Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties

Tang, Deng; Zhang, Weiguo; Tang, Xiaohu

doi:10.1007/s10623-011-9587-9

Cited by 21 publications

(14 citation statements)

References 13 publications

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“…Motivated by the related work from Burnett [ 18 ] and Izbenko [ 19 ], we considered the application of an algebraic procedure to improve our results. Contrary to their work, we decided not to use bent functions, instead we employ the work from Tang [ 32 ] to build an initial population of individuals with high nonlinearity. Thus, the only change appears in the initialization procedure of the population.…”

Section: Population-based Proposalsmentioning

confidence: 99%

“…Tang [ 32 ] proposes a method capable of constructing balanced BFs of even number of variables with relatively high nonlinearity. Their construction is based on a modification of the Maiorana-McFarland [ 20 ] method to construct bent BFs.…”

Section: Population-based Proposalsmentioning

confidence: 99%

“…The initialization strategy allows to generate up to 1310400 BFs with nonlinearity equal to 488. In order to make 50 independent runs and each one with a population size equal to 350, we built 17,500 (

) individuals with nonlinearity equal to 488 with the initialization algorithm [ 32 ]. Each population was employed with the three evolutionary methods: MAC-REDDCC, LMA-REDDC and LMA-GRE.…”

Section: Population-based Proposalsmentioning

confidence: 99%

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Metaheuristics in the Optimization of Cryptographic Boolean Functions

López-López

Sosa-Gómez

Segura

et al. 2020

Entropy

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Generating Boolean Functions (BFs) with high nonlinearity is a complex task that is usually addresses through algebraic constructions. Metaheuristics have also been applied extensively to this task. However, metaheuristics have not been able to attain so good results as the algebraic techniques. This paper proposes a novel diversity-aware metaheuristic that is able to excel. This proposal includes the design of a novel cost function that combines several information from the Walsh Hadamard Transform (WHT) and a replacement strategy that promotes a gradual change from exploration to exploitation as well as the formation of clusters of solutions with the aim of allowing intensification steps at each iteration. The combination of a high entropy in the population and a lower entropy inside clusters allows a proper balance between exploration and exploitation. This is the first memetic algorithm that is able to generate 10-variable BFs of similar quality than algebraic methods. Experimental results and comparisons provide evidence of the high performance of the proposed optimization mechanism for the generation of high quality BFs.

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Section: Population-based Proposalsmentioning

confidence: 99%

Section: Population-based Proposalsmentioning

confidence: 99%

) individuals with nonlinearity equal to 488 with the initialization algorithm [ 32 ]. Each population was employed with the three evolutionary methods: MAC-REDDCC, LMA-REDDC and LMA-GRE.…”

Section: Population-based Proposalsmentioning

confidence: 99%

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Metaheuristics in the Optimization of Cryptographic Boolean Functions

López-López

Sosa-Gómez

Segura

et al. 2020

Entropy

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“…Reference [10] derived a new bound on the sum-of-squares indicator and gave a method to construct balanced Boolean functions with ( ≥ 6) variables by the disjoint spectra functions, where is an even integer, satisfying strict avalanche criterion, high nonlinearity, and lower . Meanwhile, some authors gave lots of constructions of Boolean functions with good , Tang [11] gave a method to construct balanced Boolean functions of variables, the constructed functions possess the highest nonlinearity and the better global avalanche characteristics ( ) property, but they only obtained an upper bound of . Reference [12] gave a method to construct high nonlinearity Boolean function.…”

Section: Introductionmentioning

confidence: 99%

Measuring the Sum-of-Squares Indicator of Boolean Functions in Encryption Algorithm for Internet of Things

Zhou¹,

Wei

Zhang

2019

Security and Communication Networks

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Encryption algorithm has an important application in ensuring the security of the Internet of Things. Boolean function is the basic component of symmetric encryption algorithm, and its many cryptographic properties are important indicators to measure the security of cryptographic algorithm. This paper focuses on the sum-of-squares indicator of Boolean function; an upper bound and a lower bound of the sum-of-squares on Boolean functions are obtained by the decomposition Boolean functions; some properties and a search algorithm of Boolean functions with the same autocorrelation (or cross-correlation) distribution are given. Finally, a construction method to obtain a balanced Boolean function with small sum-of-squares indicator is derived by decomposition Boolean functions. Compared with the known balanced Boolean functions, the constructed functions have the higher nonlinearity and the better global avalanche characteristics property.

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“…Unfortunately, they are not balanced and cannot be directly used in many cryptographic systems. Therefore, the construction of balanced functions with high nonlinearity and good autocorrelation properties has been become an important challenge and it was extensively studied in [1,5,8,9] and the best trade-off was given in [11].…”

Section: Introductionmentioning

confidence: 99%

Construction of balanced Boolean functions with high nonlinearity, good local and global avalanche characteristics

Sun

Zhang

2016

Front. Math. China

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Boolean functions possessing multiple cryptographic criteria play an important role in the design of symmetric cryptosystems. The following criteria for cryptographic Boolean functions are often considered: high nonlinearity, balancedness, strict avalanche criterion, and global avalanche characteristics. The trade-off among these criteria is a difficult problem and has attracted many researchers. In this paper, two construction methods are provided to obtain balanced Boolean functions with high nonlinearity. Besides, the constructed functions satisfy strict avalanche criterion and have good global avalanche characteristics property. The algebraic immunity of the constructed functions is also considered.

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Construction of balanced Boolean functions with high nonlinearity and good autocorrelation properties

Cited by 21 publications

References 13 publications

Metaheuristics in the Optimization of Cryptographic Boolean Functions

Metaheuristics in the Optimization of Cryptographic Boolean Functions

Measuring the Sum-of-Squares Indicator of Boolean Functions in Encryption Algorithm for Internet of Things

Construction of balanced Boolean functions with high nonlinearity, good local and global avalanche characteristics

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