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X25519

Overview#

X25519 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:

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".

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