A secret d is signed using a one-way function f, resulting in the signature s. The signature s is then encrypted with the symmetric key p that is the public key of the public-private key pair used to sign d, using a modulo-2 addition Vernam cipher, and then encrypted again with symmetric key d (the same secret) also using modulo-2 addition, resulting in the proof c.

The public-private key pairs are one-time use only, and a new proof c included in each transaction, used to authenticate the next transaction.

Collision-resistance for public-private key pairs, secret d, and the proof c

The Teikhos cipher relies on that each proof c can only be generated from a single public-private key pair, regardless of the secret d. Since the signature s (a one-way function applied to d) is hard to predict, finding collisions is a hard problem.

Fortifying math-based asymmetric cryptography with non-mathematical symmetric cryptography

The greek τεῖχος (teîkhos) means wall or fortification, and the idea in the Teikhos signature scheme is that the resistance to brute force would rely mainly on symmetric cryptography, while the authentication relies on asymmetric cryptography, and so it combines the best of two world.

Asymmetric cryptography is based on a mathematical relation between the public key, private key and digital signature, and that means that it is easier to hack. The "teikhos cipher" hides all of that away, shrinking the surface area for attacking the asymmetric cryptography to a brief time-window between when a transaction has been broadcasted to the miners until when those miners have included it in the consensus.