package callipyge

Introduction

Each Curve25519 user has a 32-byte secret key and a 32-byte public key. Each set of two Curve25519 users has a 32-byte shared secret used to authenticate and encrypt messages between the two users.

Alice has a secret-key a. Bob has a secret-key b. 9 is base key - in this implementation curve25519(a, b, 9) = curve25519_base(a, b)

Alice, Bob 's shared secret: curve25519(a, curve25519(b, 9)) Bob, Alice 's shared secret: curve25519(b, curve25519(a, 9))

and curve25519(a, curve25519(b, 9)) = curve25519(b, curve25519(a, 9))

A hash of the shared secret curve25519(a, curve25519(b, 9)) is used as the key for a secret-key authentification system (to authenticate messages), or as the key for a secret-key authenticated-encryption system (to simultaneously encrypt and authenticate messages).

The curve25519 function is Fp-restricted x-coordinate scalar multiplication on E(Fp^2), where p is the prime number 2^255 - 19 and E is the elliptic curve y^2 = x^3 + 486662 * x^2 + x^2.