Quadratic Equations from APN Power Functions

Jung Hee CHEON  Dong Hoon LEE  

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E89-A   No.1   pp.19-27
Publication Date: 2006/01/01
Online ISSN: 1745-1337
DOI: 10.1093/ietfec/e89-a.1.19
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)
Category: Symmetric Key Cryptography
Keyword: 
algebraic attack,  quadratic equations,  almost perfect nonlinear (APN),  linear independence,  nonlinearity,  

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Summary: 
We develop several tools to derive quadratic equations from algebraic S-boxes and to prove their linear independence. By applying them to all known almost perfect nonlinear (APN) power functions and the inverse function, we can estimate the resistance against algebraic attacks. As a result, we can show that APN functions have different resistance against algebraic attacks, and especially S-boxes with Gold or Kasami exponents have very weak resistance.