Curve 25519 and Rust
The core of the security on the Web comes down to … elliptic curve cryptography (ECC). With the ECDH (Elliptic Curve Diffie Hellman) handshake method, we have an almost perfect way to generate a shared key between Bob and Alice, without Eve ever finding it out. And so we turn to Curve 25519, and which is one of the best elliptic curves around. It uses the Montgomery curve form of:
And where we take a base point (G), and then create a private key (n), and then determine our public key (nG). With this nG is the point G added n times (G+G+…G). Curve 25519 was created by Daniel J Bernstein, and who has contributed so much to cybersecurity. The form he chose was:
and where p=2²⁵⁵-19. It thus gave 128-bit security levels, and which is currently strong enough in most applications. The base point chosen is x=9, and which gives a point of:
P=( 9 , 14781619447589544791020593568409986887264606134616475288964881837755586237401 )The point adding and scaling uses the method defined in RFC 7748 [here]:
In Curve 25519, we have a base point of G, and then take a secret key of sk. The public key is the sk.G. With this curve we just take the y-co-ordinate…
