_GROUP_get_seed_len(const EC_GROUP *); | |
49 | size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len); | |
50 | ||
51 | int EC_GROUP_get_degree(const EC_GROUP *group); | |
52 | ||
53 | int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx); | |
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54 | int EC_GROUP_check_named_curve(const EC_GROUP *group, int nist_only, |
55 | BN_CTX *ctx); | |
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56 | |
57 | int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx); | |
58 | ||
59 | int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx); | |
60 | ||
61 | int EC_GROUP_get_basis_type(const EC_GROUP *); | |
62 | int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k); | |
1bc74519 | 63 | int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1, |
e9b77246 | 64 | unsigned int *k2, unsigned int *k3); |
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65 | |
66 | =head1 DESCRIPTION | |
67 | ||
df3d1e84 | 68 | EC_GROUP_copy() copies the curve B<src> into B<dst>. Both B<src> and B<dst> must use the same EC_METHOD. |
aafbe1cc | 69 | |
df3d1e84 | 70 | EC_GROUP_dup() creates a new EC_GROUP object and copies the content from B<src> to the newly created |
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71 | EC_GROUP object. |
72 | ||
df3d1e84 | 73 | EC_GROUP_method_of() obtains the EC_METHOD of B<group>. |
aafbe1cc | 74 | |
df3d1e84 | 75 | EC_GROUP_set_generator() sets curve parameters that must be agreed by all participants using the curve. These |
0d4fb843 | 76 | parameters include the B<generator>, the B<order> and the B<cofactor>. The B<generator> is a well defined point on the |
aafbe1cc | 77 | curve chosen for cryptographic operations. Integers used for point multiplications will be between 0 and |
186bb907 | 78 | n-1 where n is the B<order>. The B<order> multiplied by the B<cofactor> gives the number of points on the curve. |
aafbe1cc | 79 | |
df3d1e84 | 80 | EC_GROUP_get0_generator() returns the generator for the identified B<group>. |
aafbe1cc | 81 | |
df3d1e84 | 82 | EC_GROUP_get_order() retrieves the order of B<group> and copies its value into |
83 | B<order>. It fails in case B<group> is not fully initialized (i.e., its order | |
84 | is not set or set to zero). | |
aafbe1cc | 85 | |
df3d1e84 | 86 | EC_GROUP_get_cofactor() retrieves the cofactor of B<group> and copies its value |
87 | into B<cofactor>. It fails in case B<group> is not fully initialized or if the | |
88 | cofactor is not set (or set to zero). | |
89 | ||
90 | The functions EC_GROUP_set_curve_name() and EC_GROUP_get_curve_name(), set and get the NID for the curve respectively | |
9b86974e | 91 | (see L<EC_GROUP_new(3)>). If a curve does not have a NID associated with it, then EC_GROUP_get_curve_name |
df3d1e84 | 92 | will return NID_undef. |
aafbe1cc | 93 | |
146ca72c DSH |
94 | The asn1_flag value is used to determine whether the curve encoding uses |
95 | explicit parameters or a named curve using an ASN1 OID: many applications only | |
96 | support the latter form. If asn1_flag is B<OPENSSL_EC_NAMED_CURVE> then the | |
97 | named curve form is used and the parameters must have a corresponding | |
98 | named curve NID set. If asn1_flags is B<OPENSSL_EC_EXPLICIT_CURVE> the | |
df3d1e84 | 99 | parameters are explicitly encoded. The functions EC_GROUP_get_asn1_flag() and |
100 | EC_GROUP_set_asn1_flag() get and set the status of the asn1_flag for the curve. | |
fc5ecadd | 101 | Note: B<OPENSSL_EC_EXPLICIT_CURVE> was added in OpenSSL 1.1.0, for |
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102 | previous versions of OpenSSL the value 0 must be used instead. Before OpenSSL |
103 | 1.1.0 the default form was to use explicit parameters (meaning that | |
104 | applications would have to explicitly set the named curve form) in OpenSSL | |
105 | 1.1.0 and later the named curve form is the default. | |
aafbe1cc | 106 | |
186bb907 | 107 | The point_conversion_form for a curve controls how EC_POINT data is encoded as ASN1 as defined in X9.62 (ECDSA). |
1bc74519 | 108 | point_conversion_form_t is an enum defined as follows: |
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109 | |
110 | typedef enum { | |
1bc74519 RS |
111 | /** the point is encoded as z||x, where the octet z specifies |
112 | * which solution of the quadratic equation y is */ | |
113 | POINT_CONVERSION_COMPRESSED = 2, | |
14f46560 | 114 | /** the point is encoded as z||x||y, where z is the octet 0x04 */ |
1bc74519 RS |
115 | POINT_CONVERSION_UNCOMPRESSED = 4, |
116 | /** the point is encoded as z||x||y, where the octet z specifies | |
aafbe1cc | 117 | * which solution of the quadratic equation y is */ |
1bc74519 | 118 | POINT_CONVERSION_HYBRID = 6 |
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119 | } point_conversion_form_t; |
120 | ||
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121 | For POINT_CONVERSION_UNCOMPRESSED the point is encoded as an octet signifying the UNCOMPRESSED form has been used followed by |
122 | the octets for x, followed by the octets for y. | |
123 | ||
124 | For any given x co-ordinate for a point on a curve it is possible to derive two possible y values. For | |
125 | POINT_CONVERSION_COMPRESSED the point is encoded as an octet signifying that the COMPRESSED form has been used AND which of | |
1bc74519 | 126 | the two possible solutions for y has been used, followed by the octets for x. |
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127 | |
128 | For POINT_CONVERSION_HYBRID the point is encoded as an octet signifying the HYBRID form has been used AND which of the two | |
129 | possible solutions for y has been used, followed by the octets for x, followed by the octets for y. | |
130 | ||
df3d1e84 | 131 | The functions EC_GROUP_set_point_conversion_form() and EC_GROUP_get_point_conversion_form(), set and get the point_conversion_form |
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132 | for the curve respectively. |
133 | ||
134 | ANSI X9.62 (ECDSA standard) defines a method of generating the curve parameter b from a random number. This provides advantages | |
135 | in that a parameter obtained in this way is highly unlikely to be susceptible to special purpose attacks, or have any trapdoors in it. | |
136 | If the seed is present for a curve then the b parameter was generated in a verifiable fashion using that seed. The OpenSSL EC library | |
df3d1e84 | 137 | does not use this seed value but does enable you to inspect it using EC_GROUP_get0_seed(). This returns a pointer to a memory block |
138 | containing the seed that was used. The length of the memory block can be obtained using EC_GROUP_get_seed_len(). A number of the | |
37f03b98 | 139 | built-in curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using |
df3d1e84 | 140 | EC_GROUP_set_seed() and passing a pointer to a memory block, along with the length of the seed. Again, the EC library will not use |
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141 | this seed value, although it will be preserved in any ASN1 based communications. |
142 | ||
df3d1e84 | 143 | EC_GROUP_get_degree() gets the degree of the field. For Fp fields this will be the number of bits in p. For F2^m fields this will be |
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144 | the value m. |
145 | ||
df3d1e84 | 146 | The function EC_GROUP_check_discriminant() calculates the discriminant for the curve and verifies that it is valid. |
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147 | For a curve defined over Fp the discriminant is given by the formula 4*a^3 + 27*b^2 whilst for F2^m curves the discriminant is |
148 | simply b. In either case for the curve to be valid the discriminant must be non zero. | |
149 | ||
df3d1e84 | 150 | The function EC_GROUP_check() performs a number of checks on a curve to verify that it is valid. Checks performed include |
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151 | verifying that the discriminant is non zero; that a generator has been defined; that the generator is on the curve and has |
152 | the correct order. | |
153 | ||
df3d1e84 | 154 | The function EC_GROUP_check_named_curve() determines if the group's domain parameters match one of the built-in curves supported by the library. |
8402cd5f SL |
155 | The curve name is returned as a B<NID> if it matches. If the group's domain parameters have been modified then no match will be found. |
156 | If the curve name of the given group is B<NID_undef> (e.g. it has been created by using explicit parameters with no curve name), | |
37f03b98 | 157 | then this method can be used to lookup the name of the curve that matches the group domain parameters. The built-in curves contain |
8402cd5f SL |
158 | aliases, so that multiple NID's can map to the same domain parameters. For such curves it is unspecified which of the aliases will be |
159 | returned if the curve name of the given group is NID_undef. | |
37f03b98 | 160 | If B<nist_only> is 1 it will only look for NIST approved curves, otherwise it searches all built-in curves. |
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161 | This function may be passed a BN_CTX object in the B<ctx> parameter. |
162 | The B<ctx> parameter may be NULL. | |
8402cd5f | 163 | |
df3d1e84 | 164 | EC_GROUP_cmp() compares B<a> and B<b> to determine whether they represent the same curve or not. |
aafbe1cc | 165 | |
df3d1e84 | 166 | The functions EC_GROUP_get_basis_type(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis() should only be called for curves |
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167 | defined over an F2^m field. Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial |
168 | function f(x). This function is either a trinomial of the form: | |
169 | ||
170 | f(x) = x^m + x^k + 1 with m > k >= 1 | |
171 | ||
172 | or a pentanomial of the form: | |
173 | ||
174 | f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1 | |
175 | ||
df3d1e84 | 176 | The function EC_GROUP_get_basis_type() returns a NID identifying whether a trinomial or pentanomial is in use for the field. The |
177 | function EC_GROUP_get_trinomial_basis() must only be called where f(x) is of the trinomial form, and returns the value of B<k>. Similarly | |
178 | the function EC_GROUP_get_pentanomial_basis() must only be called where f(x) is of the pentanomial form, and returns the values of B<k1>, | |
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179 | B<k2> and B<k3> respectively. |
180 | ||
181 | =head1 RETURN VALUES | |
182 | ||
df3d1e84 | 183 | The following functions return 1 on success or 0 on error: EC_GROUP_copy(), EC_GROUP_set_generator(), EC_GROUP_check(), |
184 | EC_GROUP_check_discriminant(), EC_GROUP_get_trinomial_basis() and EC_GROUP_get_pentanomial_basis(). | |
185 | ||
186 | EC_GROUP_dup() returns a pointer to the duplicated curve, or NULL on error. | |
187 | ||
188 | EC_GROUP_method_of() returns the EC_METHOD implementation in use for the given curve or NULL on error. | |
189 | ||
190 | EC_GROUP_get0_generator() returns the generator for the given curve or NULL on error. | |
191 | ||
192 | EC_GROUP_get_order() returns 0 if the order is not set (or set to zero) for | |
193 | B<group> or if copying into B<order> fails, 1 otherwise. | |
194 | ||
195 | EC_GROUP_get_cofactor() returns 0 if the cofactor is not set (or is set to zero) for B<group> or if copying into B<cofactor> fails, 1 otherwise. | |
aafbe1cc | 196 | |
df3d1e84 | 197 | EC_GROUP_get_curve_name() returns the curve name (NID) for B<group> or will return NID_undef if no curve name is associated. |
aafbe1cc | 198 | |
df3d1e84 | 199 | EC_GROUP_get_asn1_flag() returns the ASN1 flag for the specified B<group> . |
aafbe1cc | 200 | |
df3d1e84 | 201 | EC_GROUP_get_point_conversion_form() returns the point_conversion_form for B<group>. |
aafbe1cc | 202 | |
df3d1e84 | 203 | EC_GROUP_get_degree() returns the degree for B<group> or 0 if the operation is not supported by the underlying group implementation. |
aafbe1cc | 204 | |
37f03b98 | 205 | EC_GROUP_check_named_curve() returns the nid of the matching named curve, otherwise it returns 0 for no match, or -1 on error. |
8402cd5f | 206 | |
be2e334f | 207 | EC_GROUP_get0_order() returns an internal pointer to the group order. |
829800b0 | 208 | EC_GROUP_order_bits() returns the number of bits in the group order. |
be2e334f | 209 | EC_GROUP_get0_cofactor() returns an internal pointer to the group cofactor. |
fa1f0306 DA |
210 | EC_GROUP_get0_field() returns an internal pointer to the group field. For curves over GF(p), this is the modulus; for curves |
211 | over GF(2^m), this is the irreducible polynomial defining the field. | |
be2e334f | 212 | |
df3d1e84 | 213 | EC_GROUP_get0_seed() returns a pointer to the seed that was used to generate the parameter b, or NULL if the seed is not |
214 | specified. EC_GROUP_get_seed_len() returns the length of the seed or 0 if the seed is not specified. | |
aafbe1cc | 215 | |
df3d1e84 | 216 | EC_GROUP_set_seed() returns the length of the seed that has been set. If the supplied seed is NULL, or the supplied seed length is |
d900a015 | 217 | 0, the return value will be 1. On error 0 is returned. |
aafbe1cc | 218 | |
df3d1e84 | 219 | EC_GROUP_cmp() returns 0 if the curves are equal, 1 if they are not equal, or -1 on error. |
aafbe1cc | 220 | |
df3d1e84 | 221 | EC_GROUP_get_basis_type() returns the values NID_X9_62_tpBasis or NID_X9_62_ppBasis (as defined in <openssl/obj_mac.h>) for a |
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222 | trinomial or pentanomial respectively. Alternatively in the event of an error a 0 is returned. |
223 | ||
224 | =head1 SEE ALSO | |
225 | ||
9e183d22 | 226 | L<crypto(7)>, L<EC_GROUP_new(3)>, |
9b86974e RS |
227 | L<EC_POINT_new(3)>, L<EC_POINT_add(3)>, L<EC_KEY_new(3)>, |
228 | L<EC_GFp_simple_method(3)>, L<d2i_ECPKParameters(3)> | |
aafbe1cc | 229 | |
8402cd5f SL |
230 | =head1 HISTORY |
231 | ||
232 | The EC_GROUP_check_named_curve() function was added in OpenSSL 3.0. | |
233 | ||
e2f92610 RS |
234 | =head1 COPYRIGHT |
235 | ||
37f03b98 | 236 | Copyright 2013-2019 The OpenSSL Project Authors. All Rights Reserved. |
e2f92610 | 237 | |
4746f25a | 238 | Licensed under the Apache License 2.0 (the "License"). You may not use |
e2f92610 RS |
239 | this file except in compliance with the License. You can obtain a copy |
240 | in the file LICENSE in the source distribution or at | |
241 | L<https://www.openssl.org/source/license.html>. | |
242 | ||
243 | =cut |