## On Generalized Feistel Networks

Authors:
Viet Tung Hoang and Phillip Rogaway

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 $n\ne m$; (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 larger domain for alternating Feistel). Prior analyses for most generalized Feistel networks established security to only $q\sim N^{0.5}$ queries.

References:
Proceedings of CRYPTO 2011

Full Version:
Full version is available in pdf