Proceedings ArticleDOI
On a construction of quadratic APN functions
Lilya Budaghyan,Claude Carlet,Gregor Leander +2 more
- pp 374-378
TLDR
Two families of APN functions are get two families are pairwise different and differ from all previously known families ofAPN functions, up to the most general equivalence notion, the CCZ-equivalence.Abstract:
In a recent paper, the authors introduced a method for constructing new quadratic APN functions from known ones. Applying this method, they obtained the function x3 + tr n (x9) which is APN over F 2 n for any positive integer n. The present paper is a continuation of this work. We give sufficient conditions on linear functions L 1 and L 2 from F 2 n to itself such that the function L 1 (x3) + L 2 (x9) is APN over F 2 n . We show that this can lead to many new cases of APN functions. In particular, we get two families of APN functions x3 + a−1 tr3 n (a3x9 + a6x18) and x3 + a−1 tr3 n (a6x18 + a12x36) over F 2 n for any n divisible by 3 and a Є F∗ 2 n . We prove that for n=9, these families are pairwise different and differ from all previously known families of APN functions, up to the most general equivalence notion, the CCZ-equivalence. We also investigate further sufficient conditions under which the conditions on the linear functions L 1 and L 2 are satisfied.read more
Citations
More filters
Book
Construction and Analysis of Cryptographic Functions
TL;DR: This book covers novel research on construction and analysis of optimal cryptographic functions such as almost perfect nonlinear (APN), almost bent (AB), planar and bent functions, and develops several new methods for construction of their infinite families.
Book ChapterDOI
On known and new differentially uniform functions
TL;DR: A way of designing functions which can possibly be APN or differentially 4-uniform and be bijective is proposed and illustrated with an example of a differentially4- uniform (n, n)-permutation for n odd.
Journal ArticleDOI
Constructing APN Functions Through Isotopic Shifts
TL;DR: In this paper, the isotopic equivalence of quadratic planar APN functions over fields of odd characteristic 2 was deduced by studying the isotope equivalence concept.
Dissertation
Mémoire d'habilitation à diriger des recherches
TL;DR: Dans le cas des CSP, Feder et Vardi ont propose la conjecture de the dichotomie, a savoir that chaque probleme CSP est soit facile (dans P) soit difficile (NP-complet), mais une trichotomie entre P, NP-complets et Pspace-completion est envisageable.
Journal ArticleDOI
A New Family of APN Quadrinomials
TL;DR: The binomial B(x) is the first known example of an Almost Perfect Nonlinear (APN) function that is not CCZ-equivalent to a power function, and has remained unclassified into any infinite family of APN functions since its discovery in 2006.
References
More filters
Book ChapterDOI
Linear cryptanalysis method for DES cipher
TL;DR: A new method is introduced for cryptanalysis of DES cipher, which is essentially a known-plaintext attack, that is applicable to an only-ciphertext attack in certain situations.
Journal ArticleDOI
Differential cryptanalysis of DES-like cryptosystems
Eli Biham,Adi Shamir +1 more
TL;DR: A new type of cryptanalytic attack is developed which can break the reduced variant of DES with eight rounds in a few minutes on a personal computer and can break any reduced variantof DES (with up to 15 rounds) using less than 256 operations and chosen plaintexts.
Book ChapterDOI
Differentially uniform mappings for cryptography
TL;DR: Differentially uniform mappings as discussed by the authors have also desirable cryptographic properties: large distance from affine functions, high nonlinear order and efficient computability, and have also been used in DES-like ciphers.
Journal ArticleDOI
Codes, Bent Functions and Permutations Suitable For DES-likeCryptosystems
TL;DR: The "coding theory" point of view for studying the existence of almost bent functions is developed, showing explicitly the links with cyclic codes and new characterizations are given by means of associated Boolean functions.
Book ChapterDOI
Vectorial Boolean Functions for Cryptography
TL;DR: To appear as a chapter of the volume " Boolean Methods and Models " , this chapter describes the construction of Boolean models and some examples show how to model Boolean functions using LaSalle's inequality.