17574

17574

يك دسته نامتناهي از توابع APN درجه 2 ناهم ارز هم ارز نگاشت هاي تواني

كارشناسي ارشد

رياضي محض - جبر

بهمن 1395

دكتر مهدي علاييان

دكتر سيدمحمدكاظم حسيني پور

رياضي

1396/04/12

1/1/1900 12:00:00 AM

Abstract: We exhibit an in fnite class of almost perfect nonlinear quadratic polynomials from F2n to F2n (n 12, n divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function. In the forthcoming version of the present paper we will proof that these functions are CCZ-inequivalent to any Gold function and to any Kasami function, in particular for n = 12, they are therefore CCZ- inequivalent to power functions. Keywords: Vectorial Boolean function, S-box, Nonlinearity, Differential uniformity, Almost perfect nonlinear, Almost bent, Affine equivalence, CCZ-equivalence.