368 lines
18 KiB
Groff
Executable File
368 lines
18 KiB
Groff
Executable File
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.\" ========================================================================
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.\"
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.IX Title "EC_GROUP_COPY 3"
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.TH EC_GROUP_COPY 3 "2020-03-02" "3.0.0-dev" "OpenSSL"
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.\" For nroff, turn off justification. Always turn off hyphenation; it makes
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.\" way too many mistakes in technical documents.
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.if n .ad l
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.nh
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.SH "NAME"
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EC_GROUP_get0_order, EC_GROUP_order_bits, EC_GROUP_get0_cofactor,
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EC_GROUP_copy, EC_GROUP_dup, EC_GROUP_method_of, EC_GROUP_set_generator,
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EC_GROUP_get0_generator, EC_GROUP_get_order, EC_GROUP_get_cofactor,
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EC_GROUP_set_curve_name, EC_GROUP_get_curve_name, EC_GROUP_set_asn1_flag,
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EC_GROUP_get_asn1_flag, EC_GROUP_set_point_conversion_form,
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EC_GROUP_get_point_conversion_form, EC_GROUP_get0_seed,
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EC_GROUP_get_seed_len, EC_GROUP_set_seed, EC_GROUP_get_degree,
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EC_GROUP_check, EC_GROUP_check_named_curve,
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EC_GROUP_check_discriminant, EC_GROUP_cmp,
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EC_GROUP_get_basis_type, EC_GROUP_get_trinomial_basis,
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EC_GROUP_get_pentanomial_basis, EC_GROUP_get0_field
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\&\- Functions for manipulating EC_GROUP objects
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.SH "SYNOPSIS"
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.IX Header "SYNOPSIS"
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.Vb 1
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\& #include <openssl/ec.h>
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\&
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\& int EC_GROUP_copy(EC_GROUP *dst, const EC_GROUP *src);
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\& EC_GROUP *EC_GROUP_dup(const EC_GROUP *src);
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\&
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\& const EC_METHOD *EC_GROUP_method_of(const EC_GROUP *group);
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\&
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\& int EC_GROUP_set_generator(EC_GROUP *group, const EC_POINT *generator,
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\& const BIGNUM *order, const BIGNUM *cofactor);
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\& const EC_POINT *EC_GROUP_get0_generator(const EC_GROUP *group);
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\&
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\& int EC_GROUP_get_order(const EC_GROUP *group, BIGNUM *order, BN_CTX *ctx);
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\& const BIGNUM *EC_GROUP_get0_order(const EC_GROUP *group);
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\& int EC_GROUP_order_bits(const EC_GROUP *group);
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\& int EC_GROUP_get_cofactor(const EC_GROUP *group, BIGNUM *cofactor, BN_CTX *ctx);
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\& const BIGNUM *EC_GROUP_get0_cofactor(const EC_GROUP *group);
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\& const BIGNUM *EC_GROUP_get0_field(const EC_GROUP *group);
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\&
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\& void EC_GROUP_set_curve_name(EC_GROUP *group, int nid);
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\& int EC_GROUP_get_curve_name(const EC_GROUP *group);
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\&
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\& void EC_GROUP_set_asn1_flag(EC_GROUP *group, int flag);
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\& int EC_GROUP_get_asn1_flag(const EC_GROUP *group);
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\&
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\& void EC_GROUP_set_point_conversion_form(EC_GROUP *group, point_conversion_form_t form);
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\& point_conversion_form_t EC_GROUP_get_point_conversion_form(const EC_GROUP *group);
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\&
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\& unsigned char *EC_GROUP_get0_seed(const EC_GROUP *x);
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\& size_t EC_GROUP_get_seed_len(const EC_GROUP *);
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\& size_t EC_GROUP_set_seed(EC_GROUP *, const unsigned char *, size_t len);
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\&
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\& int EC_GROUP_get_degree(const EC_GROUP *group);
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\&
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\& int EC_GROUP_check(const EC_GROUP *group, BN_CTX *ctx);
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\& int EC_GROUP_check_named_curve(const EC_GROUP *group, int nist_only,
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\& BN_CTX *ctx);
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\&
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\& int EC_GROUP_check_discriminant(const EC_GROUP *group, BN_CTX *ctx);
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\&
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\& int EC_GROUP_cmp(const EC_GROUP *a, const EC_GROUP *b, BN_CTX *ctx);
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\&
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\& int EC_GROUP_get_basis_type(const EC_GROUP *);
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\& int EC_GROUP_get_trinomial_basis(const EC_GROUP *, unsigned int *k);
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\& int EC_GROUP_get_pentanomial_basis(const EC_GROUP *, unsigned int *k1,
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\& unsigned int *k2, unsigned int *k3);
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.Ve
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.SH "DESCRIPTION"
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.IX Header "DESCRIPTION"
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\&\fIEC_GROUP_copy()\fR copies the curve \fBsrc\fR into \fBdst\fR. Both \fBsrc\fR and \fBdst\fR must use the same \s-1EC_METHOD\s0.
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.PP
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\&\fIEC_GROUP_dup()\fR creates a new \s-1EC_GROUP\s0 object and copies the content from \fBsrc\fR to the newly created
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\&\s-1EC_GROUP\s0 object.
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.PP
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\&\fIEC_GROUP_method_of()\fR obtains the \s-1EC_METHOD\s0 of \fBgroup\fR.
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.PP
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\&\fIEC_GROUP_set_generator()\fR sets curve parameters that must be agreed by all participants using the curve. These
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parameters include the \fBgenerator\fR, the \fBorder\fR and the \fBcofactor\fR. The \fBgenerator\fR is a well defined point on the
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curve chosen for cryptographic operations. Integers used for point multiplications will be between 0 and
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n\-1 where n is the \fBorder\fR. The \fBorder\fR multiplied by the \fBcofactor\fR gives the number of points on the curve.
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.PP
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\&\fIEC_GROUP_get0_generator()\fR returns the generator for the identified \fBgroup\fR.
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.PP
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\&\fIEC_GROUP_get_order()\fR retrieves the order of \fBgroup\fR and copies its value into
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\&\fBorder\fR. It fails in case \fBgroup\fR is not fully initialized (i.e., its order
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is not set or set to zero).
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.PP
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\&\fIEC_GROUP_get_cofactor()\fR retrieves the cofactor of \fBgroup\fR and copies its value
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into \fBcofactor\fR. It fails in case \fBgroup\fR is not fully initialized or if the
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cofactor is not set (or set to zero).
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.PP
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The functions \fIEC_GROUP_set_curve_name()\fR and \fIEC_GROUP_get_curve_name()\fR, set and get the \s-1NID\s0 for the curve respectively
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(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
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will return NID_undef.
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.PP
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The asn1_flag value is used to determine whether the curve encoding uses
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explicit parameters or a named curve using an \s-1ASN1\s0 \s-1OID:\s0 many applications only
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support the latter form. If asn1_flag is \fB\s-1OPENSSL_EC_NAMED_CURVE\s0\fR then the
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named curve form is used and the parameters must have a corresponding
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named curve \s-1NID\s0 set. If asn1_flags is \fB\s-1OPENSSL_EC_EXPLICIT_CURVE\s0\fR the
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parameters are explicitly encoded. The functions \fIEC_GROUP_get_asn1_flag()\fR and
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\&\fIEC_GROUP_set_asn1_flag()\fR get and set the status of the asn1_flag for the curve.
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Note: \fB\s-1OPENSSL_EC_EXPLICIT_CURVE\s0\fR was added in OpenSSL 1.1.0, for
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previous versions of OpenSSL the value 0 must be used instead. Before OpenSSL
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1.1.0 the default form was to use explicit parameters (meaning that
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applications would have to explicitly set the named curve form) in OpenSSL
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1.1.0 and later the named curve form is the default.
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.PP
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The point_conversion_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).
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point_conversion_form_t is an enum defined as follows:
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.PP
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.Vb 10
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\& typedef enum {
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\& /** the point is encoded as z||x, where the octet z specifies
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\& * which solution of the quadratic equation y is */
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\& POINT_CONVERSION_COMPRESSED = 2,
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\& /** the point is encoded as z||x||y, where z is the octet 0x04 */
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\& POINT_CONVERSION_UNCOMPRESSED = 4,
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\& /** the point is encoded as z||x||y, where the octet z specifies
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\& * which solution of the quadratic equation y is */
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\& POINT_CONVERSION_HYBRID = 6
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\& } point_conversion_form_t;
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.Ve
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.PP
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For \s-1POINT_CONVERSION_UNCOMPRESSED\s0 the point is encoded as an octet signifying the \s-1UNCOMPRESSED\s0 form has been used followed by
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the octets for x, followed by the octets for y.
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.PP
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For any given x co-ordinate for a point on a curve it is possible to derive two possible y values. For
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\&\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
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the two possible solutions for y has been used, followed by the octets for x.
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.PP
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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
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possible solutions for y has been used, followed by the octets for x, followed by the octets for y.
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.PP
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The functions \fIEC_GROUP_set_point_conversion_form()\fR and \fIEC_GROUP_get_point_conversion_form()\fR, set and get the point_conversion_form
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for the curve respectively.
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.PP
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\&\s-1ANSI\s0 X9.62 (\s-1ECDSA\s0 standard) defines a method of generating the curve parameter b from a random number. This provides advantages
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in that a parameter obtained in this way is highly unlikely to be susceptible to special purpose attacks, or have any trapdoors in it.
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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
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does not use this seed value but does enable you to inspect it using \fIEC_GROUP_get0_seed()\fR. This returns a pointer to a memory block
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containing the seed that was used. The length of the memory block can be obtained using \fIEC_GROUP_get_seed_len()\fR. A number of the
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built-in curves within the library provide seed values that can be obtained. It is also possible to set a custom seed using
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\&\fIEC_GROUP_set_seed()\fR and passing a pointer to a memory block, along with the length of the seed. Again, the \s-1EC\s0 library will not use
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this seed value, although it will be preserved in any \s-1ASN1\s0 based communications.
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.PP
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\&\fIEC_GROUP_get_degree()\fR 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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the value m.
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.PP
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The function \fIEC_GROUP_check_discriminant()\fR calculates the discriminant for the curve and verifies that it is valid.
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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
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simply b. In either case for the curve to be valid the discriminant must be non zero.
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.PP
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The function \fIEC_GROUP_check()\fR performs a number of checks on a curve to verify that it is valid. Checks performed include
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verifying that the discriminant is non zero; that a generator has been defined; that the generator is on the curve and has
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the correct order.
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.PP
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The function \fIEC_GROUP_check_named_curve()\fR determines if the group's domain parameters match one of the built-in curves supported by the library.
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The curve name is returned as a \fB\s-1NID\s0\fR if it matches. If the group's domain parameters have been modified then no match will be found.
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If the curve name of the given group is \fBNID_undef\fR (e.g. it has been created by using explicit parameters with no curve name),
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then this method can be used to lookup the name of the curve that matches the group domain parameters. The built-in curves contain
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aliases, so that multiple \s-1NID\s0's can map to the same domain parameters. For such curves it is unspecified which of the aliases will be
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returned if the curve name of the given group is NID_undef.
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If \fBnist_only\fR is 1 it will only look for \s-1NIST\s0 approved curves, otherwise it searches all built-in curves.
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This function may be passed a \s-1BN_CTX\s0 object in the \fBctx\fR parameter.
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The \fBctx\fR parameter may be \s-1NULL\s0.
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.PP
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\&\fIEC_GROUP_cmp()\fR compares \fBa\fR and \fBb\fR to determine whether they represent the same curve or not.
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.PP
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The functions \fIEC_GROUP_get_basis_type()\fR, \fIEC_GROUP_get_trinomial_basis()\fR and \fIEC_GROUP_get_pentanomial_basis()\fR should only be called for curves
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defined over an F2^m field. Addition and multiplication operations within an F2^m field are performed using an irreducible polynomial
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function f(x). This function is either a trinomial of the form:
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.PP
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f(x) = x^m + x^k + 1 with m > k >= 1
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.PP
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or a pentanomial of the form:
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.PP
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f(x) = x^m + x^k3 + x^k2 + x^k1 + 1 with m > k3 > k2 > k1 >= 1
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.PP
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The function \fIEC_GROUP_get_basis_type()\fR returns a \s-1NID\s0 identifying whether a trinomial or pentanomial is in use for the field. The
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function \fIEC_GROUP_get_trinomial_basis()\fR must only be called where f(x) is of the trinomial form, and returns the value of \fBk\fR. Similarly
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the function \fIEC_GROUP_get_pentanomial_basis()\fR must only be called where f(x) is of the pentanomial form, and returns the values of \fBk1\fR,
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\&\fBk2\fR and \fBk3\fR respectively.
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.SH "RETURN VALUES"
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.IX Header "RETURN VALUES"
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The following functions return 1 on success or 0 on error: \fIEC_GROUP_copy()\fR, \fIEC_GROUP_set_generator()\fR, \fIEC_GROUP_check()\fR,
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\&\fIEC_GROUP_check_discriminant()\fR, \fIEC_GROUP_get_trinomial_basis()\fR and \fIEC_GROUP_get_pentanomial_basis()\fR.
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.PP
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\&\fIEC_GROUP_dup()\fR returns a pointer to the duplicated curve, or \s-1NULL\s0 on error.
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.PP
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\&\fIEC_GROUP_method_of()\fR returns the \s-1EC_METHOD\s0 implementation in use for the given curve or \s-1NULL\s0 on error.
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.PP
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\&\fIEC_GROUP_get0_generator()\fR returns the generator for the given curve or \s-1NULL\s0 on error.
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.PP
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\&\fIEC_GROUP_get_order()\fR returns 0 if the order is not set (or set to zero) for
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\&\fBgroup\fR or if copying into \fBorder\fR fails, 1 otherwise.
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.PP
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\&\fIEC_GROUP_get_cofactor()\fR returns 0 if the cofactor is not set (or is set to zero) for \fBgroup\fR or if copying into \fBcofactor\fR fails, 1 otherwise.
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.PP
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\&\fIEC_GROUP_get_curve_name()\fR returns the curve name (\s-1NID\s0) for \fBgroup\fR or will return NID_undef if no curve name is associated.
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.PP
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\&\fIEC_GROUP_get_asn1_flag()\fR returns the \s-1ASN1\s0 flag for the specified \fBgroup\fR .
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.PP
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\&\fIEC_GROUP_get_point_conversion_form()\fR returns the point_conversion_form for \fBgroup\fR.
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.PP
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\&\fIEC_GROUP_get_degree()\fR returns the degree for \fBgroup\fR or 0 if the operation is not supported by the underlying group implementation.
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.PP
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\&\fIEC_GROUP_check_named_curve()\fR returns the nid of the matching named curve, otherwise it returns 0 for no match, or \-1 on error.
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.PP
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\&\fIEC_GROUP_get0_order()\fR returns an internal pointer to the group order.
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\&\fIEC_GROUP_order_bits()\fR returns the number of bits in the group order.
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\&\fIEC_GROUP_get0_cofactor()\fR returns an internal pointer to the group cofactor.
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\&\fIEC_GROUP_get0_field()\fR returns an internal pointer to the group field. For curves over \s-1GF\s0(p), this is the modulus; for curves
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over \s-1GF\s0(2^m), this is the irreducible polynomial defining the field.
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.PP
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\&\fIEC_GROUP_get0_seed()\fR returns a pointer to the seed that was used to generate the parameter b, or \s-1NULL\s0 if the seed is not
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|
specified. \fIEC_GROUP_get_seed_len()\fR returns the length of the seed or 0 if the seed is not specified.
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.PP
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\&\fIEC_GROUP_set_seed()\fR returns the length of the seed that has been set. If the supplied seed is \s-1NULL\s0, or the supplied seed length is
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0, the return value will be 1. On error 0 is returned.
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.PP
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\&\fIEC_GROUP_cmp()\fR returns 0 if the curves are equal, 1 if they are not equal, or \-1 on error.
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.PP
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\&\fIEC_GROUP_get_basis_type()\fR 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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|
trinomial or pentanomial respectively. Alternatively in the event of an error a 0 is returned.
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.SH "SEE ALSO"
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|
.IX Header "SEE ALSO"
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|
\&\fIcrypto\fR\|(7), \fIEC_GROUP_new\fR\|(3),
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|
\&\fIEC_POINT_new\fR\|(3), \fIEC_POINT_add\fR\|(3), \fIEC_KEY_new\fR\|(3),
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\&\fIEC_GFp_simple_method\fR\|(3), \fId2i_ECPKParameters\fR\|(3)
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|
.SH "HISTORY"
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|
.IX Header "HISTORY"
|
|
The \fIEC_GROUP_check_named_curve()\fR function was added in OpenSSL 3.0.
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.SH "COPYRIGHT"
|
|
.IX Header "COPYRIGHT"
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|
Copyright 2013\-2019 The OpenSSL Project Authors. All Rights Reserved.
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.PP
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|
Licensed under the Apache License 2.0 (the \*(L"License\*(R"). You may not use
|
|
this file except in compliance with the License. You can obtain a copy
|
|
in the file \s-1LICENSE\s0 in the source distribution or at
|
|
<https://www.openssl.org/source/license.html>.
|