DocumentCode :
112457
Title :
Finding Biaffine and Quadratic Equations for S-Boxes Based on Power Mappings
Author :
Gupta, Kishan Chand ; Ray, Indranil Ghosh
Author_Institution :
Indian Stat. Inst., Kolkata, India
Volume :
61
Issue :
4
fYear :
2015
fDate :
Apr-15
Firstpage :
2200
Lastpage :
2209
Abstract :
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(n6).
Keywords :
computational complexity; cryptography; S-boxes; cryptanalysis; linearly independent multivariate biaffine; polynomial time algorithm; power mappings; quadratic equations; Boolean functions; Ciphers; Mathematical model; Polynomials; Time complexity; Vectors; Algebraic attacks; Bi-affine equations; Power mapping; Quadratic equations; S-box; algebraic attacks; power mapping; quadratic equations;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.2014.2387052
Filename :
7000605
Link To Document :
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