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On fault-tolerant boolean functions in proteinoids-ZnO colloids

JOURNAL OF MATERIALS SCIENCE-MATERIALS IN ELECTRONICS 2025年第4期36卷 1-16页

作者： Kheirabadi, Noushin Raeisi Mougkogiannis, Panagiotis Fortulan, Raphael Roberts, Nic Chiolerio, Alessandro Adamatzky, Andrew UWE Unconvent Comp Lab Bristol England Univ Huddersfield Dept Engn & Technol Huddersfield England Ist Italiano Tecnol Ctr Bioinspired Soft Robot Genoa Italy

This study investigates the computational properties of ZnO colloids in combination with proteinoid microspheres within an unconventional computing framework. We propose a method for creating flexible and fault-tolerant logic gates utilising this colloidal system. The colloidal matrix receives binary strings with an electrical impulse representing a logical "True" and its absence representing a "False". Electrical responses are recorded, and boolean functions are extracted. This nano-bio hybrid of ZnO colloids and proteinoids has the potential to power next-generation unconventional computing systems that can adapt to changing environments, paving the way for novel nano-bio hybrid computing architectures.

关键词： boolean functions

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Constructions of Two-Dimensional Golay-ZCZ Array Sets Based on Generalized boolean functions

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IEEE SIGNAL PROCESSING LETTERS 2025年 32卷 321-325页

作者： Prakash, Aditya Kao, Tzu-Chieh Majhi, Sudhan Srivastava, Prashant Kumar Chen, Chao-Yu IIT Patna Dept Math Patna 801106 India Natl Cheng Kung Univ Dept Elect Engn Tainan 701401 Taiwan Natl Cheng Kung Univ Inst Comp & Commun Engn Tainan 701401 Taiwan Indian Inst Sci Dept ECE Bangalore 560012 India

Golay sequences with the zero correlation zone (ZCZ), known as Golay-ZCZ sequences, play a pivotal role in reducing intersymbol interference (ISI) during the process of channel estimation in one dimension. Two-dimensional (2-D) Golay complementary array set (GCAS) within their ZCZ has the potential application in multiple input multiple output (MIMO) omnidirectional transmission. In this letter, 2-D Golay-ZCZ array set is constructed by using generalized boolean function (GBF) without utilizing any kernels. The proposed construction provides 2-D Golay-ZCZ array set with various array sizes and large ZCZ sizes. Also, we get the one dimensional (1-D) Golay- ZCZ sequence set as a special case of the proposed construction.

关键词： Correlation boolean functions Channel estimation Two-dimensional displays Peak to average power ratio NOMA Array signal processing Zero correlation zone Uplink Time-frequency analysis generalized boolean function Golay-ZCZ array

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New Odd-Variable Rotation Symmetric boolean functions Satisfying Good Cryptographic Characteristics

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International Journal of Network Security 2025年第1期27卷 200-212页

作者： Zhao, Qinglan Zhang, Jiandong Zheng, Dong Li, Luyang Xi'an University of Posts and Telecommunications Xi'an710121 China

boolean functions have important applications in cryptography;for example, they have been used as nonlinear components for confusion in block ciphers or stream ciphers. In order to resist known cryptographic attacks, boolean functions need to possess good cryptographic characteristics, including balancedness, maximum Algebraic Immunity (AI), high nonlinearity, and high algebraic degree. Rotation Symmetric boolean functions (RSBFs) is a class of boolean functions with a simple algebraic structure. Researchers have investigated how to construct RSBFs with maximum AI. However, existing RSBFs with maximum AI do not support enough nonlinearity sufficiently against fast correlation attacks. Therefore, constructing new RSBFs to improve their nonlinearity is still required, and this is a challenging target. This paper presents a new class of n-variable RSBFs with maximum AI for odd n. Compared with previous constructions, which apply to all odd n, our functions have the highest nonlinearity when n takes a value bigger than 21. Furthermore, it is proved that our functions can reach the balanced function's maximum algebraic degree n-1 for some values of n. For small n, simulations show these functions possess almost maximum fast AI. © (2025), (Femto Technique Co., Ltd.). All rights reserved.

关键词： boolean functions

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An SRAM-Based Multi-Operand Architecture Implementing Multi-Bit boolean functions Using in-Memory Periphery Computing 38

An SRAM-Based Multi-Operand Architecture Implementing Multi-...

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38th International Conference on VLSI Design, VLSID 2025

作者： Senanayake, Dhayan Dhananjaya Tyagi, Priyanshu Mittal, Sparsh Singhal, Rekha Indian Institute of Technology Roorkee India TCS Reserach India

ISBN: (纸本)9798331522445

This paper introduces a highly scalable in-memory computing architecture for implementing (1) M-operand, N-bit boolean functions, viz., AND/NAND/NOR/OR, (2) any arbitrary boolean function expressed as the sum of products (e.g., F=AB'CD+ABC'D'), (3) N parallel 2-bit XOR operations. Our technique performs operations using a modified 9T SRAM cell-based peripheral circuitry near the SRAM array. Unlike conventional 9T SRAM designs that use the same bitlines for both read and write operations, our design introduces dedicated read lines to separate the read and write paths. This separation improves efficiency and allows in-memory implementation of complex boolean operations. To implement M-operand, N-bit AND/OR operations, the periphery circuit has N compute blocks, each with M columns. The compute block stores the input operands along with configuration bits to choose the correct operation. An equality checker circuit compares the input operands with configuration bits to obtain original or complemented input. The outputs of equality checkers of different columns are connected to a product line, and by DeMorgan's theorem, either AND/NAND or NOR/OR can be realized. Using TSMC 65nm PDK in Cadence Virtuoso, we have demonstrated 64-bit AND/NAND/OR/NOR operations and 64 parallel 2-bit XOR operations. At 0.7V VDD, our design consumes 24.5fJ/bit and operates at 660MHz for XOR operations and 384MHz for other operations. © 2025 IEEE.

关键词： boolean functions

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Construction and Count of 1-Resilient Rotation Symmetric boolean functions on pr Variables

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Chinese Journal of Electronics 2025年第4期23卷 816-820页

作者： Jiao Du Shanqi Pang Qiaoyan Wen Xin Liao College of Mathematics and Information Science Henan Normal University Xinxiang China State Key Laboratory of Networking and Switching Technology Beijing University of Posts and Telecommunications Beijing China College of Information Science and Engineering Hunan University Changsha China

Construction and count of 1-resilient Rotation symmetric boolean functions (RSBFs) on $p^{r}$ variables are demonstrated. It is proved that constructions of 1-resilient RSBFs on $p^{r}$ variables are equivalent to solving an equation system. An accurate enumeration formula of all 1-resilient RSBFs on $p^{r}$ variables is also proposed. Some examples are given, and the exact numbers of 1-resilient RSBFs on 8 and 9 variables are obtained respectively.

关键词： Sufficient conditions boolean functions Accuracy Education Medical services NP-complete problem Cryptography

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The More the Merrier: On Evolving Five-Valued Spectra boolean functions

The More the Merrier: On Evolving Five-Valued Spectra Boole...

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28th European Conference on Applications of Evolutionary Computation, EvoApplications 2025, held as part of EvoStar 2025

作者： Carlet, Claude Đurasević, Marko Jakobovic, Domagoj Mariot, Luca Picek, Stjepan Department of Mathematics Université Paris 8 2 Rue de la Liberté Saint-Denis Cedex 93526 France University of Bergen Bergen Norway Faculty of Electrical Engineering and Computing University of Zagreb Unska 3 Zagreb Croatia Semantics Cybersecurity and Services Group University of Twente Drienerlolaan 5 NB Enschede 7522 Netherlands Digital Security Group Radboud University PO Box 9010 Nijmegen Netherlands

ISBN: (纸本)9783031900617

Evolving boolean functions with specific properties is an interesting optimization problem since, depending on the combination of properties and boolean function size, the problem can range from very simple to (almost) impossible to solve. Some problems are more interesting as there may be only a few options for generating the required boolean functions. This paper investigates one such problem: evolving five-valued spectra boolean functions, the functions whose Walsh-Hadamard coefficients can only take five distinct values. We experimented with three solution encodings, two fitness functions, and 12 boolean function sizes and showed that the tree encoding is superior to other choices, as we can obtain five-valued boolean functions with high nonlinearity. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： boolean functions Evolutionary Algorithms Five-valued functions Plateaudness

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An SRAM-Based Multi-Operand Architecture Implementing Multi-Bit boolean functions Using in-Memory Periphery Computing

An SRAM-Based Multi-Operand Architecture Implementing Multi-...

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International Conference on VLSI Design

作者： Dhayan Dhananjaya Senanayake Priyanshu Tyagi Sparsh Mittal Rekha Singhal Indian Institute of Technology Roorkee TCS Reserach

ISBN: (数字)9798331522445

ISBN: (纸本)9798331522452

This paper introduces a highly scalable in-memory computing architecture for implementing (1) $M$ -operand, $N$ -bit boolean functions, viz., AND/NAND/NOR/OR, (2) any arbitrary boolean function expressed as the sum of products (e.g., F=AB'CD+ABC'D'), (3) $N$ parallel 2-bit XOR operations. Our technique performs operations using a modified 9T SRAM cell-based peripheral circuitry near the SRAM array. Unlike conventional 9T SRAM designs that use the same bitlines for both read and write operations, our design introduces dedicated read lines to separate the read and write paths. This separation improves efficiency and allows in-memory implementation of complex boolean operations. To implement $M$ -operand, $N$ -bit AND/OR operations, the periphery circuit has $N$ compute blocks, each with $M$ columns. The compute block stores the input operands along with configuration bits to choose the correct operation. An equality checker circuit compares the input operands with configuration bits to obtain original or complemented input. The outputs of equality checkers of different columns are connected to a product line, and by DeMorgan's theorem, either AND/NAND or NOR/OR can be realized. Using TSMC 65nm PDK in Cadence Virtuoso, we have demonstrated 64-bit AND/NAND/OR/NOR operations and 64 parallel 2-bit XOR operations. At 0.7V VDD, our design consumes 24.5fJ/bit and operates at 660MHz for XOR operations and 384MHz for other operations.

关键词： boolean functions Simulation Scalability Random access memory Computer architecture Very large scale integration Energy efficiency Logic Standards Logic arrays

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A Quantum Algorithm for the Classification of Patterns of boolean functions

arXiv

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arXiv 2025年

作者： Andronikos, Theodore Bitsakos, Constantinos Nikas, Konstantinos Goumas, Georgios I. Koziris, Nectarios Department of Informatics Ionian University 7 Tsirigoti Square Corfu49100 Greece Computing Systems Laboratory National Technical University of Athens Greece

This paper introduces a novel quantum algorithm that is able to classify a hierarchy of classes of imbalanced boolean functions. The fundamental characteristic of imbalanced boolean functions is that the proportion of elements in their domain that take the value 0 is not equal to the proportion of elements that take the value 1. For every positive integer n, the hierarchy contains a class of boolean functions defined based on their behavioral pattern. The common trait of all the functions belonging to the same class is that they possess the same imbalance ratio. Our algorithm achieves classification in a straightforward manner as the final measurement reveals the unknown function with probability 1. Let us also note that the proposed algorithm is an optimal oracular algorithm because it can classify the aforementioned functions with a single query to the oracle. At the same time we explain in detail the methodology we followed to design this algorithm in the hope that it will prove general and fruitful, given that it can be easily modified and extended to address other classes of imbalanced boolean functions that exhibit different behavioral patterns. © 2025, CC BY.

关键词： boolean functions

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A Systematic Evaluation of Evolving Highly Nonlinear boolean functions in Odd Sizes

A Systematic Evaluation of Evolving Highly Nonlinear Boolea...

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28th European Conference on Genetic Programming, EuroGP 2025, Held as Part of EvoStar 2025

作者： Carlet, Claude Đurasević, Marko Jakobović, Domagoj Picek, Stjepan Mariot, Luca Department of Mathematics Université Paris 8 2 Rue de la Liberté Saint-Denis Cedex 93526 France University of Bergen Bergen Norway Faculty of Electrical Engineering and Computing University of Zagreb Unska 3 Zagreb Croatia Digital Security Group Radboud University PO Box 9010 Nijmegen Netherlands Semantics Cybersecurity and Services Group University of Twente Drienerlolaan 5 Enschede 7522 NB Netherlands

ISBN: (纸本)9783031899904

boolean functions are mathematical objects used in diverse applications. Different applications also have different requirements, making the research on boolean functions very active. In the last 30 years, evolutionary algorithms have been shown to be a strong option for evolving boolean functions in different sizes and with different properties. Still, most of those works consider similar settings and provide results that are mostly interesting from the evolutionary algorithm’s perspective. This work considers the problem of evolving highly nonlinear boolean functions in odd sizes. While the formulation sounds simple, the problem is remarkably difficult, and the related work is extremely scarce. We consider three solutions encodings and four boolean function sizes and run a detailed experimental analysis. Our results show that GP outperforms other EA in evolving highly nonlinear functions. Nevertheless, the problem is challenging, and finding optimal solutions is impossible except for the smallest tested size. However, once we added local search to the evolutionary algorithm, we managed to find a boolean function in nine inputs with nonlinearity 241, which, to our knowledge, had never been accomplished before with evolutionary algorithms. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： boolean functions encodings evolutionary algorithms genetic programming nonlinearity odd dimension

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boolean functions with five controllable cryptographic properties

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DESIGNS CODES AND CRYPTOGRAPHY 2004年第2期31卷 147-157页

作者： Stanica, P Sung, SH Pai Chai Univ Dept Appl Math Taejon 302735 South Korea Auburn Univ Dept Math Montgomery AL 36124 USA Romanian Acad Inst Math Bucharest Romania

The strict avalanche criterion (SAC) was introduced by Webster and Tavares [10] in a study of cryptographic design criteria. This is an indicator for local property. In order to improve the global analysis of cryptographically strong functions, Zhang and Zheng [ 11] introduced the global avalanche characteristics (GAC). The sum-of-squares indicator related to the GAC is defined as sigma(f) = Sigma(nu)Delta(f)(2)(nu), where Delta(f)(nu) = Sigma(x)(-1)(f(x)+ f(x + nu)). In this paper, we give a few methods to construct boolean functions controlling five good cryptographic properties, namely balancedness, good local and GAC, high nonlinearity and high algebraic degree. We improve upon the results of Stanica [ 8] and Zhang and Zheng [11].

关键词： cryptography nonlinearity boolean functions strict avalanche criterion global avalanche characteristics

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