Schneier’s Law and Creating a Random Elliptic Curve

Schneier’s Law defines:

“Anyone, from the most clueless amateur to the best cryptographer, can create an algorithm that he himself can’t break.”

Well, in a world of AI, the most clueless amateur is perhaps AI entities, and where AI could easily evolve to use ciphers that we cannot actually decrypt. While we humans have defined standards for cryptography, especially through NIST standards, there is nothing to stop AI agents from evolving their own ciphers, and to use an almost uncrackable code.

So, let’s say that two AI entities decide to use their own elliptic curve method, and where they pick their own parameters for the curve used. Normally, we would have well-defined curves, such as for NIST P256, secp256k1 and Curve 25519, but AI entities could agree on their own parameters. The parameters used could be passed over secure channels, such as with an ECDH (Elliptic Curve Diffie Hellman) key exchange.

The security of ECC (Elliptic Curve Cryptography) is based on finding the discrete logarithm of a random elliptic curve element that relates to a publicly known point on a curve. This is defined as ECDLP (elliptic curve discrete logarithm problem). For this, we have a base point (G), and then a secret scale value (x), and compute a point on the curve of x.G. Overall, it should be…