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Quadratic Equations from APN Power Functions
Jung Hee CHEON Dong Hoon LEE
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E89A
No.1
pp.1927 Publication Date: 2006/01/01
Online ISSN: 17451337
DOI: 10.1093/ietfec/e89a.1.19
Print ISSN: 09168508 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,
Full Text: PDF(181.6KB)>>
Summary:
We develop several tools to derive quadratic equations from algebraic Sboxes 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 Sboxes with Gold or Kasami exponents have very weak resistance.

