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Revisiting Key-Alternating Feistel Ciphers for Shorter Keys and Multi-user Security

  • Chun Guo
  • Lei WangEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11272)

Abstract

Key-Alternating Feistel (KAF) ciphers, a.k.a. Feistel-2 models, refer to Feistel networks with round functions of the form \(F_i(k_i\oplus x_i)\), where \(k_i\) is the (secret) round-key and \(F_i\) is a public random function. This model roughly captures the structures of many famous Feistel ciphers, and the most prominent instance is DES.

Existing provable security results on KAF assumed independent round-keys and round functions (ASIACRYPT 2004 & FSE 2014). In this paper, we investigate how to achieve security under simpler and more realistic assumptions: with round-keys derived from a short main-key, and hopefully with identical round functions.

For birthday-type security, we consider 4-round KAF, investigate the minimal conditions on the way to derive the four round-keys, and prove that when such adequately derived keys and the same round function are used, the 4-round KAF is secure up to \(2^{n/2}\) queries.

For beyond-birthday security, we focus on 6-round KAF. We prove that when the adjacent round-keys are independent, and independent round-functions are used, the 6 round KAF is secure up to \(2^{2n/3}\) queries. To our knowledge, this is the first beyond-birthday security result for KAF without assuming completely independent round-keys.

Our results hold in the multi-user setting as well, constituting the first non-trivial multi-user provable security results on Feistel ciphers. We finally demonstrate applications of our results on designing key-schedules and instantiating keyed sponge constructions.

Keywords

Blockcipher Provable security Multi-user security Key-alternating cipher Feistel cipher Key-schedule design Keyed sponge 

Notes

Acknowledgements

We thank the reviewers for invaluable comments, and for pointing [25] to us. Chun Guo is funded in part by the ERC project 724725 (acronym SWORD), and would like to thank François-Xavier Standaert for the invaluable support. Lei Wang is supported by National Natural Science Foundation of China (61602302, 61472250, 61672347), Natural Science Foundation of Shanghai (16ZR1416400), Shanghai Excellent Academic Leader Funds (16XD1401300), 13th five-year National Development Fund of Cryptography (MMJJ20170114).

Finally we thank Yaobin Shen for identifying a flaw (in Lemma 5) in an earlier version of the proof, and Christian Rechberger and Damian Vizár for the discussion on multi-party computation.

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Copyright information

© International Association for Cryptologic Research 2018

Authors and Affiliations

  1. 1.ICTEAM/ELEN/Crypto GroupUniversité Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Shanghai Jiao Tong UniversityShanghaiChina
  3. 3.Westone Cryptologic Research CenterBeijingChina

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