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Title:
Crooked Indifferentiability of the Feistel Construction
Authors: Alexander Russell, Qiang Tang, Jiadong Zhu
Abstract:The Feistel construction is a fundamental technique for building pseudorandom permutations and block ciphers. This paper shows that a simple adaptation of the construction is resistant, even to algorithm substitution attacks—that is, adversarial subversion—of the component round functions. Specifically, we establish that a Feistel-based construction with more than 337n/\log(1/\epsilon) rounds can transform a subverted random function—which disagrees with the original one at a small fraction (denoted by \epsilon) of inputs—into an object that is \emph{crooked-indifferentiable} from a random permutation, even if the adversary is aware of all the randomness used in the transformation. Here, n denotes the length of both the input and output of the round functions that underlie the Feistel cipher. We also provide a lower bound showing that the construction cannot use fewer than 2n/\log(1/\epsilon) rounds to achieve crooked-indifferentiable security.
ePrint: https://eprint.iacr.org/2024/1456
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