!!! Overview [{$pagename}] is a mathematical function that performs scalar multiplication on the Montgomery form of the [Curve25519] and is defined in [RFC 7748]Daniel J. Bernstein proposed: * [{$pagename}] 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] [{$pagename}]. Compared with the [ECDH] [Key-Exchange] [protocol], the most notable feature of the [{$pagename}] 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|year 1985], "Use of Elliptic Curves in Cryptography".!! More Information There might be more information for this subject on one of the following: [{ReferringPagesPlugin before='*' after='\n' }] ---- * [#1] - [Curve25519|Wikipedia:Curve25519|target='_blank'] - based on information obtained 2017-06-17- * [#2] - [A Deep Dive into X25519|https://medium.com/@CoinExChain/a-deep-dive-into-x25519-7a926e8a91c7|target='_blank'] - based on information obtained 2020-02-20 * [#3] - [SECURE COMMUNICATION USING AUTHENTICATED CHANNELS|http://secu.famillepasini.ch/files/2009/phd/pasini_phd_thesis.pdf|target='_blank'] - based on information obtained 2020-02-20 * [#4] - [Use of Elliptic Curves in Cryptography|https://www.researchgate.net/publication/221355411_Use_of_Elliptic_Curves_in_Cryptography|target='_blank'] - based on information obtained 2020-02-20