On data complexity of distinguishing attacks versus message recovery attacks on stream ciphers

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Research Article

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Designs, Codes, and Cryptography


We revisit the different approaches used in the literature to estimate the data complexity of distinguishing attacks on stream ciphers and analyze their inter-relationships. In the process, we formally argue which approach is applicable (or not applicable) in what scenario. To our knowledge, this is the first kind of such an exposition. We also perform a rigorous statistical analysis of the message recovery attack that exploits a distinguisher and show that in practice there is a significant gap between the data complexities of a message recovery attack and the underlying distinguishing attack. This gap is not necessarily determined by a constant factor as a function of the false positive and negative rate, as one would expect. Rather this gap is also a function of the number of samples of the distinguishing attack. We perform a case study on RC4 stream cipher to demonstrate that the typical complexities for message recovery attack inferred in the literature are but under-estimates and the actual estimates are quite larger.

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