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Title:
Cycle Slicer: An Algorithm for Building Permutations on Special Domains
Authors: Sarah Miracle, Scott Yilek
Abstract:We introduce an algorithm called Cycle Slicer that gives new solutions to two important problems in format-preserving encryption: domain targeting and domain completion. In domain targeting, where we wish to use a cipher on domain \mathcal{X} to construct a cipher on a smaller domain \mathcal{S} \subseteq \mathcal{X}, using Cycle Slicer leads to a significantly more efficient solution than Miracle and Yilekâs Reverse Cycle Walking (ASIACRYPT 2016) in the common setting where the size of \mathcal{S} is large relative to the size of \mathcal{X}. In domain completion, a problem recently studied by Grubbs, Ristenpart, and Yarom (EUROCRYPT 2017) in which we wish to construct a cipher on domain \mathcal{X} while staying consistent with existing mappings in a lazily-sampled table, Cycle Slicer provides an alternative construction with better worst-case running time than the Zig-Zag construction of Grubbs et al. Our analysis of Cycle Slicer uses a refinement of the Markov chain techniques for analyzing matching exchange processes, which were originally developed by Czumaj and Kutylowski (Rand. Struct. & Alg. 2000).
ePrint: https://eprint.iacr.org/2017/873
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