**Cryptographic Properties and Application of a Generalized Unbalanced Feistel Network Structure (Revised Version)**

*Jiali Choy and Guanhan Chew and Khoongming Khoo and Huihui Yap*

**Abstract: **In this paper, we study GF-NLFSR, a Generalized Unbalanced Feis-
tel Network (GUFN) which can be considered as an extension of the outer function FO of the KASUMI block cipher. We show that the differential and linear probabilities of any n + 1 rounds of an n-cell GF-NLFSR are both bounded by p^2, where the corresponding probability of the round function is p. Besides analyzing security against differential and linear cryptanalysis, we provide a
frequency distribution for upper bounds on the true differential and linear hull probabilities. From the frequency distribution, we deduce that the proportion of input-output differences/mask values with probability bounded by p^n is close to 1 whereas only a negligible proportion has probability bounded by p^2. We also recall an n^2-round integral attack distinguisher and (n^2+n-2)-round
impossible impossible differential distinguisher on the n-cell GF-NLFSR by Li et al. and Wu et al. As an application, we design a new 30-round block cipher Four-Cell+ based on a 4-cell GF-NLFSR. We prove the security of Four-Cell+ against differential, linear, and boomerang attack. Four-Cell+ also resists existing key recovery attacks based on the 16-round integral attack distinguisher and
18-round impossible differential distinguisher. Furthermore, Four-Cell+ can be shown to be secure against other attacks such as higher order differential attack, cube attack, interpolation attack, XSL attack and slide attack.

**Category / Keywords: **secret-key cryptography / Block Ciphers, Generalized Unbalanced Feistel Network, Differential Probability, Linear Hull Probability

**Publication Info: **ACISP 2009

**Date: **received 22 Apr 2009, last revised 30 Jul 2009

**Contact author: **cjiali at dso org sg

**Available format(s): **PDF | BibTeX Citation

**Note: **This is a revised version of our ACISP 2009 paper. We have updated the analysis of integral and impossible differential attacks to include improved results of Li et al. and Wu et al. We have also modified the design of our proposed cipher Four-Cell to Four-
Cell+ for better protection against the improved attacks.

**Version: **20090731:024502 (All versions of this report)

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