=head1 DESCRIPTION
-Within the library there are two forms of elliptic curve that are of interest. The first form is those defined over the
-prime field Fp. The elements of Fp are the integers 0 to p-1, where p is a prime number. This gives us a revised
+Within the library there are two forms of elliptic curve that are of interest.
+The first form is those defined over the prime field Fp. The elements of Fp are
+the integers 0 to p-1, where p is a prime number. This gives us a revised
elliptic curve equation as follows:
y^2 mod p = x^3 +ax + b mod p
-The second form is those defined over a binary field F2^m where the elements of the field are integers of length at
-most m bits. For this form the elliptic curve equation is modified to:
+The second form is those defined over a binary field F2^m where the elements of
+the field are integers of length at most m bits. For this form the elliptic
+curve equation is modified to:
y^2 + xy = x^3 + ax^2 + b (where b != 0)
-Operations in a binary field are performed relative to an B<irreducible polynomial>. All such curves with OpenSSL
-use a trinomial or a pentanomial for this parameter.
+Operations in a binary field are performed relative to an
+B<irreducible polynomial>. All such curves with OpenSSL use a trinomial or a
+pentanomial for this parameter.
-A new curve can be constructed by calling EC_GROUP_new_ex, using the implementation provided by B<meth> (see
-L<EC_GFp_simple_method(3)>) and associated with the library context B<ctx>
-(see L<OPENSSL_CTX(3)>).
-The B<ctx> parameter may be NULL in which case the default library context is used.
+A new curve can be constructed by calling EC_GROUP_new_ex(), using the
+implementation provided by B<meth> (see L<EC_GFp_simple_method(3)>) and
+associated with the library context B<ctx> (see L<OPENSSL_CTX(3)>).
+The B<ctx> parameter may be NULL in which case the default library context is
+used.
It is then necessary to call EC_GROUP_set_curve() to set the curve parameters.
EC_GROUP_new_from_ecparameters() will create a group from the
specified B<params> and
-EC_GROUP_new_from_ecpkparameters() will create a group from the specific PK B<params>.
+EC_GROUP_new_from_ecpkparameters() will create a group from the specific PK
+B<params>.
-EC_GROUP_new is the same as EC_GROUP_new_ex() except that the library context
+EC_GROUP_new() is the same as EC_GROUP_new_ex() except that the library context
used is always the default library context.
-EC_GROUP_set_curve() sets the curve parameters B<p>, B<a> and B<b>. For a curve over Fp B<b>
-is the prime for the field. For a curve over F2^m B<p> represents the irreducible polynomial - each bit
-represents a term in the polynomial. Therefore there will either be three or five bits set dependent on whether
-the polynomial is a trinomial or a pentanomial.
+EC_GROUP_set_curve() sets the curve parameters B<p>, B<a> and B<b>. For a curve
+over Fp B<b> is the prime for the field. For a curve over F2^m B<p> represents
+the irreducible polynomial - each bit represents a term in the polynomial.
+Therefore there will either be three or five bits set dependent on whether the
+polynomial is a trinomial or a pentanomial.
EC_group_get_curve() obtains the previously set curve parameters.
-EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m() are synonyms for EC_GROUP_set_curve(). They are defined for
-backwards compatibility only and should not be used.
-
-EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m() are synonyms for EC_GROUP_get_curve(). They are defined for
-backwards compatibility only and should not be used.
-
-The functions EC_GROUP_new_curve_GFp and EC_GROUP_new_curve_GF2m are shortcuts for calling EC_GROUP_new and then the
-EC_GROUP_set_curve function. An appropriate default implementation method will be used.
-
-Whilst the library can be used to create any curve using the functions described above, there are also a number of
-predefined curves that are available. In order to obtain a list of all of the predefined curves, call the function
-EC_get_builtin_curves(). The parameter B<r> should be an array of EC_builtin_curve structures of size B<nitems>. The function
-will populate the B<r> array with information about the built-in curves. If B<nitems> is less than the total number of
-curves available, then the first B<nitems> curves will be returned. Otherwise the total number of curves will be
-provided. The return value is the total number of curves available (whether that number has been populated in B<r> or
-not). Passing a NULL B<r>, or setting B<nitems> to 0 will do nothing other than return the total number of curves available.
+EC_GROUP_set_curve_GFp() and EC_GROUP_set_curve_GF2m() are synonyms for
+EC_GROUP_set_curve(). They are defined for backwards compatibility only and
+should not be used.
+
+EC_GROUP_get_curve_GFp() and EC_GROUP_get_curve_GF2m() are synonyms for
+EC_GROUP_get_curve(). They are defined for backwards compatibility only and
+should not be used.
+
+The functions EC_GROUP_new_curve_GFp() and EC_GROUP_new_curve_GF2m() are
+shortcuts for calling EC_GROUP_new() and then the EC_GROUP_set_curve() function.
+An appropriate default implementation method will be used.
+
+Whilst the library can be used to create any curve using the functions described
+above, there are also a number of predefined curves that are available. In order
+to obtain a list of all of the predefined curves, call the function
+EC_get_builtin_curves(). The parameter B<r> should be an array of
+EC_builtin_curve structures of size B<nitems>. The function will populate the
+B<r> array with information about the built-in curves. If B<nitems> is less than
+the total number of curves available, then the first B<nitems> curves will be
+returned. Otherwise the total number of curves will be provided. The return
+value is the total number of curves available (whether that number has been
+populated in B<r> or not). Passing a NULL B<r>, or setting B<nitems> to 0 will
+do nothing other than return the total number of curves available.
The EC_builtin_curve structure is defined as follows:
typedef struct {
const char *comment;
} EC_builtin_curve;
-Each EC_builtin_curve item has a unique integer id (B<nid>), and a human readable comment string describing the curve.
+Each EC_builtin_curve item has a unique integer id (B<nid>), and a human
+readable comment string describing the curve.
-In order to construct a built-in curve use the function EC_GROUP_new_by_curve_name_ex and provide the B<nid> of the curve to
-be constructed and the associated library context to be used in B<ctx> (see L<OPENSSL_CTX(3)>).
-The B<ctx> value may be NULL in which case the default library context is used.
+In order to construct a built-in curve use the function
+EC_GROUP_new_by_curve_name_ex() and provide the B<nid> of the curve to be
+constructed and the associated library context to be used in B<ctx> (see
+L<OPENSSL_CTX(3)>). The B<ctx> value may be NULL in which case the default
+library context is used.
-EC_GROUP_new_by_curve_name is the same as EC_GROUP_new_by_curve_name_ex except
-that the default library context is always used.
+EC_GROUP_new_by_curve_name() is the same as EC_GROUP_new_by_curve_name_ex()
+except that the default library context is always used.
-EC_GROUP_free frees the memory associated with the EC_GROUP.
+EC_GROUP_free() frees the memory associated with the EC_GROUP.
If B<group> is NULL nothing is done.
-EC_GROUP_clear_free is deprecated: it was meant to destroy any sensitive data
+EC_GROUP_clear_free() is deprecated: it was meant to destroy any sensitive data
held within the EC_GROUP and then free its memory, but since all the data stored
in the EC_GROUP is public anyway, this function is unnecessary.
-Its use can be safely replaced with EC_GROUP_free.
+Its use can be safely replaced with EC_GROUP_free().
If B<group> is NULL nothing is done.
=head1 RETURN VALUES
-All EC_GROUP_new* functions return a pointer to the newly constructed group, or NULL on error.
+All EC_GROUP_new* functions return a pointer to the newly constructed group, or
+NULL on error.
-EC_get_builtin_curves returns the number of built-in curves that are available.
+EC_get_builtin_curves() returns the number of built-in curves that are
+available.
-EC_GROUP_set_curve_GFp, EC_GROUP_get_curve_GFp, EC_GROUP_set_curve_GF2m, EC_GROUP_get_curve_GF2m return 1 on success or 0 on error.
+EC_GROUP_set_curve_GFp(), EC_GROUP_get_curve_GFp(), EC_GROUP_set_curve_GF2m(),
+EC_GROUP_get_curve_GF2m() return 1 on success or 0 on error.
=head1 SEE ALSO
=item *
-EC_GROUP_new_ex and EC_GROUP_new_by_curve_name_ex were added in OpenSSL 3.0.
+EC_GROUP_new_ex() and EC_GROUP_new_by_curve_name_ex() were added in OpenSSL 3.0.
=item *
-EC_GROUP_clear_free() was deprecated in OpenSSL 3.0; use EC_GROUP_free() instead.
+EC_GROUP_clear_free() was deprecated in OpenSSL 3.0; use EC_GROUP_free()
+instead.
=back
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