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2013•Unpublished venueRequires access

A Matrix Approach for Constructing Quadratic APN Functions.

Yuyin Yu, Ming‐Sheng Wang, Yongqiang Li

Open publisher page 4 citations

Abstract

Abstract—We find a one to one correspondence between quadratic APN functions without linear and 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 F27, 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 F28 have been found. With our method, we have found more than 1000 classes of new CCZ-inequivalent quadratic APN functions, and this number is still arising quickly. Index Terms—APN, quadratic functions, EA-equivalence, CCZ-equivalence. I.

About this research paper

What this paper is about

Abstract—We find a one to one correspondence between quadratic APN functions without linear and 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 F27, 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 F28 have been found. With our method, we have found more than 1000 classes of new CCZ-inequivalent quadratic APN functions, and this number is still arising quickly. Index Terms—APN, quadratic functions, EA-equivalence, CCZ-equivalence. I.

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Available abstract

Abstract—We find a one to one correspondence between quadratic APN functions without linear and 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 F27, 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 F28 have been found. With our method, we have found more than 1000 classes of new CCZ-inequivalent quadratic APN functions, and this number is still arising quickly. Index Terms—APN, quadratic functions, EA-equivalence, CCZ-equivalence. I.

Key concepts: Quadratic equation, Quadratic model, Quadratic function, Mathematics, Constant (computer programming), Matrix (chemical analysis), Construct (python library), Function (biology)

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