openssl/doc/man7/EVP_PKEY-EC.pod

=pod

=head1 NAME

EVP_PKEY-EC,
EVP_KEYMGMT-EC
- EVP_PKEY EC keytype and algorithm support

=head1 DESCRIPTION

The B<EC> keytype is implemented in OpenSSL's default provider.

=head2 Common EC parameters

The normal way of specifying domain parameters for an EC curve is via the
curve name "group". For curves with no curve name, explicit parameters can be
used that specify "field-type", "p", "a", "b", "generator" and "order".
Explicit parameters are supported for backwards compability reasons, but they
are not compliant with multiple standards (including RFC5915) which only allow
named curves.

The following KeyGen/Gettable/Import/Export types are available for the
built-in EC algorithm:

=over 4

=item "group" (B<OSSL_PKEY_PARAM_GROUP_NAME>) <utf8 string>

The curve name.

=item "field-type" (B<OSSL_PKEY_PARAM_EC_FIELD_TYPE>) <utf8 string>

The value should be either "prime-field" or "characteristic-two-field",
which correspond to prime field Fp and binary field F2^m.

=item "p" (B<OSSL_PKEY_PARAM_EC_P>) <unsigned integer>

For a curve over Fp I<p> is the prime for the field. For a curve over F2^m I<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.

=item "a" (B<OSSL_PKEY_PARAM_EC_A>) <unsigned integer>

=item "b" (B<OSSL_PKEY_PARAM_EC_B>) <unsigned integer>

=item "seed" (B<OSSL_PKEY_PARAM_EC_SEED>) <octet string>

I<a> and I<b> represents the coefficients of the curve
For Fp:   y^2 mod p = x^3 +ax + b mod p OR
For F2^m: y^2 + xy = x^3 + ax^2 + b

I<seed> is an optional value that is for information purposes only.
It represents the random number seed used to generate the coefficient I<b> from a
random number.

=item "generator" (B<OSSL_PKEY_PARAM_EC_GENERATOR>) <octet string>

=item "order" (B<OSSL_PKEY_PARAM_EC_ORDER>) <unsigned integer>

=item "cofactor" (B<OSSL_PKEY_PARAM_EC_COFACTOR>) <unsigned integer>

The I<generator> is a well defined point on the curve chosen for cryptographic
operations. The encoding conforms with Sec. 2.3.3 of the SECG SEC 1 ("Elliptic Curve
Cryptography") standard. See EC_POINT_oct2point().
Integers used for point multiplications will be between 0 and
I<order> - 1.
I<cofactor> is an optional value.
I<order> multiplied by the I<cofactor> gives the number of points on the curve.

=item "use-cofactor-flag" (B<OSSL_PKEY_PARAM_USE_COFACTOR_ECDH>) <integer>

Enable Cofactor DH (ECC CDH) if this value is 1, otherwise it uses normal EC DH
if the value is zero. The cofactor variant multiplies the shared secret by the
EC curve's cofactor (note for some curves the cofactor is 1).

=item "encoding" (B<OSSL_PKEY_PARAM_EC_ENCODING>) <utf8 string>

Set the format used for serializing the EC group parameters.
Valid values are "explicit" or "named_curve". The default value is "named_curve".

See also L<EVP_KEYEXCH-ECDH(7)> for the related
B<OSSL_EXCHANGE_PARAM_EC_ECDH_COFACTOR_MODE> parameter that can be set on a
per-operation basis.

=item "pub" (B<OSSL_PKEY_PARAM_PUB_KEY>) <octet string>

The public key value in EC point format.

=item "priv" (B<OSSL_PKEY_PARAM_PRIV_KEY>) <unsigned integer>

The private key value.

=item "tls-encoded-pt" (B<OSSL_PKEY_PARAM_TLS_ENCODED_PT>) <octet string>

Used for getting and setting the encoding of the EC public key used in key
exchange message for the TLS protocol.

=back

The following Gettable types are also available for the built-in EC algorithm:

=over 4

=item "basis-type" (B<OSSL_PKEY_PARAM_EC_CHAR2_TYPE>) <utf8 string>

Supports the values "tpBasis" for a trinomial or "ppBasis" for a pentanomial.
This field is only used for a binary field F2^m.

=item "m" (B<OSSL_PKEY_PARAM_EC_CHAR2_M>) <integer>

=item "tp" (B<OSSL_PKEY_PARAM_EC_CHAR2_TP_BASIS>) <integer>

=item "k1" (B<OSSL_PKEY_PARAM_EC_CHAR2_PP_K1>) <integer>

=item "k2" (B<OSSL_PKEY_PARAM_EC_CHAR2_PP_K2>) <integer>

=item "k3" (B<OSSL_PKEY_PARAM_EC_CHAR2_PP_K3>) <integer>

These fields are only used for a binary field F2^m.
I<m> is the degree of the binary field.

I<tp> is the middle bit of a trinomial so its value must be in the
range m > tp > 0.

I<k1>, I<k2> and I<k3> are used to get the middle bits of a pentanomial such
that m > k3 > k2 > k1 > 0

=back

=head1 EXAMPLES

An B<EVP_PKEY> context can be obtained by calling:

    EVP_PKEY_CTX *pctx =
        EVP_PKEY_CTX_new_from_name(NULL, "EC", NULL);

An B<EVP_PKEY> ECDSA or ECDH key can be generated with a "P-256" named group by
calling:

    EVP_PKEY *key = NULL;
    OSSL_PARAM params[2];
    EVP_PKEY_CTX *gctx =
        EVP_PKEY_CTX_new_from_name(NULL, "EC", NULL);

    EVP_PKEY_keygen_init(gctx);

    params[0] = OSSL_PARAM_construct_utf8_string(OSSL_PKEY_PARAM_GROUP_NAME,
                                                 "P-256", 0);
    params[1] = OSSL_PARAM_construct_end();
    EVP_PKEY_CTX_set_params(gctx, params);

    EVP_PKEY_gen(gctx, &key);

    EVP_PKEY_print_private(bio_out, key, 0, NULL);
    ...
    EVP_PKEY_free(key);
    EVP_PKEY_CTX_free(gctx);

An B<EVP_PKEY> EC CDH (Cofactor Diffie-Hellman) key can be generated with a
"K-571" named group by calling:

    int use_cdh = 1;
    EVP_PKEY *key = NULL;
    OSSL_PARAM params[3];
    EVP_PKEY_CTX *gctx =
        EVP_PKEY_CTX_new_from_name(NULL, "EC", NULL);

    EVP_PKEY *key = NULL;
    OSSL_PARAM params[3];
    EVP_PKEY_CTX *gctx = EVP_PKEY_CTX_new_from_name(NULL, "EC", NULL);

    EVP_PKEY_keygen_init(gctx);

    params[0] = OSSL_PARAM_construct_utf8_string(OSSL_PKEY_PARAM_GROUP_NAME,
                                                 "K-571", 0);
    /*
     * This curve has a cofactor that is not 1 - so setting CDH mode changes
     * the behaviour. For many curves the cofactor is 1 - so setting this has
     * no effect.
     */
    params[1] = OSSL_PARAM_construct_int(OSSL_PKEY_PARAM_USE_COFACTOR_ECDH,
                                         &use_cdh);
    params[2] = OSSL_PARAM_construct_end();
    EVP_PKEY_CTX_set_params(gctx, params);

    EVP_PKEY_gen(gctx, &key);
    EVP_PKEY_print_private(bio_out, key, 0, NULL);
    ...
    EVP_PKEY_free(key);
    EVP_PKEY_CTX_free(gctx);

=head1 SEE ALSO

L<EVP_KEYMGMT(3)>,
L<EVP_PKEY(3)>,
L<provider-keymgmt(7)>,
L<EVP_SIGNATURE-ECDSA(7)>,
L<EVP_KEYEXCH-ECDH(7)>

=head1 COPYRIGHT

Copyright 2020 The OpenSSL Project Authors. All Rights Reserved.

Licensed under the Apache License 2.0 (the "License").  You may not use
this file except in compliance with the License.  You can obtain a copy
in the file LICENSE in the source distribution or at
L<https://www.openssl.org/source/license.html>.

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