# Information Security and Cryptography Research Group

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

### Grégory Demay, Peter Gaži, Ueli Maurer, and Björn Tackmann

2014 IEEE International Symposium on Information Theory (ISIT), pp. 1707-1711, Jun 2014.

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.

## BibTeX Citation

@inproceedings{DGMT14,
author       = {Grégory Demay and Peter Gaži and Ueli Maurer and Björn Tackmann},
title        = {Optimality of Non-Adaptive Strategies: The Case of Parallel Games},
booktitle    = {2014 IEEE International Symposium on Information Theory (ISIT)},
pages        = {1707-1711},
year         = {2014},
month        = {6},
}