Implement the key agreement using Curve25519 and Curve448, as described in RFC 7748. So what do you do if you want to use the same key hardware for key chord and signature? There are a few options: in cryptography, Curve25519 is an elliptical curve that offers 128 bits of security (256-bit key size) and was designed to be used with the diffie-Hellman key chord scheme (ECDH) of the diffie-Hellman elliptical curve (ECDH). It is one of the fastest ECC turns and is not covered by known patents. [1] Reference implementation is public domain software. [2] [3] RFC 7748 defines a key tuning system that is more efficient and secure than the existing Diffie-Hellman elliptical curve (ECDH) system. The main objective of this PEC is an API and an implementation for this standard. Other implementation objectives are: Source: github.com/longcpp/CryptoInAction/blob/master/intro-ed25519/190902-intro-x25519.pdf Curve25519 is an elliptical curve above the finished field „Mathbb F_p“, \$p – 2-{255} – 19, where comes the 25519 part of the name. In particular, it`s the montgomery curve \$y 2 x-3 – 486662 x-2 x, but you don`t need to know the details, except that it was designed to admit a quick calculation of \$x (n]P) that is \$n and \$x (P)“, which is useful to the key diffie-Hellman chord. X25519 is a Diffie-Hellman function developed from Curve25519. A public key X25519 is the encoding of coordinates \$x a point on Curve25519, hence the name X25519. This cryptoSE question answered why use Ed25519 about Curve25519 for signatures, but why not use Ed25519 for key exchange? For most applications, the shared_key must be transferred to a key bypass function. This allows you to mix additional information into the key, bypassing several keys and destroying any structure that may be present.

(Marginal note: Sometimes the Montgomery form is written with the letters \$u and \$v, as in \$v 2 – u`3 – 486662 u`2 `u`, especially if you draw a contrast with another form like Weierstrass or Edwards.) The original Curve25519 paper defined it as a function of a different hellman (DH). Daniel J. Bernstein has since proposed to use the name Curve25519 for the underlying curve and the name X25519 for the DH function. [4] The protocol uses the compressed elliptical point (only coordinates X), allowing efficient use of the Montgomery scale for ECDH, with only XZ coordinates. [6] To encrypt with these keys, we recommend using the github.com/digitalbazaar/minimal-cipher-Bibliothek.