Low c-Differential Uniformity for the Gold Function Modified on a Subfield

2021 ◽  
pp. 131-137
Author(s):  
Pantelimon Stănică
Keyword(s):  
Differential Uniformity ◽  
Gold Function

scholarly journals Differentially low uniform permutations from known 4-uniform functions

2020 ◽  
Author(s):  
Marco Calderini
Keyword(s):  
Block Cipher ◽  
Differential Uniformity ◽  
Good Resistance ◽  
Gold Function ◽  
Differential Attacks

Abstract Functions with low differential uniformity can be used in a block cipher as S-boxes since they have good resistance to differential attacks. In this paper we consider piecewise constructions for permutations with low differential uniformity. In particular, we give two constructions of differentially 6-uniform functions, modifying the Gold function and the Bracken–Leander function on a subfield.

scholarly journals More Low Differential Uniformity Permutations over F22k with k Odd

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yue Leng ◽  
Jinyang Chen ◽  
Tao Xie
Keyword(s):  
Block Ciphers ◽  
Algebraic Degree ◽  
Differential Uniformity ◽  
Numerical Examples ◽  
High Nonlinearity ◽  
Substitution Boxes ◽  
Theoretical Results

Permutations with low differential uniformity, high algebraic degree, and high nonlinearity over F22k can be used as the substitution boxes for many block ciphers. In this paper, several classes of low differential uniformity permutations are constructed based on the method of choosing two permutations over F22k to get the desired permutations. The resulted low differential uniformity permutations have high algebraic degrees and nonlinearities simultaneously, which provide more choices for the substitution boxes. Moreover, some numerical examples are provided to show the efficacy of the theoretical results.

scholarly journals Evolving Dynamic S-Boxes Using Fractional-Order Hopfield Neural Network Based Scheme

Entropy ◽  
2020 ◽  
Vol 22 (7) ◽  
pp. 717 ◽  
Author(s):  
Musheer Ahmad ◽  
Eesa Al-Solami
Keyword(s):  
Neural Network ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Performance Assessments ◽  
Comparison Analysis ◽  
Differential Uniformity ◽  
High Nonlinearity ◽  
Substitution Boxes ◽  
Strict Avalanche Criterion ◽  
Independence Criterion

Static substitution-boxes in fixed structured block ciphers may make the system vulnerable to cryptanalysis. However, key-dependent dynamic substitution-boxes (S-boxes) assume to improve the security and robustness of the whole cryptosystem. This paper proposes to present the construction of key-dependent dynamic S-boxes having high nonlinearity. The proposed scheme involves the evolution of initially generated S-box for improved nonlinearity based on the fractional-order time-delayed Hopfield neural network. The cryptographic performance of the evolved S-box is assessed by using standard security parameters, including nonlinearity, strict avalanche criterion, bits independence criterion, differential uniformity, linear approximation probability, etc. The proposed scheme is able to evolve an S-box having mean nonlinearity of 111.25, strict avalanche criteria value of 0.5007, and differential uniformity of 10. The performance assessments demonstrate that the proposed scheme and S-box have excellent features, and are thus capable of offering high nonlinearity in the cryptosystem. The comparison analysis further confirms the improved security features of anticipated scheme and S-box, as compared to many existing chaos-based and other S-boxes.

scholarly journals On weak differential uniformity of vectorial Boolean functions as a cryptographic criterion

2016 ◽  
Vol 27 (5) ◽  
pp. 359-372 ◽  
Author(s):  
Riccardo Aragona ◽  
Marco Calderini ◽  
Daniele Maccauro ◽  
Massimiliano Sala
Keyword(s):  
Boolean Functions ◽  
Differential Uniformity ◽  
Vectorial Boolean Functions

scholarly journals A quantum algorithm to approximate the linear structures of Boolean functions

2016 ◽  
Vol 28 (1) ◽  
pp. 1-13 ◽  
Author(s):  
HONGWEI LI ◽  
LI YANG
Keyword(s):  
Boolean Functions ◽  
High Probability ◽  
Success Probability ◽  
Quantum Algorithm ◽  
Linear Structure ◽  
Differential Uniformity ◽  
Linear Structures ◽  
High Success Probability ◽  
Time Required ◽  
Quantum Speedup

A quantum algorithm to determine approximations of linear structures of Boolean functions is presented and analysed. Similar results have already been published (see Simon's algorithm) but only for some promise versions of the problem, and it has been shown that no exponential quantum speedup can be obtained for the general (no promise) version of the problem. In this paper, no additional promise assumptions are made. The approach presented is based on the method used in the Bernstein–Vazirani algorithm to identify linear Boolean functions and on ideas from Simon's period finding algorithm. A proper combination of these two approaches results here to a polynomial-time approximation to the linear structures set. Specifically, we show how the accuracy of the approximation with high probability changes according to the running time of the algorithm. Moreover, we show that the time required for the linear structure determine problem with high success probability is related to so called relative differential uniformity δf of a Boolean function f. Smaller differential uniformity is, shorter time is needed.

More permutation polynomials with differential uniformity six

2017 ◽  
Vol 61 (3) ◽  
Author(s):  
Ziran Tu ◽  
Xiangyong Zeng ◽  
Zhiyong Zhang
Keyword(s):  
Permutation Polynomials ◽  
Differential Uniformity

scholarly journals Revisiting some results on APN and algebraic immune functions

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Claude Carlet
Keyword(s):  
Boolean Functions ◽  
The Other ◽  
Immune Functions ◽  
Apn Functions ◽  
Power Functions ◽  
Differential Uniformity ◽  
Open Problems ◽  
Apn Function ◽  
Almost Perfect Nonlinear

<p style='text-indent:20px;'>We push a little further the study of two recent characterizations of almost perfect nonlinear (APN) functions. We state open problems about them, and we revisit in their perspective a well-known result from Dobbertin on APN exponents. This leads us to a new result about APN power functions and more general APN polynomials with coefficients in a subfield <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{F}_{2^k} $\end{document}</tex-math></inline-formula>, which eases the research of such functions. It also allows to construct automatically many differentially uniform functions from them (this avoids calculations for proving their differential uniformity as done in a recent paper, which are tedious and specific to each APN function). In a second part, we give simple proofs of two important results on Boolean functions, one of which deserves to be better known but needed clarification, while the other needed correction.</p>

scholarly journals Differential uniformity and the associated codes of cryptographic functions

2019 ◽  
Vol 13 (4) ◽  
pp. 579-600 ◽  
Author(s):  
Pascale Charpin ◽  
◽  
Jie Peng ◽  
Keyword(s):  
Differential Uniformity
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