International Association for Cryptologic Research

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Paper: Provably Secure Reflection Ciphers

Authors:
Tim Beyne , KU Leuven
Yu Long Chen , KU Leuven
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Conference: CRYPTO 2022
Abstract: This paper provides the first analysis of reflection ciphers such as PRINCE from a provable security viewpoint. As a first contribution, we initiate the study of key-alternating reflection ciphers in the ideal permutation model. Specifically, we prove the security of the two-round case and give matching attacks. The resulting security bound takes form $O(qp^2/2^{2n}+q^2/2^n)$, where q is the number of construction evaluations and p is the number of direct adversarial queries to the underlying permutation. Since the two-round construction already achieves an interesting security lower bound, this result can also be of interest for the construction of reflection ciphers based on a single public permutation. Our second contribution is a generic key-length extension method for reflection ciphers. It provides an attractive alternative to the FX construction, which is used by PRINCE and other concrete key-alternating reflection ciphers. We show that our construction leads to better security with minimal changes to existing designs. The security proof is in the ideal cipher model and relies on a reduction to the two-round Even-Mansour cipher with a single round key. In order to obtain the desired result, we sharpen the bad-transcript analysis and consequently improve the best-known bounds for the single-key Even-Mansour cipher with two rounds. This improvement is enabled by a new sum-capture theorem that is of independent interest.
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BibTeX
@inproceedings{crypto-2022-32250,
  title={Provably Secure Reflection Ciphers},
  publisher={Springer-Verlag},
  author={Tim Beyne and Yu Long Chen},
  year=2022
}