检索结果-内蒙古大学图书馆

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

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

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

A Review of Lightweight Cryptographic Schemes and Fundamental Cryptographic Characteristics of boolean functions

引用

Advances in Internet of Things 2022年第1期12卷 9-17页

作者： Nahla Fatahelrahman Ibrahim Johnson Ihyeh Agbinya Faculty of Computer Science and Information Technology Sudan University of Science and Technology (SUST) Khartoum Sudan School of Information Technology and Engineering Melbourne Institute of Technology Melbourne Victoria Australia

In this paper, we survey a number of studies in the literature on improving lightweight systems in the Internet of Things (IoT). The paper illustrates recent development of boolean cryptographic function Application and how it assists in using hardware such as the internet of things. For a long time there seems to be little progress in applying pure mathematics in providing security since the wide progress made by George Boole and Shannon. We discuss cryptanalysis of boolean functions to avoid trapdoors and vulnerabilities in the development of block ciphers. It appears that there is significant progress. A comparative analysis of lightweight cryptographic schemes is reported in terms of execution time, code size and throughput. Depending on the schemes and the structure of the algorithms, these parameters change but remain within reasonable values making them suited for Internet of things applications. The driving force of lightweight cryptography (LWC) stems mainly from its direct applications in the real world since it provides solutions to actual problems faced by designers of IoT systems. Broadly speaking, lightweight cryptographic algorithms are designed to achieve two main goals. The first goal of a cryptographic algorithm is to withstand all known cryptanalytic attacks and thus to be secure in the black-box model. The second goal is to build the cryptographic primitive in such a way that its implementations satisfy a clearly specified set of constraints that depend on a case-by-case basis.

关键词： Internet of Things Lightweight Cryptographic Scheme vectorial boolean functions IoT Differential Cryptanalysis

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

Low c-differential and c-boomerang uniformity of the swapped inverse function

引用

DISCRETE MATHEMATICS 2021年第10期344卷 112543-112543页

作者： Stanica, Pantelimon Naval Postgrad Sch Appl Math Dept Monterey CA 93943 USA

Modifying the binary inverse function in a variety of ways, like swapping two output points has been known to produce a 4-differential uniform permutation function. Recently, in [21] it was shown that this swapped version of the inverse function has boomerang uniformity exactly 10, if n equivalent to 0 (mod 6), 8, if n equivalent to 3 (mod 6), and 6, if n not equivalent to 0 (mod 3). Based upon the c-differential and c-boomerang uniformity notions we defined in [16], respectively, [30], in this paper we characterize the c-differential and c-boomerang uniformity for the (0, 1)-swapped inverse function in even characteristic, x(2n-2) + x(2n-1) + (x + 1)(2n-1) on F-2n: we show that for all c not equal 1, the c-differential uniformity is upper bounded by 4 and the c-boomerang uniformity by 5 with both bounds being attained for n >= 4. Published by Elsevier B.V.

关键词： vectorial boolean functions c-differential uniformity c-boomerang uniformity Finite field equations

来源：评论

学校读者我要写书评

暂无评论

NEW CONSTRUCTIONS OF vectorial boolean functions WITH GOOD CRYPTOGRAPHIC PROPERTIES

引用

INTERNATIONAL JOURNAL OF FOUNDATIONS OF COMPUTER SCIENCE 2012年第3期23卷 749-760页

作者： Dong, Deshuai Qu, Longjiang Fu, Shaojing Li, Chao Natl Univ Def Technol Coll Sci Changsha 410073 Hunan Peoples R China Natl Univ Def Technol Sch Comp Sci Changsha 410073 Hunan Peoples R China

vectorial boolean functions play an important role in cryptography. How to construct vectorial boolean functions with good cryptographic properties is a nice problem that worth to be investigated. In this paper we present several constructions of balanced vectorial boolean functions with high algebraic immunity, high (or optimum) algebraic degree, and very high nonlinearity. In some cases, the constructed functions also achieve optimum algebraic immunity.

关键词： vectorial boolean functions algebraic immunity nonlinearity

来源：评论

学校读者我要写书评

暂无评论

On (2n/3-1)-Resilient (n, 2)-functions

On (2n/3-1)-Resilient (n, 2)-Functions

引用

IEEE International Symposium on Information Theory (ISIT)

作者： Krotov, Denis S. Sobolev Inst Math Novosibirsk 630090 Russia

ISBN: (纸本)9781538692912

A {00,01,10,11}-valued function on the vertices of the n-cube is called a t-resilient (n,2)-function if it has the same number of 00s, 01s, 10s and 11s among the vertices of every subcube of dimension t. The Friedman and Fon-Der-Flaass bounds on the correlation immunity order say that such a function must satisfy t <= 2n/3 - 1;moreover, the (2n/3 - 1)-resilient (n,2)-functions correspond to the equitable partitions of the n-cube with the quotient matrix [[0, r, r, r], [r, 0, r, r], [r, r, 0, r], [r, r, r, 0]], r = n/3. We suggest constructions of such functions and corresponding partitions, show connections with Latin hypercubes and binary 1-perfect codes, characterize the non-full-rank and the reducible functions from the considered class, and discuss the possibility to make a complete characterization of the class.

关键词： vectorial boolean functions resilient boolean functions correlation-immune functions equitable partitions Latin hypercubes

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

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

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：