## Cryptology ePrint Archive: Report 2020/1073

Tight Security Analysis of 3-Round Key-Alternating Cipher with A Single Permutation

Yusai Wu and Liqing Yu and Zhenfu Cao and Xiaolei Dong

Abstract: The tight security bound of the Key-Alternating Cipher (KAC) construction whose round permutations are independent from each other has been well studied. Then a natural question is how the security bound will change when we use fewer permutations in a KAC construction. In CRYPTO 2014, Chen et al. proved that 2-round KAC with a single permutation (2KACSP) has the same security level as the classic one (i.e., 2-round KAC). But we still know little about the security bound of incompletely-independent KAC constructions with more than 2 rounds. In this paper,we will show that a similar result also holds for 3-round case. More concretely, we prove that 3-round KAC with a single permutation (3KACSP) is secure up to $\varTheta(2^{\frac{3n}{4}})$ queries, which also caps the security of 3-round KAC. To avoid the cumbersome graphical illustration used in Chen et al.'s work, a new representation is introduced to characterize the underlying combinatorial problem. Benefited from it, we can handle the knotty dependence in a modular way, and also show a plausible way to study the security of $r$KACSP. Technically, we abstract a type of problems capturing the intrinsic randomness of $r$KACSP construction, and then propose a high-level framework to handle such problems. Furthermore, our proof techniques show some evidence that for any $r$, $r$KACSP has the same security level as the classic $r$-round KAC in random permutation model.

Category / Keywords: secret-key cryptography / KAC, KACSP, Dependence, Provable Security, Indistinguishability, Random Permutation Model

Original Publication (with major differences): IACR-ASIACRYPT-2020

Date: received 4 Sep 2020, last revised 29 Nov 2020

Contact author: yusaiwu at 126 com,lqyups@126 com,zfcao@sei ecnu edu cn,dong-xl@sei ecnu edu cn

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2020/1073

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