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131 .IX Title "EC_GROUP_copy 3"
132 .TH EC_GROUP_copy 3 "2018-11-20" "1.0.2q" "OpenSSL"
133 .\" For nroff, turn off justification. Always turn off hyphenation; it makes
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138 EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of, EC_GROUP_set_generator, EC_GROUP_get0_generator, EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_set_curve_name, EC_GROUP_get_curve_name, EC_GROUP_set_asn1_flag, EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form, EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed, EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree, EC_GROUP_check, EC_GROUP_check_discriminant, EC_GROUP_cmp, EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis, EC_GROUP_get_pentanomial_basis \- Functions for manipulating EC_GROUP objects.
140 .IX Header "SYNOPSIS"
142 \& #include <openssl/ec.h>
143 \& #include <openssl/bn.h>
145 \& int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
146 \& EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
148 \& const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
150 \& int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator, const BIGNUM *order, const BIGNUM *cofactor);
151 \& const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
153 \& int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
154 \& int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
156 \& void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
157 \& int EC_GROUP_get_curve_name(const EC_GROUP *group);
159 \& void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
160 \& int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
162 \& void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
163 \& point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *);
165 \& unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
166 \& size_t EC_GROUP_get_seed_len(const EC_GROUP *);
167 \& size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
169 \& int EC_GROUP_get_degree(const EC_GROUP *group);
171 \& int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
173 \& int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
175 \& int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
177 \& int EC_GROUP_get_basis_type(const EC_GROUP *);
178 \& int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
179 \& int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
180 \& unsigned int *k2, unsigned int *k3);
183 .IX Header "DESCRIPTION"
184 EC_GROUP_copy copies the curve \fBsrc\fR into \fBdst\fR. Both \fBsrc\fR and \fBdst\fR must use the same \s-1EC_METHOD.\s0
186 EC_GROUP_dup creates a new \s-1EC_GROUP\s0 object and copies the content from \fBsrc\fR to the newly created
187 \&\s-1EC_GROUP\s0 object.
189 EC_GROUP_method_of obtains the \s-1EC_METHOD\s0 of \fBgroup\fR.
191 EC_GROUP_set_generator sets curve paramaters that must be agreed by all participants using the curve. These
192 paramaters include the \fBgenerator\fR, the \fBorder\fR and the \fBcofactor\fR. The \fBgenerator\fR is a well defined point on the
193 curve chosen for cryptographic operations. Integers used for point multiplications will be between 0 and
194 n\-1 where n is the \fBorder\fR. The \fBorder\fR multipied by the \fBcofactor\fR gives the number of points on the curve.
196 EC_GROUP_get0_generator returns the generator for the identified \fBgroup\fR.
198 The functions EC_GROUP_get_order and EC_GROUP_get_cofactor populate the provided \fBorder\fR and \fBcofactor\fR parameters
199 with the respective order and cofactors for the \fBgroup\fR.
201 The functions EC_GROUP_set_curve_name and EC_GROUP_get_curve_name, set and get the \s-1NID\s0 for the curve respectively
202 (see \fIEC_GROUP_new\fR\|(3)). If a curve does not have a \s-1NID\s0 associated with it, then EC_GROUP_get_curve_name
205 The asn1_flag value on a curve is used to determine whether there is a specific \s-1ASN1 OID\s0 to describe the curve or not.
206 If the asn1_flag is 1 then this is a named curve with an associated \s-1ASN1 OID.\s0 If not then asn1_flag is 0. The functions
207 EC_GROUP_get_asn1_flag and EC_GROUP_set_asn1_flag get and set the status of the asn1_flag for the curve. If set then
208 the curve_name must also be set.
210 The point_coversion_form for a curve controls how \s-1EC_POINT\s0 data is encoded as \s-1ASN1\s0 as defined in X9.62 (\s-1ECDSA\s0).
211 point_conversion_form_t is an enum defined as follows:
215 \& /** the point is encoded as z||x, where the octet z specifies
216 \& * which solution of the quadratic equation y is */
217 \& POINT_CONVERSION_COMPRESSED = 2,
218 \& /** the point is encoded as z||x||y, where z is the octet 0x02 */
219 \& POINT_CONVERSION_UNCOMPRESSED = 4,
220 \& /** the point is encoded as z||x||y, where the octet z specifies
221 \& * which solution of the quadratic equation y is */
222 \& POINT_CONVERSION_HYBRID = 6
223 \& } point_conversion_form_t;
226 For \s-1POINT_CONVERSION_UNCOMPRESSED\s0 the point is encoded as an octet signifying the \s-1UNCOMPRESSED\s0 form has been used followed by
227 the octets for x, followed by the octets for y.
229 For any given x co-ordinate for a point on a curve it is possible to derive two possible y values. For
230 \&\s-1POINT_CONVERSION_COMPRESSED\s0 the point is encoded as an octet signifying that the \s-1COMPRESSED\s0 form has been used \s-1AND\s0 which of
231 the two possible solutions for y has been used, followed by the octets for x.
233 For \s-1POINT_CONVERSION_HYBRID\s0 the point is encoded as an octet signifying the \s-1HYBRID\s0 form has been used \s-1AND\s0 which of the two
234 possible solutions for y has been used, followed by the octets for x, followed by the octets for y.
236 The functions EC_GROUP_set_point_conversion_form and EC_GROUP_get_point_conversion_form set and get the point_conversion_form
237 for the curve respectively.
239 \&\s-1ANSI X9.62\s0 (\s-1ECDSA\s0 standard) defines a method of generating the curve parameter b from a random number. This provides advantages
240 in that a parameter obtained in this way is highly unlikely to be susceptible to special purpose attacks, or have any trapdoors in it.
241 If the seed is present for a curve then the b parameter was generated in a verifiable fashion using that seed. The OpenSSL \s-1EC\s0 library
242 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
243 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
244 builtin curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using
245 EC_GROUP_set_seed and passing a pointer to a memory block, along with the length of the seed. Again, the \s-1EC\s0 library will not use
246 this seed value, although it will be preserved in any \s-1ASN1\s0 based communications.
248 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
251 The function EC_GROUP_check_discriminant calculates the discriminant for the curve and verifies that it is valid.
252 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
253 simply b. In either case for the curve to be valid the discriminant must be non zero.
255 The function EC_GROUP_check performs a number of checks on a curve to verify that it is valid. Checks performed include
256 verifying that the discriminant is non zero; that a generator has been defined; that the generator is on the curve and has
259 EC_GROUP_cmp compares \fBa\fR and \fBb\fR to determine whether they represent the same curve or not.
261 The functions EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis and EC_GROUP_get_pentanomial_basis should only be called for curves
262 defined over an F2^m field. Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial
263 function f(x). This function is either a trinomial of the form:
265 f(x) = x^m + x^k + 1 with m > k >= 1
267 or a pentanomial of the form:
269 f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
271 The function EC_GROUP_get_basis_type returns a \s-1NID\s0 identifying whether a trinomial or pentanomial is in use for the field. The
272 function EC_GROUP_get_trinomial_basis must only be called where f(x) is of the trinomial form, and returns the value of \fBk\fR. Similary
273 the function EC_GROUP_get_pentanomial_basis must only be called where f(x) is of the pentanomial form, and returns the values of \fBk1\fR,
274 \&\fBk2\fR and \fBk3\fR respectively.
276 .IX Header "RETURN VALUES"
277 The following functions return 1 on success or 0 on error: EC_GROUP_copy, EC_GROUP_set_generator, EC_GROUP_check,
278 EC_GROUP_check_discriminant, EC_GROUP_get_trinomial_basis and EC_GROUP_get_pentanomial_basis.
280 EC_GROUP_dup returns a pointer to the duplicated curve, or \s-1NULL\s0 on error.
282 EC_GROUP_method_of returns the \s-1EC_METHOD\s0 implementation in use for the given curve or \s-1NULL\s0 on error.
284 EC_GROUP_get0_generator returns the generator for the given curve or \s-1NULL\s0 on error.
286 EC_GROUP_get_order, EC_GROUP_get_cofactor, EC_GROUP_get_curve_name, EC_GROUP_get_asn1_flag, EC_GROUP_get_point_conversion_form
287 and EC_GROUP_get_degree return the order, cofactor, curve name (\s-1NID\s0), \s-1ASN1\s0 flag, point_conversion_form and degree for the
288 specified curve respectively. If there is no curve name associated with a curve then EC_GROUP_get_curve_name will return 0.
290 EC_GROUP_get0_seed returns a pointer to the seed that was used to generate the parameter b, or \s-1NULL\s0 if the seed is not
291 specified. EC_GROUP_get_seed_len returns the length of the seed or 0 if the seed is not specified.
293 EC_GROUP_set_seed returns the length of the seed that has been set. If the supplied seed is \s-1NULL,\s0 or the supplied seed length is
294 0, the return value will be 1. On error 0 is returned.
296 EC_GROUP_cmp returns 0 if the curves are equal, 1 if they are not equal, or \-1 on error.
298 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
299 trinomial or pentanomial respectively. Alternatively in the event of an error a 0 is returned.
301 .IX Header "SEE ALSO"
302 \&\fIcrypto\fR\|(3), \fIec\fR\|(3), \fIEC_GROUP_new\fR\|(3),
303 \&\fIEC_POINT_new\fR\|(3), \fIEC_POINT_add\fR\|(3), \fIEC_KEY_new\fR\|(3),
304 \&\fIEC_GFp_simple_method\fR\|(3), \fId2i_ECPKParameters\fR\|(3)