»ã±¨±êÌâ (Title)£ºÒ»Àà»ùÓÚDillonÖ¸ÊýµÄ³¬Bentº¯Êý(Hyper-Bent Functions from Dillon Exponents)

»ã±¨ÈË (Speaker)£º ÌÆ´ºÃ÷ ½ÌÊÚ£¨Î÷ÄϽ»Í¨´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê11ÔÂ18ÈÕ(ÖÜÁù) 15£º00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿ F309

Ô¼ÇëÈË(Inviter)£º¶¡Ñó

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»ã±¨ÌáÒª£ºHyper-bent functions are a class of important bent Boolean functions, which achieve maximum distance from all bijective monomial functions, and provide further security towards approximation attacks. Being describled by a stricter definition, hyper-bent functions are much more difficult to characterize than bent functions. In 2008, Charpin and Gong presented a characterization of hyper-bentness of Boolean functions with multiple trace terms obtained via Dillon-like functions with coefficients in the subfield in terms of some exponential sums. In this talk we are interested in the characterization of hyper-bentness of such functions with coefficients in the extension field. By employing Mobius transformation, we give connections among the property of hyper-bentness, the exponential sum involving Dickson polynomials and the number of rational points on some associated hyperelliptic curves. The effectiveness of this new method can be seen from the characterization of a new class of binomial hyper-bent functions with coefficients in extension fields.