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Paper: Provable Security of (Tweakable) Block Ciphers Based on Substitution-Permutation Networks

Authors:
Benoît Cogliati
Yevgeniy Dodis
Jonathan Katz
Jooyoung Lee
John P. Steinberger
Aishwarya Thiruvengadam
Zhe Zhang
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DOI: 10.1007/978-3-319-96884-1_24
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Presentation: Slides
Conference: CRYPTO 2018
Abstract: Substitution-Permutation Networks (SPNs) refer to a family of constructions which build a wn-bit block cipher from n-bit public permutations (often called S-boxes), which alternate keyless and “local” substitution steps utilizing such S-boxes, with keyed and “global” permutation steps which are non-cryptographic. Many widely deployed block ciphers are constructed based on the SPNs, but there are essentially no provable-security results about SPNs.In this work, we initiate a comprehensive study of the provable security of SPNs as (possibly tweakable) wn-bit block ciphers, when the underlying n-bit permutation is modeled as a public random permutation. When the permutation step is linear (which is the case for most existing designs), we show that 3 SPN rounds are necessary and sufficient for security. On the other hand, even 1-round SPNs can be secure when non-linearity is allowed. Moreover, 2-round non-linear SPNs can achieve “beyond-birthday” (up to $$2^{2n/3}$$ 22n/3 adversarial queries) security, and, as the number of non-linear rounds increases, our bounds are meaningful for the number of queries approaching $$2^n$$ 2n. Finally, our non-linear SPNs can be made tweakable by incorporating the tweak into the permutation layer, and provide good multi-user security.As an application, our construction can turn two public n-bit permutations (or fixed-key block ciphers) into a tweakable block cipher working on wn-bit inputs, 6n-bit key and an n-bit tweak (for any $$w\ge 2$$ w≥2); the tweakable block cipher provides security up to $$2^{2n/3}$$ 22n/3 adversarial queries in the random permutation model, while only requiring w calls to each permutation, and 3w field multiplications for each wn-bit input.
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BibTeX
@inproceedings{crypto-2018-28857,
  title={Provable Security of (Tweakable) Block Ciphers Based on Substitution-Permutation Networks},
  booktitle={Advances in Cryptology – CRYPTO 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={10991},
  pages={722-753},
  doi={10.1007/978-3-319-96884-1_24},
  author={Benoît Cogliati and Yevgeniy Dodis and Jonathan Katz and Jooyoung Lee and John P. Steinberger and Aishwarya Thiruvengadam and Zhe Zhang},
  year=2018
}