Some Saturation Characteristics of XOR Sum of Balance Functions

Yasutaka IGARASHI  Toshinobu KANEKO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E95-A   No.1   pp.2-7
Publication Date: 2012/01/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E95.A.2
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Symmetric Cryptography
balance function,  saturation characteristics,  Hadamard transform,  Extended Hamming code,  convolution,  block cipher,  CLEFIA,  

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CLEFIA is a 128-bit block cipher proposed by Shirai et al. in 2007. On its saturation attack, Tsunoo et al. reported peculiar saturation characteristics in 2010. They formulated some hypotheses on the existence of the characteristics with no proof. In this paper we have theoretically proved their hypotheses. In their attack scenario, we show that the mod-2 distribution is a code word of Extended Hamming code, and then proof is given by using the property of Hadamard transform.