Cui, Jingyi Guo, Jiansheng
Published in
Quantum Information Processing

Compared with Boolean functions, multi-output Boolean functions (a.k.a. vectorial Boolean functions) are commonly used in classical cryptography. More generally, many cryptographic primitives can be treated as multi-output Boolean functions. Hence, the research on property testing of multi-output Boolean functions is meaningful for the design and c...

Cui, Jingyi Guo, Jiansheng Xu, Linhong Li, Mingming
Published in
Quantum Information Processing

In classical cryptography, many cryptographic primitives could be treated as multi-output Boolean functions. The analysis of such functions is of great interest for cryptologists owing to their wide ranges of applications. Since each multi-output Boolean function can be uniquely determined by its Walsh transform, the Walsh spectra could reveal the ...

ghorbani, modjtaba dehmer, matthias taghvayi-yazdelli, vahid emmert-streib, frank

In this paper, we present four product operations to construct cryptographic boolean functions from smaller ones with predictable Walsh spectrum. A lot of cryptographic properties of boolean functions can be presented by their Walsh spectrum. In our method, we use the product of Cayley graphs to present new boolean functions with desired Walsh spec...

Li, Hongwei
Published in
Quantum Information Processing

A quantum algorithm to evaluate the resiliency of a Boolean function is explored. Recently, Chakraborty and Maitra (Cryptogr Commun 8(3):401–413, 2016) have provided quantum algorithms to check the non-resiliency of a Boolean function. However, the shortage of their algorithms is that they just output YES or NO. Refining one of the algorithms, a qu...

Charpin, Pascale Peng, Jie

The associated codes of almost perfect nonlinear (APN) functions have been widely studied. In this paper we consider more generally the codes associated with functions that have differential uniformity at least 4. We emphasize, for such a function F , the role of codewords of weight 3 and 4 and of some cosets of its associated code C F. We give som...

Nguyen, Nhan Khanh Huu

The implementation value of multi-output Boolean functions in logic synthesis FPGA can be reduced by using Walsh spectral representation. This paper proposes an algorithm for calculating the maximum coefficient of the autocorrelation function of BF without generating a truth table, using the heuristic procedure limits the maximum autocorrelation co...

Nguyen, Nhan Khanh Huu

The implementation value of multi-output Boolean functions in logic synthesis FPGA can be reduced by using Walsh spectral representation. This paper proposes an algorithm for calculating the maximum coefficient of the autocorrelation function of BF without generating a truth table, using the heuristic procedure limits the maximum autocorrelation co...

Qu, LongJiang Tan, Yin Li, Chao
Published in
Science China Information Sciences

Recently, a family of quadratic APN functions was demonstrated by Bracken et al. to exist over \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathbb{F}_{2^{2k} } $\end...

Lauradoux, Cédric Videau, Marion

We present the properties of a new class of Boolean functions defined as the sum of m symmetric functions with decreasing number of variables and degrees. The choice of this construction is justified by the possibility to study these functions by using tools existing for symmetric functions. On the one hand we show that the synthesis is well unders...

Liu, Wenfen Li, Shiqu
Published in
Applied Mathematics-A Journal of Chinese Universities

In this paper the decomposition formula of Walsh spectrum of boolean functions is used to construct a class of nonlinear resilient functions.