--- res: bibo_abstract: - |- Efficient zero-knowledge proofs of knowledge for group homomorphisms are essential for numerous systems in applied cryptography. Especially, Σ-protocols for proving knowledge of discrete logarithms in known and hidden order groups are of prime importance. Yet, while these proofs can be performed very efficiently within groups of known order, for hidden order groups the respective proofs are far less efficient. This paper shows strong evidence that this efficiency gap cannot be bridged. Namely, while there are efficient protocols allowing a prover to cheat only with negligibly small probability in the case of known order groups, we provide strong evidence that for hidden order groups this probability is bounded below by 1/2 for all efficient Σ-protocols not using common reference strings or the like. We prove our results for a comprehensive class of Σ-protocols in the generic group model, and further strengthen them by investigating certain instantiations in the plain model.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Endre foaf_name: Bangerter, Endre foaf_surname: Bangerter - foaf_Person: foaf_givenName: Jan foaf_name: Camenisch, Jan foaf_surname: Camenisch - foaf_Person: foaf_givenName: Stephan foaf_name: Stephan Krenn foaf_surname: Krenn foaf_workInfoHomepage: http://www.librecat.org/personId=329FCCF0-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0003-2835-9093 bibo_doi: 10.1007/978-3-642-11799-2 bibo_volume: 5978 dct_date: 2010^xs_gYear dct_publisher: Springer@ dct_title: Efficiency Limitations for Σ-Protocols for Group Homomorphisms@ ...