17678

17678

خانواده اي نا متناهي از توابع APN دوجمله اي درجه دو

كارشناسي ارشد

رياضي محض - جبر

اسفند 1395

دكتر مهدي علائيان

دكتر سيد كاظم حسيني پور

رياضي

n = 4k كه F٢n به F٢n تام از 􀍬 از دو جمله اي هاي درجه دوم غير خط 􀍬 در اين پايان نامه خانواده اي نامتناه شناخته APN 􀍬 اين توابع با توابع توان k ̸= كنيم كه براي ١

1396/04/25

1/1/1900 12:00:00 AM

We exhibit an infinite class of almost perfect nonlinear quadratic binomials from Fn 2 to Fn 2 with n = 4k and k odd. We prove that these functions are CCZ -inequivalent to known APN power functions when k ̸= 1. In particular it means that for n = 12; 20; 28, they are CCZ-inequivalent to any power function. . Keywords: Affine equivalence, Almost bent, Almost perfect nonlinear, CCZ-equivalence, Differential uniformity, Nonlinearity, S-box, Vectorial Boolean function