Quadratic Equations from APN Power Functions*A part of this paper was published in FSE 2004 [6].

  • Authors:

  • Jung Hee Cheon;Dong Hoon Lee

  • Affiliations:

  • The author is with the Faculty of Seoul National University, Korea. E-mail: jhcheon@math.snu.ac.kr,;The author is with National Security Research Institute, Korea.

  • Venue:
  • IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
  • Year:
  • 2006

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Abstract

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.