Overview#

X25519 is a mathematical function that performs scalar multiplication on the Montgomery form of the Curve25519 and is defined in RFC 7748Daniel J. Bernstein proposed:

• X25519 be the name of the Diffie-Hellman Key-Exchange protocol
• Curve25519 be the name of the Elliptic Curve

25519 indicates that the characteristic of the bottom prime number field on which the Elliptic Curve depends is 2²⁵⁵-19.

Based on Curve25519, Bernstein constructed the Diffie-Hellman Key-Exchange protocol X25519.

Compared with the ECDH Key-Exchange protocol, the most notable feature of the X25519 protocol is that it only depends on the x coordinate of the point on the Elliptic Curve. The idea of constructing an ECDH key exchange protocol using only x coordinates originally came from the paper published by Victor Millier in 1985, "Use of Elliptic Curves in Cryptography".!! More Information There might be more information for this subject on one of the following:

• Curve25519
• CurveCP
• CurveZMQ
• Ed25519
• Javascript Object Signing and Encryption
• Quick UDP Internet Connections
• RFC 8418
• TLS 1.3
• The Onion Router

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• [#1] - Curve25519 - based on information obtained 2017-06-17-
• [#2] - A Deep Dive into X25519 - based on information obtained 2020-02-20
• [#3] - SECURE COMMUNICATION USING AUTHENTICATED CHANNELS - based on information obtained 2020-02-20
• [#4] - Use of Elliptic Curves in Cryptography - based on information obtained 2020-02-20