Revisiting Key-Alternating Feistel Ciphers: Reducing Key-size, and Multi-user Security

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Presented at Asiacrypt2018 2018 by

Chun Wang

Key-Alternating Feistel (KAF) ciphers, a.k.a. Feistel-2 models, refer to Feistel networks with round functions of the form Fi(ki⊕xi) , where ki is the (secret) round-key and Fi 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 2n/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 22n/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.