The Design of Boolean Functions by Modified Hill Climbing Method

Izbenko, Yuriy; Kovtun, Vladislav; Kuznetsov, Alexandr

doi:10.1109/itng.2009.102

Cited by 38 publications

(23 citation statements)

References 6 publications

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“…The obtained results of the distribution on the non-linearity of the entire set of M-NLFSR sized below 6  L are summarized in Table 5. The Tables 6 and 7 As it can be seen from the results above, M-NLFSR simultaneously achieve the maximum possible stability and maximum nonlinearity [13][14][15][16][17][18][19]. Moreover, all m-optimal functions are also msaturated (in Tables 6-9 .…”

Section: Correlation Immunitymentioning

confidence: 95%

Combining and Filtering Functions in the Framework of Nonlinear-Feedback Shift Register

Кuznetsov¹,

Potii²,

Poluyanenko³

et al. 2020

IJC

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Strong cryptography of stream ciphers is determined according to the ability of the generated pseudorandom sequence to resist analytical attacks. One of the main components of the pseudorandom stream cipher sequence generating algorithm is Boolean functions for combining and filtering. The paper considers the possibility of applying nonlinear-feedback shift registers that generate a maximum length sequence as a combining or filtering function. The main indicators of cryptographic strength of such functions as: balance, the prohibitions presence, correlation immunity and nonlinearity are examined in this work. The study analyzes and demonstrates correlation immunity and nonlinearity experimental values for all nonlinear feedback shift registers that generate a maximum length sequence, for register sizes up to 6 cells inclusively, and register sizes up to 9 cells inclusively with algebraic degree of the polynomial under 2. The possibility of optimizing the process of selecting Boolean functions according to the criteria of maximum correlation immunity and nonlinearity with various algebraic degrees and minimization of the number of monomials in the polynomial is studied.

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Section: Correlation Immunitymentioning

confidence: 95%

Combining and Filtering Functions in the Framework of Nonlinear-Feedback Shift Register

Кuznetsov¹,

Potii²,

Poluyanenko³

et al. 2020

IJC

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“…In order to partially avoid this drawback, some authors consider some of the advances performed with algebraic constructions. Particularly, References [ 18 , 19 ] proposed trajectory-based search methods that operate with bent BFs . They randomly adjust the bent BF to convert it on a balanced BF.…”

Section: Literature Reviewmentioning

confidence: 99%

“…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.…”

Section: Population-based Proposalsmentioning

confidence: 99%

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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“…In particular, the algebraic properties of S-blocks of modern block ciphers are investigated in [5][6][7] and their influence on sustainability to algebraic cryptanalysis is shown. In [8][9][10][11], combinatorial properties of non-linear knots in the context of the security evaluation of various encryption modes and key schedules were properties are examined; in [24] the method of simulation of annealing is investigated; evolutionary methods are studied in [25,26]; papers [27,28] are dedicated to the heuristic methods of gradient search.…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this paper is to continue studies of the method of gradient descent, first proposed in [28], an assessment of its computational complexity in comparison with the closest analog in [27]. For this purpose, the necessary terms and definitions in Section 2 are introduced; the heuristic methods studied in [27,28] are summarized in Section 3 and the calculated data for the required number of operations for the realization of gradient descent (Table I) is provided. Section 4 evaluates the properties of the gradient-lift method for the formation of high non-linear correlation-immune cryptographic Boolean functions.…”

Section: Introductionmentioning

confidence: 99%

Heuristic Methods for the Design of Cryptographic Boolean Functions

Moskovchenko¹,

Кuznetsov²,

Kavun³

et al. 2019

IJC

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In this article, heuristic methods of hill climbing for cryptographic Boolean functions satisfying the required properties of balance, nonlinearity, autocorrelation, and other stability indicators are considered. A technique for estimating the computational efficiency of gradient search methods, based on the construction of selective (empirical) distribution functions characterizing the probability of the formation of Boolean functions with indices of stability not lower than required, is proposed. As an indicator of computational efficiency, an average number of attempts is proposed to be performed using a heuristic method to form a cryptographic Boolean function with the required properties. Comparative assessments of the effectiveness of the heuristic methods are considered. The results of investigations of the cryptographic properties of the formed Boolean functions in comparison with the best known assessments are given. On the basis of the conducted research, it can be concluded that the functions constructed in accordance with the developed method have high persistence indexes and exceed the known functions by these indicators.

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The Design of Boolean Functions by Modified Hill Climbing Method

Cited by 38 publications

References 6 publications

Combining and Filtering Functions in the Framework of Nonlinear-Feedback Shift Register

Combining and Filtering Functions in the Framework of Nonlinear-Feedback Shift Register

Metaheuristics in the Optimization of Cryptographic Boolean Functions

Heuristic Methods for the Design of Cryptographic Boolean Functions

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