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Chosen-Key Secure Even-Mansour Cipher from a Single Permutation

Authors:
Shanjie Xu , Key Laboratory of Cryptologic Technology and Information Security of Ministry of Education, Shandong University, Qingdao, Shandong, China; School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China
Qi Da , Key Laboratory of Cryptologic Technology and Information Security of Ministry of Education, Shandong University, Qingdao, Shandong, China; School of Cyber Science and Technology, Shandong University, Qingdao, Shandong, China
Chun Guo
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DOI: 10.46586/tosc.v2023.i1.244-287
URL: https://tosc.iacr.org/index.php/ToSC/article/view/10314
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Abstract: At EUROCRYPT 2015, Cogliati and Seurin proved that the 4-round Iterated Even-Mansour (IEM) cipher with Independent random Permutations and no key schedule EMIP4(k, u) = k⊕p4 ( k⊕p3 ( k⊕p2 (k⊕p1 (k⊕u)))) is sequentially indifferentiable from an ideal cipher, which implies chosen-key security in the sense of correlation intractability. In practice, however, blockciphers such as the AES typically employ the same permutation at each round. To bridge the gap, we prove that the 4-round IEM cipher EMSP[φ]p4 (k, u) = k4⊕p (k3⊕p (k2⊕p(k1⊕p(k0⊕u)))), whose round keys ki = φi(k) are derived using an affine permutation φ : {0, 1}n → {0, 1}n with certain properties, is sequentially indifferentiable from an ideal cipher. The function φ can be a linear orthomorphism, or φ(k) := k≫a for some fixed integer a using cyclic shift. To our knowledge, this is the first indifferentiability-type result for blockciphers using identical round functions.
BibTeX
@article{tosc-2023-33060,
  title={Chosen-Key Secure Even-Mansour Cipher from a Single Permutation},
  journal={IACR Transactions on Symmetric Cryptology},
  publisher={Ruhr-Universität Bochum},
  volume={2023, Issue 1},
  pages={244-287},
  url={https://tosc.iacr.org/index.php/ToSC/article/view/10314},
  doi={10.46586/tosc.v2023.i1.244-287},
  author={Shanjie Xu and Qi Da and Chun Guo},
  year=2023
}