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-.\" $OpenBSD: X25519.3,v 1.5 2019/08/19 13:08:26 schwarze Exp $
-.\" contains some text from: BoringSSL curve25519.h, curve25519.c
-.\" content also checked up to: OpenSSL f929439f Mar 15 12:19:16 2018 +0000
-.\"
-.\" Copyright (c) 2015 Google Inc.
-.\" Copyright (c) 2018 Ingo Schwarze <schwarze@openbsd.org>
-.\"
-.\" Permission to use, copy, modify, and/or distribute this software for any
-.\" purpose with or without fee is hereby granted, provided that the above
-.\" copyright notice and this permission notice appear in all copies.
-.\"
-.\" THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHORS DISCLAIM ALL WARRANTIES
-.\" WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
-.\" MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHORS BE LIABLE FOR
-.\" ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
-.\" WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
-.\" ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
-.\" OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
-.\"
-.Dd $Mdocdate: August 19 2019 $
-.Dt X25519 3
-.Os
-.Sh NAME
-.Nm X25519 ,
-.Nm X25519_keypair
-.Nd Elliptic Curve Diffie-Hellman primitive based on Curve25519
-.Sh SYNOPSIS
-.In openssl/curve25519.h
-.Ft int
-.Fo X25519
-.Fa "uint8_t out_shared_key[X25519_KEY_LENGTH]"
-.Fa "const uint8_t private_key[X25519_KEY_LENGTH]"
-.Fa "const uint8_t peer_public_value[X25519_KEY_LENGTH]"
-.Fc
-.Ft void
-.Fo X25519_keypair
-.Fa "uint8_t out_public_value[X25519_KEY_LENGTH]"
-.Fa "uint8_t out_private_key[X25519_KEY_LENGTH]"
-.Fc
-.Sh DESCRIPTION
-Curve25519 is an elliptic curve over a prime field specified in RFC 7748.
-The prime field is defined by the prime number 2^255 - 19.
-.Pp
-.Fn X25519
-is the Diffie-Hellman primitive built from Curve25519 as described
-in RFC 7748 section 5.
-Section 6.1 describes the intended use in an Elliptic Curve Diffie-Hellman
-(ECDH) protocol.
-.Pp
-.Fn X25519
-writes a shared key to
-.Fa out_shared_key
-that is calculated from the given
-.Fa private_key
-and the
-.Fa peer_public_value
-by scalar multiplication.
-Do not use the shared key directly, rather use a key derivation
-function and also include the two public values as inputs.
-.Pp
-.Fn X25519_keypair
-sets
-.Fa out_public_value
-and
-.Fa out_private_key
-to a freshly generated public/private key pair.
-First, the
-.Fa out_private_key
-is generated with
-.Xr arc4random_buf 3 .
-Then, the opposite of the masking described in RFC 7748 section 5
-is applied to it to make sure that the generated private key is never
-correctly masked.
-The purpose is to cause incorrect implementations on the peer side
-to consistently fail.
-Correct implementations will decode the key correctly even when it is
-not correctly masked.
-Finally, the
-.Fa out_public_value
-is calculated from the
-.Fa out_private_key
-by multiplying it with the Montgomery base point
-.Vt uint8_t u[32] No = Brq 9 .
-.Pp
-The size of a public and private key is
-.Dv X25519_KEY_LENGTH No = 32
-bytes each.
-.Sh RETURN VALUES
-.Fn X25519
-returns 1 on success or 0 on error.
-Failure can occur when the input is a point of small order.
-.Sh SEE ALSO
-.Xr ECDH_compute_key 3
-.Rs
-.%A D. J. Bernstein
-.%R A state-of-the-art Diffie-Hellman function:\
-    How do I use Curve25519 in my own software?
-.%U http://cr.yp.to/ecdh.html
-.Re
-.Sh STANDARDS
-RFC 7748: Elliptic Curves for Security