Welcome to the resource topic for 2013/007
Title:
A Matrix Approach for Constructing Quadratic APN Functions
Authors: Yuyin Yu, Mingsheng Wang, 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.
ePrint: https://eprint.iacr.org/2013/007
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