## Cryptology ePrint Archive: Report 2010/470

**Two identification protocols based on Cayley graphs of Coxeter groups**

*Feli\'u Sagols and Guillermo Morales-Luna*

**Abstract: **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.

**Category / Keywords: **Authentication, Coxeter groups, identification protocols, random spanning trees, word problem

**Date: **received 3 Sep 2010, last revised 27 Jan 2011

**Contact author: **gmorales at cs cinvestav mx

**Available format(s): **PDF | BibTeX Citation

**Note: **A flaw has been corrected. It is necessary to fix a threshold for the lengths of the responses to the challenges.

**Version: **20110127:122818 (All versions of this report)

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