A few more functions that are not APN infinitely often
نویسندگان
چکیده
We consider exceptional APN functions on F2m , which by definition are functions that are APN on infinitely many extensions of F2m . Our main result is that polynomial functions of odd degree are not exceptional, provided the degree is not a Gold number (2 +1) or a Kasami-Welch number (4 −2k +1). We also have partial results on functions of even degree, and functions that have degree 2 + 1. ∗Research supported by the Claude Shannon Institute, Science Foundation Ireland Grant 06/MI/006
منابع مشابه
Some more functions that are not APN infinitely often. The case of Gold and Kasami exponents
We prove a necessary condition for some polynomials of Gold and Kasami degree to be APN over Fqn for large n.
متن کاملSome More Functions That Are Not APN Infinitely Often. The Case of Kasami exponents
We prove a necessary condition for some polynomials of Kasami degree to be APN over Fqn for large n.
متن کاملQuadratic Binomial APN Functions and Absolutely Irreducible Polynomials
We show that many quadratic binomial functions of the form cx i +2 j + dx u +2 v (c, d ∈ GF (2m)) are not APN infinitely often. This is of interest in the light of recent discoveries of new families of quadratic binomial APN functions. The proof uses the Weil bound from algebraic geometry.
متن کاملA new large class of functions not APN infinitely often
In this paper, we show that there is no vectorial Boolean function of degree 4e, with e satisfaying certain conditions, which is APN over infinitely many extensions of its field of definition. It is a new step in the proof of the conjecture of Aubry, McGuire and Rodier. Vectorial Boolean function and Almost Perfect Non-linear functions and Algebraic surface and CCZ equivalence
متن کاملAPN Power Functions Over GF(2) for Infinitely Many n
I present some results towards a classification of power functions that are Almost Perfect Nonlinear (APN), or equivalently differentially 2-uniform, over F2n for infinitely many n. APN functions are useful in constructing S-boxes in AES-like cryptosystems. An application of Weil’s theorem on absolutely irreducible curves shows that a monomial x is not APN over F2n for all sufficiently large n ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009