Revisiting Lower and Upper Bounds for Selective Decommitments.
Rafail Ostrovsky, Vanishree Rao, Alessandra Scafuro +1 more
In [DNRS99, DNRS03], Dwork et al. opened the fundamental question of existence of commitment schemes that are secure against selective opening attacks (SOA, for short). In [BHY09] Bellare, Hofheinz, and Yilek, and Hofheinz in [Hof11] solved this problem positively by presenting a scheme which is based on non-black-box use of a one-way permutation and which has superconstant number of rounds. The achieved solution however opened other challenging questions on improvements of round complexity and on possibility of obtaining fully black-box schemes where access to an underlying primitive and to an adversary are black-box only. Recently, in TCC 2011, Xiao ([Xia11a]) investigated on how to achieve (nearly) optimal SOA-secure commitment schemes where optimality is in the sense of both the round complexity and the black-box use of cryptographic primitives. The work of Xiao focuses on a simulation-based security notion of SOA. Moreover, the various results in [Xia11a] focus only on either parallel or concurrent SOA. In this work we first point out various issues in the claims of [Xia11a] that actually re-open several of the questions left open in [BHY09, Hof11]. Then, we provide new lower bounds and concrete constructions that produce a very different state-of-the-art compared to the one given in [Xia11a]. More specifically, denoting by (x, y) the round complexity of a scheme that requires x rounds in the commitment phase and y rounds in the decommitment phase, and by considering only (like in [Xia11a]) the setting of black-box simulation for SOA-security, we show that: 1. There is an issue in the result of [Xia11a] on the existence of (3, 1)-round schemes for parallel SOA; in fact, we are able to contradict their impossibility result by presenting a (3, 1)-round scheme based on black-box use of trapdoor commitments. Moreover, we can instantiate such a scheme with a non-black-box use of a one-way function, thus producing a (3, 1)-round scheme based on any one-way function that improves the result of [BHY09, Hof11] from logarithmic round complexity to 3 (optimal), also under optimal complexity assumptions. We also show a (3, 3)-round scheme based on black-box use of any one-way permutation. 2. There is an issue in the proof of security for parallel composition of the (4, 1)-round scheme given in [Xia11a]; thus such scheme may not be secure. We show instead a (4, 1)-round scheme based on black-box use of any weak trapdoor commitment scheme, and a (5, 1)round scheme based on black-box use of any one-way permutation. 3. There is an issue in the proof of security of the concurrent SOA-secure scheme of [Xia11a]. This issue emerges under the case where the simulator cannot itself efficiently sample from ∗Departments of Computer Science and Department of Mathematics, UCLA, 3732D Boelter Hall, Los Angeles CA 90095-1596, U.S. Email: rafail@cs.ucla.edu †Department of Computer Science, UCLA, 3771 Boelter Hall, Los Angeles CA 90095-1596, U.S. Email: vanishri@cs.ucla.edu ‡Dipartimento di Informatica, University of Salerno, Italy. Email. scafuro@dia.unisa.it §Dipartimento di Informatica, University of Salerno, Italy. Email. visconti@dia.unisa.it
•Jan 1, 2011•1 citation