Cryptology ePrint Archive: Report 2014/299

Optimality of Non-Adaptive Strategies: The Case of Parallel Games

Grégory Demay and Peter Gaži and Ueli Maurer and Björn Tackmann

Abstract: Most cryptographic security proofs require showing that two systems are indistinguishable. A central tool in such proofs is that of a game, where winning the game means provoking a certain condition, and it is shown that the two systems considered cannot be distinguished unless this condition is provoked. Upper bounding the probability of winning such a game, i.e., provoking this condition, for an arbitrary strategy is usually hard, except in the special case where the best strategy for winning such a game is known to be non-adaptive.

A sufficient criterion for ensuring the optimality of non-adaptive strategies is that of conditional equivalence to a system, a notion introduced in [Mau02]. In this paper, we show that this criterion is not necessary to ensure the optimality of non-adaptive strategies by giving two results of independent interest: 1) the optimality of non-adaptive strategies is not preserved under parallel composition; 2) in contrast, conditional equivalence is preserved under parallel composition.

Category / Keywords: foundations / indistinguishability proofs, conditional equivalence, random systems, parallel composition

Original Publication (in the same form): 2014 IEEE International Symposium on Information Theory (ISIT)

Date: received 28 Apr 2014, last revised 28 Apr 2014

Contact author: gregory demay at inf ethz ch

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Version: 20140430:121105 (All versions of this report)

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