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BFROU: A Reconfigurable Operation Unit Design Approach Using NPN Equivalence and Reed-Muller Logic Unit for Boolean Functions in Stream Ciphers 认领 引用
1
作者 Zhaoxu Zhou Yanjiang Liu +1 位作者 Zibin Dai Junwei Li 《Computers, Materials & Continua》 SCIE EI 2026年第8期806-832,共27页
Stream ciphers are simple to implement and fast at encrypting and decrypting data,making them very important in information security.Boolean functions are a core part of stream ciphers.However,their mainstream hardwar... Stream ciphers are simple to implement and fast at encrypting and decrypting data,making them very important in information security.Boolean functions are a core part of stream ciphers.However,their mainstream hardware implementations face two main problems,including wasted area resources and excessive critical path delay.These issues limit the energy efficiency and integration level of stream cipher chips.To address these problems,this paper proposes an energy-efficient design method for a 64-bit Boolean function reconfigurable operation unit(BFROU),aiming to improve the computational efficiency of Boolean functions in stream ciphers.To optimize the design of BFROU,this paper takes the NPN equivalence theory as a guide.First,customized designs at the transistor level were performed for both 2-and 3-variable RM logic units(denoted as TRM).On this basis,this paper uses the port sharing strategy to further optimize the design of 4-to-6-variable TRM logic units and construct a multi-variable TRM process library.Then,by combining multi-variable TRM logic units with the mathematical definition of Boolean functions,this paper proposes a theoretical model of BFROU.Based on this model and combined with the statistical analysis results of Boolean functions,the optimal TRM unit configuration is determined,and the overall optimization of the 64-bit BFROU is finally completed.Experimental results show that when TRM-3 and TRM-4 units are mixed as the first-level operation module of BFROU,its area-delay product(ADP)reaches the minimum.The 64-bit BFROU unit implemented according to this scheme has an actual measured area of 137.28μm2 and a critical path delay of 0.278 ns under the SMIC 40 nm typical process corner.This unit supports Boolean function operations with up to 64 variables,and 94.4%of the functions can complete mapping within 2 iterations.Compared with existing schemes such as look-up table(LUT)architecture and And-Inverter Cone(AIC)array,the BFROU proposed in this paper has obvious advantages in area,delay,ADP and number of iterations,providing effective hardware support for the design of high-energy-efficiency stream cipher chips. 展开更多
关键词 Boolean function reconfigurable operation unit stream cipher TRM units NPN equivalence theory
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Construction of Even-Variable 2-Output Almost Optimal Five-Valued Spectra Boolean Functions 认领 引用
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作者 SONG Chao-Fan JI Yan-Han SUN Yu-Juan 《密码学报（中英文）》 CSCD 北大核心 2025年第3期714-728,共15页
Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively ... Five-valued Boolean functions play an important role in the design of symmetric cryptography.While the design and properties of single-output almost optimal five-valued spectra Boolean functions have been extensively studied over the past few decades,there has been limited research on the construction of almost optimal five-valued spectra vectorial Boolean functions.In this paper,we present a construction method for even-variable 2-output almost optimal five-valued spectra balanced Boolean functions,whose Walsh spectra values belong to the set{0,±2n/2,±2n/2+1},at the same time,we discuss the existence of sufficient conditions in the construction.Additionally,this paper presents a novel construction method for balanced single-output Boolean functions with even variables featuring a special five-valued spectral structure,whose Walsh spectra values are constrained to the set{0,±2n/2,±3·2n/2}.These functions provide new canonical examples for the study of Boolean function spectral theory. 展开更多
关键词 Boolean function Walsh transform semi-bent function five-valued function totally disjoint spectra functions
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A Class of Rotation Symmetric Boolean Functions with Optimum Algebraic Immunity 认领 引用 被引量：5
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作者 LI Chunlei ZENG Xiangyong +1 位作者 SU Wei HU Lei 《Wuhan University Journal of Natural Sciences》 CAS 2008年第6期702-706,共5页
For an odd integer n ≥ 7, this paper presented a class of n-variable rotation symmetric Boolean functions （RSBFs） with optimum algebraic immunity. The nonlinearity of the constructed functions is determined.
关键词 rotation symmetric Boolean functions（RSBFs） algebraic immunity nonlinearity balancedness Krawtchouk polynomial
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Construction of Balanced Rotation Symmetric Boolean Functions with Optimal Algebraic Immunity 认领 引用 被引量：1
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作者 ZHANG Wenying 《Wuhan University Journal of Natural Sciences》 CAS 2014年第4期301-306,共6页
Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This ... Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents one main result to find balanced rotation symmetric Boolean functions with maximum algebraic immunity. Through swapping the values of two orbits of rotation class of the majority function, a class of 4k＋l variable Boolean functions with maximum algebraic immu- nity is constructed. The function f（x） we construct always has terms of degree n-2 independence of what ever n is. And the nonlinearity off（x） is relatively good for large n. 展开更多
关键词 Boolean function algebraic attack Walsh spectrum algebraic degree algebraic immunity （AI）
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Evolutionary Design of Boolean Functions 认领 引用
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作者 WANG Zhang-yi ZHANG Huan-guo +1 位作者 QIN Zhong-ping MENG Qing-shu 《Wuhan University Journal of Natural Sciences》 EI CAS 2005年第1期179-182,共4页
We use evolutionaly computing to synthesize Boolean functions randomly Byusing specific crossover and mutation operator,in evolving process and modifying search space andfitness function,we get some high non-linearity... We use evolutionaly computing to synthesize Boolean functions randomly Byusing specific crossover and mutation operator,in evolving process and modifying search space andfitness function,we get some high non-linearity functions which have other good cryptographycharacteristics such as autocorrelation etc Comparing to other heuristic search techniques,evolutionary computing approach is more effective because of global search strategy and implicitparallelism. 展开更多
关键词 Boolean function non-linearity evolutionary computing
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The Walsh Transform of a Class of Boolean Functions 认领 引用
6
作者 JIANG Niu ZHUO Zepeng +1 位作者 CHEN Guolong WANG Liting 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2021年第6期453-458,共6页
The Walsh transform is an important tool to investigate cryptographic properties of Boolean functions.This paper is devoted to study the Walsh transform of a class of Boolean functions defined as g(x)=f(x)Trn1(x... The Walsh transform is an important tool to investigate cryptographic properties of Boolean functions.This paper is devoted to study the Walsh transform of a class of Boolean functions defined as g(x)=f(x)Trn1(x)+h(x)Trn1(δx),by making use of the known conclusions of Walsh transform and the properties of trace function,and the conclusion is obtained by generalizing an existing result. 展开更多
关键词 Boolean function Walsh transform trace function
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Construction of Odd-Variable Boolean Function with Maximum Algebraic Immunity Using Univariate Polynomial Representation 认领 引用
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作者 Zhao Wentao Fu Shaojing +1 位作者 Li Chao Qu Longjiang 《China Communications》 SCIE CSCD 2012年第10期33-39,共7页
To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation o... To protect against algebraic attacks, a high algebraic immunity is now an important criterion for Boolean functions used in stream ciphers. In this paper, a new method based on a univariate polynomial representation of Boolean functions is proposed. The proposed method is used to constmct Boolean functions with an odd number of variables and with maximum algebraic immunity. We also discuss the nonlinearity of the constructed functions. Moreover, a lower bound is deter- mined for the number of Boolean functions with rmximum algebraic immunity. 展开更多
关键词 cryptography boolean function alge- braic attack algebraic immunity
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Find Better Boolean Functions in the Affine Equivalence Class 认领 引用 被引量：2
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作者 CHEN Wei-hong LI Na 《Chinese Quarterly Journal of Mathematics》 北大核心 2005年第4期395-400,共6页
The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this ... The Boolean functions in an affine equivalence class are of the same algebraicdegree and nonlinearity, but may satisfy different order of correlation immunity and propa-gation criterion. A method is presented in this paper to find Boolean functions with higherorder correlation immunity or satisfying higher order propagation criterion in an affine equiv-alence class. 8 AES s-box functions are not better Boolean functions in their affine equiva-lence class. 展开更多
关键词 Boolean function Walsh spectra balance nonlinearity correlation immunity propagation criterion AES s-box
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On the construction of cryptographically strong Boolean functions with desirable trade-off 认领 引用 被引量：1
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作者 REN Kui PARK Jaemin KIM Kwangjo 《Journal of Zhejiang University-SCIENCE A》 CAS 2005年第5期358-364,共7页
This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the res... This paper proposes a practical algorithm for systematically generating strong Boolean functions (f:GF(2) n →GF(2)) with cryptographic meaning. This algorithm takes bent function as input and directly outputs the resulted Boolean function in terms of truth table sequence. This algorithm was used to develop two classes of balanced Boolean functions, one of which has very good cryptographic properties:nl(f)=2 2k?1?2k+2k?2 (n=2k), with the sum-of-squares avalanche characteristic off satisfying σf=24k+23k+2+23k-2 and the absolute avalanche characteristic off satisfying σf=24k+23k+2+23k-2. This is the best result up to now compared to existing ones. Instead of bent sequences, starting from random Boolean functions was also tested in the algorithm. Experimental results showed that starting from bent sequences is highly superior to starting from random Boolean functions. Key words Boolean functions - Bent sequences - Nonlinearity - GAC - PC - Balancedness Document code A CLC number TP301.6 展开更多
关键词 Boolean functions Bent sequences Nonlinearity GAC PC Balancedness
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A Review of Lightweight Cryptographic Schemes and Fundamental Cryptographic Characteristics of Boolean Functions 认领 引用
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作者 Nahla Fatahelrahman Ibrahim Johnson Ihyeh Agbinya 《Advances in Internet of Things》 2022年第1期9-17,共9页
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 a... 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. 展开更多
关键词 Internet of Things Lightweight Cryptographic Scheme Vectorial Boolean Functions IoT Differential Cryptanalysis
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On Boolean Functions Associated to Finite Aligned Spaces 认领 引用
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作者 Jose Manuel dos Santos Simoes Pereira 《Journal of Mathematics and System Science》 2018年第3期74-76,共3页
Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated ... Boolean or switching functions can be associated to finite aligned spaces in a way similar to the way they can be associated to finite topological spaces. We prove a characterization of switching functions associated to aligned spaces which is similar to the one we have given for switching functions associated to finite topological spaces. 展开更多
关键词 Aligned space topological space boolean function switching function.
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Some results on the algebraic immunity of Boolean functions 认领 引用 被引量：1
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作者 XU Li-qing CHEN hao 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2011年第2期102-105,共4页
From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity（AI） of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary conditio... From the motivation of algebraic attacks on stream and block ciphers,the concept of algebraic immunity（AI） of a Boolean function was introduced and studied extensively.High algebraic immunity is a necessary condition for resisting algebraic attacks.In this paper,we give some lower bounds on the algebraic immunity of Boolean functions.The results are applied to give lower bounds on the AI of symmetric Boolean functions and rotation symmetric Boolean functions.Some balanced rotation symmetric Boolean functions with their AI near the maximum possible value「n/2」are constructed. 展开更多
关键词 algebraic attack Boolean function AI symmetric Boolean function rotation symmetric Boolean function
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The autocorrelation distribution of balanced Boolean function 认领 引用 被引量：5
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作者 Yu ZHOU Weiguo ZHANG +2 位作者 Juan LI Xinfeng DONG Guozhen XIAO 《Frontiers of Computer Science》 SCIE EI CSCD 2013年第2期272-278,共7页
The global avalanche characteristics （the sum- of-squares indicator and the absolute indicator） measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. （1999） gave the lower ... The global avalanche characteristics （the sum- of-squares indicator and the absolute indicator） measure the overall avalanche characteristics of a cryptographic Boolean function. Sung et al. （1999） gave the lower bound on the sum- of-squares indicator for a balanced Boolean function satisfy- ing the propagation criterion with respect to some vectors. In this paper, if balanced Boolean functions satisfy the propaga- tion criterion with respect to some vectors, we give three nec- essary and sufficient conditions on the auto-correlation distri- bution of these functions reaching the minimum the bound on the sum-of-squares indicator. And we also find all Boolean functions with 3-variable, 4-variable, and 5-variable reaching the minimum the bound on the sum-of-squares indicator. 展开更多
关键词 Boolean functions auto-correlation distribu-tion global avalanche characteristics balanced propagationcriterion
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Construction of 1-Resilient Boolean Functions with Optimal Algebraic Immunity and Good Nonlinearity 认领 引用 被引量：6
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作者 潘森杉 傅晓彤 张卫国 《Journal of Computer Science & Technology》 SCIE EI CSCD 2011年第2期269-275,共7页
This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in assoc... This paper presents a construction for a class of 1-resilient functions with optimal algebraic immunity on an even number of variables. The construction is based on the concatenation of two balanced functions in associative classes. For some n, a part of 1-resilient functions with maximum algebraic immunity constructed in the paper can achieve almost optimal nonlinearity. Apart from their high nonlinearity, the functions reach Siegenthaler＇s upper bound of algebraic degree. Also a class of l-resilient functions on any number n 〉 2 of variables with at least sub-optimal algebraic immunity is provided. 展开更多
关键词 stream ciphers Boolean functions 1-resilient algebraic immunity algebraic degree
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A Construction of 1-Resilient Boolean Functions with Good Cryptographic Properties 认领 引用 被引量：2
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作者 SHAN Jinyong HU Lei +1 位作者 ZENG Xiangyong LI Chunlei 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2018年第4期1042-1064,共23页
This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic im... This paper proposes a general method to construct 1-resilient Boolean functions by modifying the Tu-Deng and Tang-Carlet-Tang functions. Cryptographic properties such as algebraic degree, nonlinearity and algebraic immunity are also considered. A sufficient condition of the modified func- tions with optimal algebraic degree in terms of the Siegenthaler bound is proposed. The authors obtain a lower bound on the nonlinearity of the Tang-Carlet-Tang functions, which is slightly better than the known result. If the authors do not break the ＂continuity＂ of the support and zero sets, the functions constructed in this paper have suboptimal algebraic immunity. Finally, four specific classes of 1-resilient Boolean functions constructed from this construction and with the mentioned good cryptographic properties are proposed. Experimental results show that there are many 1-resilient Boolean functions have higher nonlinearities than known l-resilient functions modified by Tu-Deng and Tang- Carlet-Tang functions. 展开更多
关键词 Algebraic immunity Boolean functions correlation immunity nonlinearity resilient
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Analysis of affinely equivalent Boolean functions 认领 引用 被引量：6
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作者 MENG QingShu ZHANG HuanGuo +1 位作者 YANG Min WANG ZhangYi 《Science in China(Series F)》 2007年第3期299-306,共8页
By some basic transforms and invariant theory, we give two results： 1） an algorithm, which can be used to judge if two Boolean functions are affinely equivalent and to obtain the equivalence relationship if they are... By some basic transforms and invariant theory, we give two results： 1） an algorithm, which can be used to judge if two Boolean functions are affinely equivalent and to obtain the equivalence relationship if they are equivalent. This is useful in studying Boolean functions and in engineering. For example, we classify all 8-variable homogeneous bent functions of degree 3 into two classes; 2） Reed-Muller codes R（4,6）/R（1,6）, R（3,7）/R（1,7） are classified efficiently. 展开更多
关键词 Boolean functions Reed-Muller code affinely equivalent invariant
On the 2~m-variable symmetric Boolean functions with maximum algebraic immunity 认领 引用 被引量：13
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作者 QU LongJiang LI Chao 《Science in China(Series F)》 2008年第2期120-127,共8页
The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtaine... The properties of the 2m-variable symmetric Boolean functions with maximum al- gebraic immunity are studied in this paper. Their value vectors, algebraic normal forms, and algebraic degrees and weights are all obtained. At last, some necessary conditions for a symmetric Boolean function on even number variables to have maximum algebraic immunity are introduced. 展开更多
关键词 algebraic immunity algebraic attack symmetric Boolean function
Construction and enumeration of Boolean functions with maximum algebraic immunity 认领 引用 被引量：4
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作者 ZHANG WenYing WU ChuanKun LIU XiangZhong 《Science in China(Series F)》 2009年第1期32-40,共9页
Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This ... Algebraic immunity is a new cryptographic criterion proposed against algebraic attacks. In order to resist algebraic attacks, Boolean functions used in many stream ciphers should possess high algebraic immunity. This paper presents two main results to find balanced Boolean functions with maximum algebraic immunity. Through swapping the values of two bits, and then generalizing the result to swap some pairs of bits of the symmetric Boolean function constructed by Dalai, a new class of Boolean functions with maximum algebraic immunity are constructed. Enumeration of such functions is also n given. For a given function p（x） with deg（p（x）） 〈 [n/2], we give a method to construct functions in the form p（x）＋q（x） which achieve the maximum algebraic immunity, where every term with nonzero coefficient in the ANF of q（x） has degree no less than [n/2]. 展开更多
关键词 cryptography algebraic attack algebraic immunity Boolean function
A Study on Monotone Self-Dual Boolean Functions 认领 引用
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作者 Mustafa ALTUN Marc D.RIEDEL 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2017年第1期43-52,共10页
This paper shows that monotone self-dual Boolean functions in irredundant disjuntive normal form （IDNF） do not have more variables than disjuncts. Monotone self-dual Boolean functions in IDNF with the same number of... This paper shows that monotone self-dual Boolean functions in irredundant disjuntive normal form （IDNF） do not have more variables than disjuncts. Monotone self-dual Boolean functions in IDNF with the same number of variables and disjuncts are examined. An algorithm is proposed to test whether a monotone Boolean function in IDNF with n variables and n disjuncts is self-dual. The runtime of the algorithm is O（n3）. 展开更多
关键词 duality problem monotone Boolean functions self-dual Boolean functions
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A NOTE ON TWO CLASSES OF BOOLEAN FUNCTIONS WITH OPTIMAL ALGEBRAIC IMMUNITY 认领 引用
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作者 WU Baofeng LIU Zhuojun +1 位作者 JIN Qingfang ZHANG Xiaoming 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2014年第4期785-794,共10页
Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture.In this paper,the authors compute the dual of the Tu-Deng functions and then sh... Tu and Deng proposed a class of bent functions which are of optimal algebraic immunity under the assumption of a combinatorial conjecture.In this paper,the authors compute the dual of the Tu-Deng functions and then show that they are still of optimal algebraic immunity under the assumption of the same conjecture.For another class of Boolean functions constructed by Tang,et al.which are of optimal algebraic immunity with similar forms to Tu-Deng functions,the authors show that they are not bent functions by using some basic properties of binary complete Kloosterman sums. 展开更多
关键词 Algebraic immunity bent function Boolean function Kloosterman sums Walsh trans-form.
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