International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: On generalized Feistel networks

Viet Tung Hoang
Phillip Rogaway
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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.
  title={On generalized Feistel networks},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography /},
  note={The conference version of this paper will appear in CRYPTO 2010. 14829 received 19 May 2010, last revised 7 Aug 2010},
  author={Viet Tung Hoang and Phillip Rogaway},