Cryptology ePrint Archive: Report 2013/007

A Matrix Approach for Constructing Quadratic APN Functions

Yuyin Yu and Mingsheng Wang and Yongqiang Li

Abstract: We find a one to one correspondence between quadratic APN functions without linear or constant terms and a special kind of matrices (We call such matrices as QAMs). Based on the nice mathematical structures of the QAMs, we have developed efficient algorithms to construct quadratic APN functions. On $\mathbb{F}_{2^7}$, we have found more than 470 classes of new CCZ-inequivalent quadratic APN functions, which is 20 times more than the known ones. Before this paper, there are only 23 classes of CCZ-inequivalent APN functions on $\mathbb{F}_{2^{8}}$ have been found. With our method, we have found more than 2000 classes of new CCZ-inequivalent quadratic APN functions, and this number is still increasing quickly.

Category / Keywords: APN, quadratic functions, EA-equivalence, CCZ-equivalence.

Date: received 6 Jan 2013, last revised 2 Apr 2013

Contact author: yuyuyin at 163 com

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Version: 20130403:031359 (All versions of this report)

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