检索结果-内蒙古大学图书馆

Determination of cryptographic tables and properties related to the revised boomerang and its application to a fundamental S-box

引用

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES boolean functions AND SEQUENCES 2025年第2期17卷 465-492页

作者： Eddahmani, Said Mesnager, Sihem Univ Paris VIII Dept Math F-93526 St Denis France Univ Sorbonne Paris Nord Lab Geometry Anal & Applicat LAGA CNRSUMR 7539 F-93430 Villetaneuse France Telecom Paris F-91120 Palaiseau France

In symmetric cryptography, vectorial boolean functions over the finite field F2n\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {F}_{2<^>n}$$\end{document} are used to construct strong S-boxes. A strong S-box must meet various criteria to resist known attacks, including differential, linear, boomerang, and their variants. To evaluate an S-box's resistance, several tables are utilized, such as the Difference Distribution Table (DDT) and the Boomerang Connectivity Table (BCT). Recent developments in boomerang attacks have revisited the concept of the boomerang switch effect, illustrating the effectiveness of this technique. As a result, a new tool called the Boomerang Difference Table (BDT) was introduced as an alternative to the traditional BCT. Additionally, two novel tables have been proposed: the Upper Boomerang Connectivity Table (UBCT) and the Lower Boomerang Connectivity Table (LBCT). These tables are enhancements over the BCT and facilitate a systematic evaluation of boomerangs that can return over multiple rounds. This paper focuses on the new tools for measuring the revisited version of boomerang attacks and the related tables UBCT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {UBCT}$$\end{document}, LBCT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\texttt {LBCT}$$\end{document}, as well as the so-called Extended Boomerang Connectivity Table (EBCT\documentclass[12pt]{minimal} \usepackage{amsmath} \usepa

关键词： vectorial boolean functions Upper Boomerang Connectivity Table (UBCT) Lower Boomerang Connectivity Table (LBCT) Extended Boomerang Connectivity Table (EBCT) Boomerang connectivity uniformity

来源：评论

学校读者我要写书评

暂无评论

On Dillon's property of (n, m)-functions

引用

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES boolean functions AND SEQUENCES 2024年第6期16卷 1449-1473页

作者： Abbondati, Matteo Calderini, Marco Villa, Irene Univ Trento Dept Math Via Sommar 14 I-38123 Povo TN Italy Univ Montpellier CNRS LIRMM Montpellier France Univ Genoa Dept Math Via Dodecaneso 35 I-16146 Genoa Italy

Dillon observed that an APN function F over F-2(n) with n greater than 2 must satisfy the condition {F(x) + F(y) + F(z) + F(x + y + z) :x, y, z is an element of F-2(n)} = F-2(n). Recently, Taniguchi (Cryptogr. Commun. 15, 627-647 2023) generalized this condition to functions defined from F-2(n) to F-2(m), with m > n, calling it the D-property. Taniguchi gave some characterizations of APN functions satisfying the D-property and provided some families of APN functions from F-2(n) to F-2(n+1) satisfying this property. In this work, we further study the D-property for (n, m)-functions with m >= n. We give some combinatorial bounds on the dimension m for the existence of such functions. Then, we characterize the D-property in terms of the Walsh transform and for quadratic functions we give a characterization of this property in terms of the ANF. We also give a simplification on checking the D-property for quadratic functions, which permits to extend some of the APN families provided by Taniguchi. We further focus on the class of the plateaued functions, providing conditions for the D-property. To conclude, we show a connection of some results obtained with the higher-order differentiability and the inverse Fourier transform.

关键词： vectorial boolean functions D-property APN functions Walsh transform Plateaued functions

来源：评论

学校读者我要写书评

暂无评论

Constructions with high algebraic degree of differentially 4-uniform (n, n-1)-functions and differentially 8-uniform (n, n-2)-functions

引用

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES boolean functions AND SEQUENCES 2018年第4期10卷 611-628页

作者： Alsalami, Yousuf Khalifa Univ Sci & Technol Dept Elect & Comp Engn Abu Dhabi U Arab Emirates

Quadratic differentially 4-uniform (n, n - 1)-functions are given in Carlet J. Adv. Math. Commun. 9(4), 541-565 (2015) where a question is raised of whether non-quadratic differentially 4-uniform (n, n - 1)- functions exist. In this paper, we give highly nonlinear differentially 4-uniform (n, n - 1)-functions of optimal algebraic degree for both n even and odd. Using the approach in Carlet J. Adv. Math. Commun. 9(4), 541-565 (2015), we construct these functions using two APN (n - 1, n - 1)-functions which are EA-equivalent Inverse functions satisfying some necessary and sufficient conditions when n is even. We slightly generalize the approach to construct differentially 4-uniform (n, n - 1)-functions from two differentially 4-uniform (n - 1, n - 1)-functions satisfying some necessary conditions. This allows us to derive the differentially 4-uniform (n, n - 1)-functions (x, x(n)) bar right arrow (x(n) + 1)x(2n-2) + x(n)alpha x(2n-2), x is an element of F2n-1, x(n) is an element of F-2, and alpha is an element of F2n-1 \F-2, where Tr-1(n-1) (alpha) = Tr-1(n-1) (1/alpha) = 1. These (n, n - 1)-functions are balanced whatever the parity of n is and are then better suited for use as S-boxes in a Feistel cipher. We also give some properties of the Walsh spectrum of these functions to prove that they are CCZ-inequivalent to the differentially 4-uniform (n, n - 1)-functions of the form L circle F, where F is a known APN (n, n)-function and L is an affine surjective (n, n - 1)-function. Finally, we also give two new constructions of differentially 8-uniform (n, n - 2)-functions from EA-equivalent Cubic functions and from EA-equivalent Inverse functions.

关键词： Block ciphers S-boxes vectorial boolean functions APN functions Differentially 4-uniform functions

来源：评论

学校读者我要写书评

暂无评论

Generalized isotopic shift construction for APN functions

引用

DESIGNS CODES AND CRYPTOGRAPHY 2021年第1期89卷 19-32页

作者： Budaghyan, Lilya Calderini, Marco Carlet, Claude Coulter, Robert Villa, Irene Univ Bergen Dept Informat PB 7803 N-5020 Bergen Norway Univ Paris 08 LAGA St Denis France Univ Delaware Dept Math Sci Newark DE 19716 USA

In this work we give several generalizations of the isotopic shift construction, introduced recently by Budaghyan et al. (IEEE Trans Inform Theory 66:5299-5309, 2020), when the initial function is a Gold function. In particular, we derive a general construction of APN functions which covers several unclassified APN functions for n = 8 and produces fifteen new APN functions for n = 9.

关键词： APN functions Isotopic shift vectorial boolean functions

来源：评论

学校读者我要写书评

暂无评论

Classification of Bent Monomials, Constructions of Bent Multinomials and Upper Bounds on the Nonlinearity of vectorial functions

引用

IEEE TRANSACTIONS ON INFORMATION THEORY 2018年第1期64卷 367-383页

作者： Xu, Yuwei Carlet, Claude Mesnager, Sihem Wu, Chuankun Chinese Acad Sci State Key Lab Informat Secur Inst Informat Engn Beijing 100093 Peoples R China Univ Chinese Acad Sci Sch Cyber Secur Beijing 100049 Peoples R China Univ Paris 08 Dept Math F-93526 St Denis France Univ Paris 13 CNRS LAGA UMR 7539 Sorbonne Paris Cite F-93430 Villetaneuse France Telecom ParisTech F-75013 Paris France Beijing Acorn Network Technol Co Ltd Beijing 100191 Peoples R China

This paper is composed of two main parts related to the nonlinearity of vectorial functions. The first part is devoted to maximally nonlinear (n, m) functions (the so-called bent vectorial functions), which contribute to an optimal resistance to both linear and differential attacks on symmetric cryptosystems. They can be used in block ciphers at the cost of additional diffusion/compression/expansion layers, or as building blocks for the construction of substitution boxes (S-boxes), and they are also useful for constructing robust codes and algebraic manipulation detection codes. A main issue on bent vectorial functions is to characterize bent monomial functions Tr-m(n) (lambda x(d)) from F-2n to F-2m (where m is a divisor of n) leading to a classification of those bent monomials. We also treat the case of functions with multiple trace terms involving general results and explicit constructions. Furthermore, we investigate some open problems raised by Pasalic et al. and Muratovic-Ribic et al. in a series of papers on vectorial functions. The second part is devoted to the nonlinearity of (n, m)-functions. No tight upper bound is known when n/2 < m < n. The covering radius bound is the only known upper bound in this range (the Sidelnikov-Chabaud-Vaudenay bound coincides with it when m = n-1 and it has no sense when m < n-1). Finding better bounds is an open problem since the 1990s. Moreover, no bound has been found during the last 23 years, which improve upon the covering radius bound for a large part of (n, m)-functions. We derive such upper bounds for functions, which are sufficiently unbalanced or which satisfy some conditions. These upper bounds imply some necessary conditions for vectorial functions to have large nonlinearity.

关键词： Symmetric cryptography block cipher boolean functions vectorial boolean functions s-boxes bent functions nonlinearity covering radius bound

来源：评论

学校读者我要写书评

暂无评论

On the boomerang uniformity of some permutation polynomials

引用

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES boolean functions AND SEQUENCES 2020年第6期12卷 1161-1178页

作者： Calderini, Marco Villa, Irene Univ Bergen Dept Informat PB 7803 N-5020 Bergen Norway

The boomerang attack, introduced by Wagner in 1999, is a cryptanalysis technique against block ciphers based on differential cryptanalysis. In particular it takes into consideration two differentials, one for the upper part of the cipher and one for the lower part, and it exploits the dependency of these two differentials. At Eurocrypt'18, Cid et al. introduced a new tool, called the Boomerang Connectivity Table (BCT), that permits to simplify this analysis. Next, Boura and Canteaut introduced an important parameter for cryptographic S-boxes called boomerang uniformity, that is the maximum value in the BCT. Very recently, the boomerang uniformity of some classes of permutations (in particular quadratic functions) have been studied by Li, Qu, Sun and Li, and by Mesnager, Tang and Xiong. In this paper we further study the boomerang uniformity of some non-quadratic differentially 4-uniform functions. In particular, we consider the case of the Bracken-Leander cubic function and three classes of 4-uniform functions constructed by Li, Wang and Yu, obtained from modifying the inverse functions.

关键词： vectorial boolean functions Boomerang uniformity Boomerang connectivity table Boomerang attack

来源：评论

学校读者我要写书评

暂无评论

An Optimal Universal Construction for the Threshold Implementation of Bijective S-Boxes

引用

IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第10期69卷 6700-6710页

作者： Piccione, Enrico Andreoli, Samuele Budaghyan, Lilya Carlet, Claude Dhooghe, Siemen Nikova, Svetla Petrides, George Rijmen, Vincent Univ Bergen N-5007 Bergen Norway Univ Bergen Selmer Ctr Secure Commun Dept Informat N-5007 Bergen Norway Univ Bergen Selmer Ctr Secure Commun N-5007 Bergen Norway Univ Bergen Dept Informat N-5007 Bergen Norway Univ Paris 08 Dept Math F-93200 St Denis France Katholieke Univ Leuven B-3000 Leuven Belgium Katholieke Univ Leuven Res Grp COSIC Cryptog & Comp Secur ESAT B-3000 Leuven Belgium Katholieke Univ Leuven Dept Elect Engn B-3000 Leuven Belgium Univ Cyprus CY-1678 Nicosia Cyprus

Threshold implementation is a method based on secret sharing to secure cryptographic ciphers (and in particular S-boxes) against differential power analysis side-channel attacks which was proposed by Nikova, Rechberger, and Rijmen in 2006. Until now, threshold implementations were only constructed for specific types of functions and some small S-boxes, but no generic construction was ever presented. In this paper, we present the first universal threshold implementation with t+ 2 shares that is applicable to any bijective S-box, where t is its algebraic degree (or is larger than the algebraic degree). While being universal, our construction is also optimal with respect to the number of shares, since the theoretically smallest possible number, t + 1, is not attainable for some bijective S-boxes. Our results enable low latency secure hardware implementations without the need for additional randomness. In particular, we apply this result to find two uniform sharings of the AES S-box. The first sharing is obtained by using the threshold implementation of the inversion in F-28 and the second by using two threshold implementations of two cubic power permutations that decompose the inversion. Area and performance figures for hardware implementations are provided.

关键词： AES DPA glitches masking permutation polynomials sharing threshold implementations vectorial boolean functions

来源：评论

学校读者我要写书评

暂无评论

Deciding EA-equivalence via invariants

引用

CRYPTOGRAPHY AND COMMUNICATIONS-DISCRETE-STRUCTURES boolean functions AND SEQUENCES 2022年第2期14卷 271-290页

作者： Kaleyski, Nikolay Univ Bergen Dept Informat Bergen Norway

We define a family of efficiently computable invariants for (n, m)-functions under EA-equivalence, and observe that, unlike the known invariants such as the differential spectrum, algebraic degree, and extended Walsh spectrum, in the case of quadratic APN functions over F(2)n with n even, these invariants take on many different values for functions belonging to distinct equivalence classes. We show how the values of these invariants can be used constructively to implement a test for EA-equivalence of functions from F-2(n) to F-2(m);to the best of our knowledge, this is the first algorithm for deciding EA-equivalence without resorting to testing the equivalence of associated linear codes.

关键词： vectorial boolean functions Almost perfect nonlinear (APN) functions Extended affine equivalence (EAequivalence) CCZ-equivalence

来源：评论

学校读者我要写书评

暂无评论

A new large class of functions not APN infinitely often

引用

DESIGNS CODES AND CRYPTOGRAPHY 2014年第2期73卷 601-614页

作者： Caullery, Florian Inst Math Marseille Marseille France

We show that there is no vectorial boolean function of degree , with some conditions on , which is APN over infinitely many extensions of its field of definition. It is a new step in the proof of the conjecture of Aub... 详细信息

关键词： vectorial boolean functions Almost perfect non-linear functions Algebraic surface CCZ equivalence

来源：评论

学校读者我要写书评

暂无评论

Highly nonlinear balanced S-boxes with improved bound on unrestricted and generalized nonlinearity

引用

APPLICABLE ALGEBRA IN ENGINEERING COMMUNICATION AND COMPUTING 2008年第4期19卷 323-338页

作者： Khoo, Khoongming Lim, Chu-Wee Gong, Guang DSO Natl Labs Singapore 118230 Singapore Univ Waterloo Dept Elect & Comp Engn Waterloo ON N2L 3G1 Canada

We construct two classes of balanced S-boxes with high nonlinearity 2(n-1) - 2((n-1)/2) for n odd. From known results, it can be deduced that for any S-box which has nonlinearity 2(n-1) -2((n-1)/2) , the unrestricted nonlinearity is lower bounded by 2(n-1) -2((m+n-1)/2) while the generalized nonlinearity is lower bounded by 2(n-1) -(2(m) -1) 2((n-1)/2). We prove that the lower bound on the unrestricted nonlinearity of both our S-box constructions can be increased to 2(n-1) -2((m+n)/2-1). For the first class of S-box, the lower bound on generalized nonlinearity can be increased to 2(n-1) -2((n-1)/2+m-1). For the second class, the generalized nonlinearity is proven to be exactly 2(n-1) -2((m+n)/2-1), which is much higher than the lower bound for our first construction. The first class of S-boxes have low maximum differential while the second class corresponds to GMW sequences, whose algebraic structure allows us to construct a larger family of S-boxes. Moreover, both classes of S-boxes can attain high algebraic degree. We also compare our constructions with some known functions with high unrestricted and/or generalized nonlinearity.

关键词： generalized nonlinearity unrestricted nonlinearity vectorial boolean functions power functions

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：