16772

16772

يك روش ماتريسي براي ساخت توابع مربعي APN

كارشناسي ارشد

رياضي محض - جبر

مهر ماه 1395

دكتر مهدي علاييان

دكتر سيد محمد كاظم حسيني پور

رياضي

1395/12/07

1/1/1900 12:00:00 AM

Abstract: We find a one to one correspondence between quadratic APN functions without linear o​r constant terms an​d 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 2000 classes of new CCZ-inequivalent quadratic APN functions, an​d this number is still increasing quickly. Keywords: Almost Perfect nonlinear, Quadratic Functions, EA -Equivalence , CCZ -Equivalence