Two identification protocols based on Cayley graphs of Coxeter groups

A challenge-response identification protocol is introduced, based on the intractability of the word problem in some Coxeter groups. A Prover builds his public key as the set of leaves of a tree in the Cayley graph of a Coxeter group, and the tree itself is his private keys. Any challenge posed by a Verifier consists of a subset of the public key, and the Prover shows his knowledge of the private key by providing a subtree having as set of leaves the challenge set. Any third party aiming to impersonate the Prover faces a form of the word problem in the Coxeter group. Although this protocol maintains the secrecy of the whole private key, it is disclosing some parts of it. A second protocol is introduced which is indeed a transcription of the already classical zero-knowledge protocol to recognize pairs of isomorphic graphs.