Another class of quadratic APN binomials over F2n: the case n divisible by 4

نویسندگان

  • Lilya Budaghyan
  • Claude Carlet
  • Gregor Leander
چکیده

We exhibit an infinite class of almost perfect nonlinear quadratic binomials from F2n to F2n with n = 4k and k odd. We prove that these functions are CCZinequivalent to known APN power functions when k 6= 1. In particular it means that for n = 12, 20, 28, they are CCZ-inequivalent to any power function.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A class of quadratic APN binomials inequivalent to power functions

We exhibit an infinite class of almost perfect nonlinear quadratic binomials 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 and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for n even they are CCZ-inequivalent to any known APN function, and in particular for n = 12,...

متن کامل

Constructing new APN functions from known ones

We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function x3 + tr(x9) over F2n . It is proven that in general this function is CCZinequivalent to the Gold functions (and therefore EA-inequivalent to power functions), to the inverse and Dobbertin mappings, and in the case n = 7 it is CCZinequiva...

متن کامل

On upper bounds for algebraic degrees of APN functions

We study the problem of existence of APN functions of algebraic degree n over F2n . We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce some non-existence results which mean, in particular, that for most of the known APN functions F over F2n the function x −1 + F (x) is not APN, and changing a value of F in a single point results in non-APN...

متن کامل

Differentially 4-uniform bijections by permuting the inverse function

Block ciphers use Substitution boxes (S-boxes) to create confusion into the cryptosystems. Functions used as S-boxes should have low differential uniformity, high nonlinearity and algebraic degree larger than 3 (preferably strictly larger). They should be fastly computable; from this viewpoint, it is better when they are in even number of variables. In addition, the functions should be bijectio...

متن کامل

APN 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 کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • IACR Cryptology ePrint Archive

دوره 2006  شماره 

صفحات  -

تاریخ انتشار 2006