On CCZ-equivalence and its use in secondary constructions of bent functions
نویسندگان
چکیده
We prove that, for bent vectorial functions, CCZ-equivalence coincides with EA-equivalence. However, we show that CCZ-equivalence can be used for constructing bent functions which are new up to CCZequivalence. Using this approach we construct classes of nonquadratic bent Boolean and bent vectorial functions.
منابع مشابه
Self-dual bent functions
A bent function is called self-dual if it is equal to its dual. It is called anti-self-dual if it is equal to the complement of its dual. A spectral characterization in terms of the Rayleigh quotient of the Sylvester Hadamard matrix is derived. Bounds on the Rayleigh quotient are given for Boolean functions in an odd number of variables. An efficient search algorithm based on the spectrum of th...
متن کاملBent and Semi-bent Functions via Linear Translators
The paper is dealing with two important subclasses of plateaued functions: bent and semi-bent functions. In the first part of the paper, we construct mainly bent and semi-bent functions in the Maiorana-McFarland class using Boolean functions having linear structures (linear translators) systematically. Although most of these results are rather direct applications of some recent results, using l...
متن کاملCCZ-equivalence and Boolean functions
We study further CCZ-equivalence of (n,m)-functions. We prove that for Boolean functions (that is, for m = 1), CCZ-equivalence coincides with EA-equivalence. On the contrary, we show that for (n,m)functions, CCZ-equivalence is strictly more general than EAequivalence when n ≥ 5 and m is greater or equal to the smallest positive divisor of n different from 1. Our result on Boolean functions allo...
متن کاملOn the Equivalence of Nonlinear Functions
Recently, many new almost perfect nonlinear (APN) and almost bent (AB) functions have been constructed. These functions F n 2 → F n 2 play an important role in cryptography. In this article, we will summarize different concepts of equivalence between these functions, and discuss some invariants. Two codes can be associated with APN and AB functions. This is useful to distinguish functions up to...
متن کاملA Theory of Highly Nonlinear Functions
Highly nonlinear functions are important as sources of low-correlation sequences, high-distance codes and cryptographic primitives, as well as for applications in combinatorics and finite geometry [3, 4]. We argue that the theory of such functions is best seen in terms of splitting factor pairs. Splitting factor pairs arise in the theory of group extensions and their second cohomology groups. T...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- IACR Cryptology ePrint Archive
دوره 2009 شماره
صفحات -
تاریخ انتشار 2009