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Paper 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.

Metadata
Available format(s)
PDF
Publication info
Published elsewhere. Unknown where it was published
Keywords
APNquadratic functionsEA-equivalenceCCZ-equivalence.
Contact author(s)
yuyuyin @ 163 com
History
2015-04-27: last of 2 revisions
2013-01-11: received
See all versions
Short URL
https://ia.cr/2013/007
License
Creative Commons Attribution
CC BY
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