Finding biaffine and quadratic equations for S-boxes based on power mappings

Kishan Chand Gupta, Indranil Ghosh Ray

Research output: Contribution to journalArticlepeer-review


S-boxes having large number of linearly independent multivariate biaffine or quadratic equations may be susceptible to certain kinds of algebraic attacks. In a 2009 IEEE-IT paper, Nawaz et al. provided a polynomial time algorithm to compute the number of such equations for finding S-boxes based on power mapping. Finding actual equations in polynomial time was still open. In this paper, techniques for finding a maximal set of linearly independent biaffine and quadratic equations are developed for S-boxes based on power mappings. Two algorithms to calculate the biaffine and quadratic equations for any (n, n) S-box based on power mapping are presented. The time complexity of both the algorithms is O(n 6 ).
Original languageEnglish
Pages (from-to)2200-2209
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number4
Early online date31 Dec 2014
Publication statusPublished - 01 Apr 2015
Externally publishedYes


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