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Higher Order Differential Attack Using Chosen Higher Order Differences

Shiho MoriaiContact Information, Takeshi ShimoyamaContact Information and Toshinobu Kaneko6, 7 Contact Information

(5)  NTT Laboratories, 1-1 Hikari-no-oka, Yokosuka 239-0847, Japan
(6)  TAO, 1-1-32 Shin-urashima-cho, Kanagawa-ku, Yokohama 221-0031, Japan
(7)  Science University of Tokyo, 2641 Yamazaki, Noda, Chiba 278-8510, Japan
Abstract
This paper introduces an improved higher order differential attack using chosen higher order differences. We can find a lower order of the higher order differential by choosing higher order differences. It follows that the designers of a block cipher can evaluate the lower bound of the number of chosen plaintexts and the complexity required for the higher order differential attack. We demonstrate an improved higher order differential attack of a CAST cipher with 5 rounds using chosen higher order differences with fewer chosen plaintexts and less complexity. Concretely, we show that a CAST cipher with 5 rounds is breakable with 216 plaintexts and < 224 times the computation of the round function, which half the values reported in Fast Software Encryption Workshop’98. We also show that it is breakable with 213 plaintexts and about 244 times the computation of the round function, which are 1/16-th of those reported in Fast Software Encryption Workshop’97.

Contact Information Shiho Moriai
Email: shiho@isl.ntt.co.jp

Contact Information Takeshi Shimoyama
Email: shimo@yokohama.tao.go.jp

Contact Information Toshinobu Kaneko
Email: kaneko@ee.noda.sut.ac.jp
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Referenced by
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  1. Yongjuan, Wang (2006) Walsh spectrum properties of rotation symmetric boolean function. Wuhan University Journal of Natural Sciences 11(6)
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