# Composition of Zero-Knowledge Proofs with Efficient Provers

 Title: Composition of Zero-Knowledge Proofs with Efficient Provers Author: Birrell, Eleanor; Vadhan, Salil P. Note: Order does not necessarily reflect citation order of authors. Citation: Birrell, Eleanor, and Salil Vadhan. 2010. Composition of zero-knowledge proofs with efficient provers. In Theory of Cryptography: 7th Theory of Cryptography Conference, TCC 2010, Zurich, Switzerland February 9-11, 2010 Proceedings. Lecture Notes on Computer Science 5978, ed. Daniele Micciancio. Full Text & Related Files: vadhan_composition.pdf (207.4Kb; PDF) Abstract: We revisit the composability of different forms of zero-knowledge proofs when the honest prover strategy is restricted to be polynomial time (given an appropriate auxiliary input). Our results are: 1.) When restricted to efficient provers, the original Goldwasser--Micali--Rackoff (GMR) definition of zero knowledge (STOC 85), here called plain zero knowledge, is closed under a constant number of sequential compositions (on the same input). This contrasts with the case of unbounded provers, where Goldreich and Krawczyk (ICALP 90, SICOMP 96) exhibited a protocol that is zero knowledge under the GMR definition, but for which the sequential composition of 2 copies is not zero knowledge. 2.) If we relax the GMR definition to only require that the simulation is indistinguishable from the verifier's view by uniform polynomial-time distinguishers, with no auxiliary input beyond the statement being proven, then again zero knowledge is not closed under sequential composition of 2 copies. 3.) We show that auxiliary-input zero knowledge with efficient provers is not closed under parallel composition of 2 copies under the assumption that there is a secure key agreement protocol (in which it is easy to recognize valid transcripts). Feige and Shamir (STOC 90) gave similar results under the seemingly incomparable assumptions that (a) the discrete logarithm problem is hard, or (b) $$UP \nsubseteq BPP$$ and one-way functions exist. Published Version: doi:10.1007/978-3-642-11799-2_34 Other Sources: http://eprint.iacr.org/2009/604.pdf Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:4892999 Downloads of this work: