Higher order differentiation over finite fields with applications to generalising the cube attack


Salagean, Ana and Winter, R. and Mandache-Salagean, Matei and Phan, Raphael Chung Wei (2016) Higher order differentiation over finite fields with applications to generalising the cube attack. Designs, Codes and Cryptography, 84 (3). pp. 425-449. ISSN 0925-1022

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Higher order differentiation was introduced in a cryptographic context by Lai. Several attacks can be viewed in the context of higher order differentiations, amongst them the cube attack of Dinur and Shamir and the AIDA attack of Vielhaber. All of the above have been developed for the binary case. We examine differentiation in larger fields, starting with the field GF(p) of integers modulo a prime p, and apply these techniques to generalising the cube attack to GF(p). The crucial difference is that now the degree in each variable can be higher than one, and our proposed attack will differentiate several times with respect to each variable (unlike the classical cube attack and its larger field version described by Dinur and Shamir, both of which differentiate at most once with respect to each variable). Connections to the Moebius/Reed Muller Transform over GF(p) are also examined. Finally we describe differentiation over finite fields GF(ps) with ps elements and show that it can be reduced to differentiation over GF(p), so a cube attack over GF(ps) would be equivalent to cube attacks over GF(p).

Item Type: Article
Uncontrolled Keywords: Higher order differentiation, Cube attack, Higher order derivative
Subjects: Q Science > QA Mathematics > QA150-272.5 Algebra
Divisions: Faculty of Engineering (FOE)
Depositing User: Ms Suzilawati Abu Samah
Date Deposited: 15 Aug 2018 13:42
Last Modified: 15 Aug 2018 13:42
URII: http://shdl.mmu.edu.my/id/eprint/6734


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