A matrix approach for constructing quadratic APN functions
نویسندگان
چکیده
منابع مشابه
A matrix approach for constructing quadratic APN functions
We find a one to one correspondence between quadratic APN functions without linear and constant terms and a special kind of matrices (We call such matrices as QAMs). Based on the nice mathematical structures of the QAMs, we have developed efficient algorithms to construct quadratic APN functions. On F27 , we have found more than 470 classes of new CCZ-inequivalent quadratic APN functions, which...
متن کاملEquivalences of quadratic APN functions
The following conjecture due to Y. Edel is affirmatively solved: two quadratic APN (almost perfect nonlinear) functions are CCZ-equivalent if and only if they are extended affine equivalent.
متن کاملConstructing 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...
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We develop several tools to derive quadratic equations from algebraic S-boxes and to prove their linear independence. By applying them to all known almost perfect nonlinear (APN) power functions and the inverse function, we can estimate the resistance against algebraic attacks. As a result, we can show that APN functions have different resistance against algebraic attacks, and especially S-boxe...
متن کاملOn the equivalence of quadratic APN functions
Establishing the CCZ-equivalence of a pair of APN functions is generally quite difficult. In some cases, when seeking to show that a putative new infinite family of APN functions is CCZ inequivalent to an already known family, we rely on computer calculation for small values of n. In this paper we present a method to prove the inequivalence of quadratic APN functions with the Gold functions. Ou...
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ژورنال
عنوان ژورنال: Designs, Codes and Cryptography
سال: 2014
ISSN: 0925-1022,1573-7586
DOI: 10.1007/s10623-014-9955-3