1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
|
=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 "decoded-from-explicit" (B<OSSL_PKEY_PARAM_EC_DECODED_FROM_EXPLICIT_PARAMS>) <integer>
Gets a flag indicating wether the key or parameters were decoded from explicit
curve parameters. Set to 1 if so or 0 if a named curve was used.
=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".
=item "point-format" (B<OSSL_PKEY_PARAM_EC_POINT_CONVERSION_FORMAT>) <UTF8 string>
Sets or gets the point_conversion_form for the I<key>. For a description of
point_conversion_forms please see L<EC_POINT_new(3)>. Valid values are
"uncompressed" or "compressed". The default value is "uncompressed".
=item "group-check" (B<OSSL_PKEY_PARAM_EC_GROUP_CHECK_TYPE>) <UTF8 string>
Sets or Gets the type of group check done when EVP_PKEY_param_check() is called.
Valid values are "default", "named" and "named-nist".
The "named" type checks that the domain parameters match the inbuilt curve parameters,
"named-nist" is similiar but also checks that the named curve is a nist curve.
The "default" type does domain parameter validation for the OpenSSL default provider,
but is equivalent to "named-nist" for the OpenSSL FIPS provider.
=item "include-public" (B<OSSL_PKEY_PARAM_EC_INCLUDE_PUBLIC>) <integer>
Setting this value to 0 indicates that the public key should not be included when
encoding the private key. The default value of 1 will include the public key.
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 encoded EC point format. This parameter is used
when importing or exporting the public key value with the EVP_PKEY_fromdata()
and EVP_PKEY_todata() functions.
=item "priv" (B<OSSL_PKEY_PARAM_PRIV_KEY>) <unsigned integer>
The private key value.
=item "encoded-pub-key" (B<OSSL_PKEY_PARAM_ENCODED_PUBLIC_KEY>) <octet string>
Used for getting and setting the encoding of an EC public key. The public key
is expected to be a point conforming to Sec. 2.3.4 of the SECG SEC 1 ("Elliptic
Curve Cryptography") standard.
=item "qx" (B<OSSL_PKEY_PARAM_EC_PUB_X>) <unsigned integer>
Used for getting the EC public key X component.
=item "qy" (B<OSSL_PKEY_PARAM_EC_PUB_Y>) <unsigned integer>
Used for getting the EC public key Y component.
=item (B<OSSL_PKEY_PARAM_DEFAULT_DIGEST>) <UTF8 string>
Getter that returns the default digest name.
(Currently returns "SHA256" as of OpenSSL 3.0).
=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
=head2 EC key validation
For EC keys, L<EVP_PKEY_param_check(3)> behaves in the following way:
For the OpenSSL default provider it uses either
L<EC_GROUP_check(3)> or L<EC_GROUP_check_named_curve(3)> depending on the flag
EC_FLAG_CHECK_NAMED_GROUP.
The OpenSSL FIPS provider uses L<EC_GROUP_check_named_curve(3)> in order to
conform to SP800-56Ar3 I<Assurances of Domain-Parameter Validity>.
For EC keys, L<EVP_PKEY_param_check_quick(3)> is equivalent to
L<EVP_PKEY_param_check(3)>.
For EC keys, L<EVP_PKEY_public_check(3)> and L<EVP_PKEY_public_check_quick(3)>
conform to SP800-56Ar3 I<ECC Full Public-Key Validation> and
I<ECC Partial Public-Key Validation> respectively.
For EC Keys, L<EVP_PKEY_private_check(3)> and L<EVP_PKEY_pairwise_check(3)>
conform to SP800-56Ar3 I<Private key validity> and
I<Owner Assurance of Pair-wise Consistency> respectively.
=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:
pkey = EVP_EC_gen("P-256");
or like this:
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_generate(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_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_generate(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_EC_gen(3)>,
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 2020-2022 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>.
=cut
|