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1 | .\" $OpenBSD: X25519.3,v 1.7 2022/12/15 17:20:48 schwarze Exp $ | ||
2 | .\" contains some text from: BoringSSL curve25519.h, curve25519.c | ||
3 | .\" content also checked up to: OpenSSL f929439f Mar 15 12:19:16 2018 +0000 | ||
4 | .\" | ||
5 | .\" Copyright (c) 2015 Google Inc. | ||
6 | .\" Copyright (c) 2018, 2022 Ingo Schwarze <schwarze@openbsd.org> | ||
7 | .\" | ||
8 | .\" Permission to use, copy, modify, and/or distribute this software for any | ||
9 | .\" purpose with or without fee is hereby granted, provided that the above | ||
10 | .\" copyright notice and this permission notice appear in all copies. | ||
11 | .\" | ||
12 | .\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHORS DISCLAIM ALL WARRANTIES | ||
13 | .\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF | ||
14 | .\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR | ||
15 | .\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES | ||
16 | .\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN | ||
17 | .\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF | ||
18 | .\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. | ||
19 | .\" | ||
20 | .\" According to the BoringSSL git history, those parts of the text in | ||
21 | .\" the present manual page that are Copyrighted by Google were probably | ||
22 | .\" written by Adam Langley <agl@google.com> in 2015. | ||
23 | .\" I fail to see any such text in the public domain files written | ||
24 | .\" by Daniel J. Bernstein and others that are included in SUPERCOP | ||
25 | .\" and that Adam Langley's BoringSSL implementation is based on. | ||
26 | .\" | ||
27 | .Dd $Mdocdate: December 15 2022 $ | ||
28 | .Dt X25519 3 | ||
29 | .Os | ||
30 | .Sh NAME | ||
31 | .Nm X25519 , | ||
32 | .Nm X25519_keypair , | ||
33 | .Nm ED25519_keypair , | ||
34 | .Nm ED25519_sign , | ||
35 | .Nm ED25519_verify | ||
36 | .Nd Elliptic Curve Diffie-Hellman and signature primitives based on Curve25519 | ||
37 | .Sh SYNOPSIS | ||
38 | .In openssl/curve25519.h | ||
39 | .Ft int | ||
40 | .Fo X25519 | ||
41 | .Fa "uint8_t out_shared_key[X25519_KEY_LENGTH]" | ||
42 | .Fa "const uint8_t private_key[X25519_KEY_LENGTH]" | ||
43 | .Fa "const uint8_t peer_public_value[X25519_KEY_LENGTH]" | ||
44 | .Fc | ||
45 | .Ft void | ||
46 | .Fo X25519_keypair | ||
47 | .Fa "uint8_t out_public_value[X25519_KEY_LENGTH]" | ||
48 | .Fa "uint8_t out_private_key[X25519_KEY_LENGTH]" | ||
49 | .Fc | ||
50 | .Ft void | ||
51 | .Fo ED25519_keypair | ||
52 | .Fa "uint8_t out_public_key[ED25519_PUBLIC_KEY_LENGTH]" | ||
53 | .Fa "uint8_t out_private_key[ED25519_PRIVATE_KEY_LENGTH]" | ||
54 | .Fc | ||
55 | .Ft int | ||
56 | .Fo ED25519_sign | ||
57 | .Fa "uint8_t *out_sig" | ||
58 | .Fa "const uint8_t *message" | ||
59 | .Fa "size_t message_len" | ||
60 | .Fa "const uint8_t public_key[ED25519_PUBLIC_KEY_LENGTH]" | ||
61 | .Fa "const uint8_t private_key_seed[ED25519_PRIVATE_KEY_LENGTH]" | ||
62 | .Fc | ||
63 | .Ft int | ||
64 | .Fo ED25519_verify | ||
65 | .Fa "const uint8_t *message" | ||
66 | .Fa "size_t message_len" | ||
67 | .Fa "const uint8_t signature[ED25519_SIGNATURE_LENGTH]" | ||
68 | .Fa "const uint8_t public_key[ED25519_PUBLIC_KEY_LENGTH]" | ||
69 | .Fc | ||
70 | .Sh DESCRIPTION | ||
71 | Curve25519 is an elliptic curve over a prime field | ||
72 | specified in RFC 7748 section 4.1. | ||
73 | The prime field is defined by the prime number 2^255 - 19. | ||
74 | .Pp | ||
75 | X25519 | ||
76 | is the Diffie-Hellman primitive built from Curve25519 as described | ||
77 | in RFC 7748 section 5. | ||
78 | Section 6.1 describes the intended use in an Elliptic Curve Diffie-Hellman | ||
79 | (ECDH) protocol. | ||
80 | .Pp | ||
81 | .Fn X25519 | ||
82 | writes a shared key to | ||
83 | .Fa out_shared_key | ||
84 | that is calculated from the given | ||
85 | .Fa private_key | ||
86 | and the | ||
87 | .Fa peer_public_value | ||
88 | by scalar multiplication. | ||
89 | Do not use the shared key directly, rather use a key derivation | ||
90 | function and also include the two public values as inputs. | ||
91 | .Pp | ||
92 | .Fn X25519_keypair | ||
93 | sets | ||
94 | .Fa out_public_value | ||
95 | and | ||
96 | .Fa out_private_key | ||
97 | to a freshly generated public/private key pair. | ||
98 | First, the | ||
99 | .Fa out_private_key | ||
100 | is generated with | ||
101 | .Xr arc4random_buf 3 . | ||
102 | Then, the opposite of the masking described in RFC 7748 section 5 | ||
103 | is applied to it to make sure that the generated private key is never | ||
104 | correctly masked. | ||
105 | The purpose is to cause incorrect implementations on the peer side | ||
106 | to consistently fail. | ||
107 | Correct implementations will decode the key correctly even when it is | ||
108 | not correctly masked. | ||
109 | Finally, the | ||
110 | .Fa out_public_value | ||
111 | is calculated from the | ||
112 | .Fa out_private_key | ||
113 | by multiplying it with the Montgomery base point | ||
114 | .Vt uint8_t u[32] No = Brq 9 . | ||
115 | .Pp | ||
116 | The size of a public and private key is | ||
117 | .Dv X25519_KEY_LENGTH No = 32 | ||
118 | bytes each. | ||
119 | .Pp | ||
120 | Ed25519 is a signature scheme using a twisted Edwards curve | ||
121 | that is birationally equivalent to Curve25519. | ||
122 | .Pp | ||
123 | .Fn ED25519_keypair | ||
124 | sets | ||
125 | .Fa out_public_key | ||
126 | and | ||
127 | .Fa out_private_key | ||
128 | to a freshly generated public/private key pair. | ||
129 | First, the | ||
130 | .Fa out_private_key | ||
131 | is generated with | ||
132 | .Xr arc4random_buf 3 . | ||
133 | Then, the | ||
134 | .Fa out_public_key | ||
135 | is calculated from the private key. | ||
136 | .Pp | ||
137 | .Fn ED25519_sign | ||
138 | signs the | ||
139 | .Fa message | ||
140 | of | ||
141 | .Fa message_len | ||
142 | bytes using the | ||
143 | .Fa public_key | ||
144 | and the | ||
145 | .Fa private_key | ||
146 | and writes the signature to | ||
147 | .Fa out_sig . | ||
148 | .Pp | ||
149 | .Fn ED25519_verify | ||
150 | checks that signing the | ||
151 | .Fa message | ||
152 | of | ||
153 | .Fa message_len | ||
154 | bytes using the | ||
155 | .Fa public_key | ||
156 | would indeed result in the given | ||
157 | .Fa signature . | ||
158 | .Pp | ||
159 | The sizes of a public and private keys are | ||
160 | .Dv ED25519_PUBLIC_KEY_LENGTH | ||
161 | and | ||
162 | .Dv ED25519_PRIVATE_KEY_LENGTH , | ||
163 | which are both 32 bytes, and the size of a signature is | ||
164 | .Dv ED25519_SIGNATURE_LENGTH No = 64 | ||
165 | bytes. | ||
166 | .Sh RETURN VALUES | ||
167 | .Fn X25519 | ||
168 | and | ||
169 | .Fn ED25519_sign | ||
170 | return 1 on success or 0 on error. | ||
171 | .Fn X25519 | ||
172 | can fail if the input is a point of small order. | ||
173 | .Fn ED25519_sign | ||
174 | always succeeds in LibreSSL, but the API reserves the return value 0 | ||
175 | for memory allocation failure. | ||
176 | .Pp | ||
177 | .Fn ED25519_verify | ||
178 | returns 1 if the | ||
179 | .Fa signature | ||
180 | is valid or 0 otherwise. | ||
181 | .Sh SEE ALSO | ||
182 | .Xr ECDH_compute_key 3 , | ||
183 | .Xr EVP_DigestSign 3 , | ||
184 | .Xr EVP_DigestVerify 3 , | ||
185 | .Xr EVP_PKEY_derive 3 , | ||
186 | .Xr EVP_PKEY_keygen 3 | ||
187 | .Rs | ||
188 | .%A Daniel J. Bernstein | ||
189 | .%R A state-of-the-art Diffie-Hellman function:\ | ||
190 | How do I use Curve25519 in my own software? | ||
191 | .%U https://cr.yp.to/ecdh.html | ||
192 | .Re | ||
193 | .Rs | ||
194 | .%A Daniel J. Bernstein | ||
195 | .%A Niels Duif | ||
196 | .%A Tanja Lange | ||
197 | .%A Peter Schwabe | ||
198 | .%A Bo-Yin Yang | ||
199 | .%T High-Speed High-Security Signatures | ||
200 | .%B Cryptographic Hardware and Embedded Systems \(em CHES 2011 | ||
201 | .%I Springer | ||
202 | .%J Lecture Notes in Computer Science | ||
203 | .%V vol 6917 | ||
204 | .%U https://doi.org/10.1007/978-3-642-23951-9_9 | ||
205 | .%C Nara, Japan | ||
206 | .%D September 29, 2011 | ||
207 | .Re | ||
208 | .Sh STANDARDS | ||
209 | RFC 7748: Elliptic Curves for Security | ||
210 | .Pp | ||
211 | RFC 8032: Edwards-Curve Digital Signature Algorithm (EdDSA) | ||