.\" $OpenBSD: X25519.3,v 1.3 2018/03/30 18:38:22 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>
.\"
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.\" purpose with or without fee is hereby granted, provided that the above
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.\"
.Dd $Mdocdate: March 30 2018 $
.Dt X25519 3
.Os
.Sh NAME
.Nm X25519 ,
.Nm X25519_keypair
.Nd Elliptic Curve Diffie-Hellman primitive based on Curve25519
.Sh SYNOPSIS
.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
.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