Mean-set attack: cryptanalysis of Sibert et al. authentication protocol

Abstract

We analyze the Sibert et al. group-based (Feige-Fiat-Shamir type) authentication protocol and show that the protocol is not computationally zero-knowledge. In addition, we provide experimental evidence that our approach is practical and can succeed even for groups with no efficiently computable length function such as braid groups. The novelty of this work is that we are not attacking the protocol by trying to solve an underlying complex algebraic problem, namely, the conjugacy search problem, but use a probabilistic approach, instead.

Intractable Group-theoretic Problems Around Zero-knowledge Proofs

“…The authors demonstrated that these schemes they de-signed are zero-knowledge proofs. On the other hand, Mosina and Ushakov [59] show that the Scheme II given here is practically not a computationally zero-knowledge proof.…”

Strong law of large numbers on graphs and groups

“…In this paper, we develop these probabilistic tools for finitely generated groups and propose practical algorithms for computing mean values (or expectations) of group/graph-valued random elements. The results of this paper form a new mathematical framework for group-based cryptography and find applications to security analysis of Sibert type authentication protocols ( [24]). …”