[Resource Topic] 2010/301: On generalized Feistel networks

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Title:
On generalized Feistel networks

Authors: Viet Tung Hoang, Phillip Rogaway

Abstract:

We prove beyond-birthday-bound security for the well-known types of generalized Feistel networks, including: (1) unbalanced Feistel networks, where the n-bit to m-bit round functions may have n\ne m; (2) alternating Feistel networks, where the round functions alternate between contracting and expanding; (3) type-1, type-2, and type-3 Feistel networks, where n-bit to n-bit round functions are used to encipher kn-bit strings for some k\ge2; and (4) numeric variants of any of the above, where one enciphers numbers in some given range rather than strings of some given size. Using a unified analytic framework we show that, in any of these settings, for any \varepsilon>0, with enough rounds, the subject scheme can tolerate CCA attacks of up to q\sim N^{1-\varepsilon} adversarial queries, where N is the size of the round functions’ domain (the size of the larger domain for alternating Feistel). This is asymptotically optimal. Prior analyses for generalized Feistel networks established security to only q\sim N^{0.5} adversarial queries.

ePrint: https://eprint.iacr.org/2010/301

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