By Rafael Pass

ISBN-10: 9172839333

ISBN-13: 9789172839335

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This follows from the fact 5 In real-life protocol executions parties that do not respond withing a specified time would be “timed-out”. 2. DEFINITIONS OF THE NEW NOTIONS 45 that T (n)-simulatability only guarantees that the output of the simulator is indistinguishable from the real execution, by an on-line distinguisher (and not by an off-line distinguisher). e. a so called straight-line simulation. Towards the goal of obtaining a definition which is robust also in the concurrent setting we restrict Definition 28 to straight-line simulators: Definition 31 Let T (n) be a class of functions that is closed under composition with any polynomial.

Interactive proofs in the RO model are defined in analogy with interactive proofs in the CRS model: Definition 24 (Interactive proof in the RO model) A pair of interactive machines, (P, V ), is called an interactive proof system in the RO model, for a language L ∈ N P, if the machine V is polynomial-time and the following two conditions hold 4 The methodology of characterizing hashfunctions as random functions had, however, already been used for a long time as a heuristic and can be traced back to the Fiat-Shamir signature scheme from 1986 [31].

Guarantee security in the On-line/Off-line Model In many settings it seems reasonable to assume that parties are given a certain on-line time and a certain, longer, off-line time. Such an on-line/off-line model can be modeled by letting parties run in polynomial time while being on-line, and time T (n) off-line. A certain type of T (n)-simulatable protocols (which we call strongly T (n)simulatable protocols) have the property of being zero-knowledge in the online/off-line model. Roughly speaking, we say that an interactive proof is strongly T (n)- simulatable if it is T (n)-simulatable and the output of the simulator is indistinguishable in time T (n) from the output of the verifier in a real interaction (whereas T (n)-simulatability only requires that these distributions are polynomial-time indistinguishable).

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Alternative Variants of Zero-Knowledge Proofs by Rafael Pass

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