On Generalized Feistel Networks

Abstract

We prove beyond-birthday-bound security for most of the well-known types of generalized Feistel networks: (1) unbalanced Feistel networks, where the n-bit to m-bit round functions may have n ≠ 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 ≥ 2; 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 e > 0, with enough rounds, the subject scheme can tolerate CCA attacks of up to q ∼ N1-e adversarial queries, where N is the size of the round functions' domain (the larger domain for alternating Feistel). Prior analyses for most generalized Feistel networks established security to only q ∼ N0.5 queries.