Magic Adversaries Versus Individual Reduction: Science Wins Either Way ? Yi Deng1;2 1 SKLOIS, Institute of Information Engineering, CAS, Beijing, P.R.China 2 State Key Laboratory of Cryptology, P. O. Box 5159, Beijing ,100878,China
[email protected] Abstract. We prove that, assuming there exists an injective one-way function f, at least one of the following statements is true: – (Infinitely-often) Non-uniform public-key encryption and key agreement exist; – The Feige-Shamir protocol instantiated with f is distributional concurrent zero knowledge for a large class of distributions over any OR NP-relations with small distinguishability gap. The questions of whether we can achieve these goals are known to be subject to black-box lim- itations. Our win-win result also establishes an unexpected connection between the complexity of public-key encryption and the round-complexity of concurrent zero knowledge. As the main technical contribution, we introduce a dissection procedure for concurrent ad- versaries, which enables us to transform a magic concurrent adversary that breaks the distribu- tional concurrent zero knowledge of the Feige-Shamir protocol into non-black-box construc- tions of (infinitely-often) public-key encryption and key agreement. This dissection of complex algorithms gives insight into the fundamental gap between the known universal security reductions/simulations, in which a single reduction algorithm or simu- lator works for all adversaries, and the natural security definitions (that are sufficient for almost all cryptographic primitives/protocols), which switch the order of qualifiers and only require that for every adversary there exists an individual reduction or simulator. 1 Introduction The seminal work of Impagliazzo and Rudich [IR89] provides a methodology for studying the lim- itations of black-box reductions.