Papers by Valentin Bakoev
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Springer eBooks, 2022
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2021 International Conference Automatics and Informatics (ICAI), Sep 30, 2021
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Discrete Mathematics, 2004
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Discrete Applied Mathematics, Aug 1, 2008
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arXiv (Cornell University), Apr 2, 2023
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Algebraic Informatics, 2019
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Report published in the Proceedings of the National Conference on "Education and Research in... more Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016The authors share their experience in the use of open educational resources in teaching algorithms and data structures.Association for the Development of the Information Society, Institute of Mathematics and Informatics Bulgarian Academy of Sciences, Plovdiv University "Paisii Hilendarski
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Here we present our arguments for a more in-depth study of the Boolean cube, which is one of the ... more Here we present our arguments for a more in-depth study of the Boolean cube, which is one of the most important discrete structures. The article contains a case study that analyses how the Boolean cube has been included and explained in more than 80 different sources. However, organized material on the Boolean cube is lacking. We examine and show why the topic of the Boolean cube deserves to be studied in the course on Discrete Structures -- a basic part of the Computer Science curriculum. The benefits of mastering such knowledge and programming skills are pointed out. A sample lecture on the $n$-dimensional Boolean cube (including selected exercises, their answers, hints or solutions) is developed and discussed. It introduces, generalizes and relates many concepts from different subjects in the area of Discrete Mathematics and outside it. So the lecturers can use the sample lecture when teaching those subjects. In this way, all these concepts become more understandable, applicable ...
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2021 International Conference Automatics and Informatics (ICAI)
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Symmetry: Culture and Science, 2021
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Informatics in Education, 2010
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Discrete Mathematics, 2004
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Discrete Applied Mathematics, 2008
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Serdica Journal of Computing, 2019
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Here we consider an approach for fast computing the algebraic degree of Boolean functions. It com... more Here we consider an approach for fast computing the algebraic degree of Boolean functions. It combines fast computing the ANF (known as ANF transform) and thereafter the algebraic degree by using the weight-lexicographic order (WLO) of the vectors of the n-dimensional Boolean cube. Byte-wise and bitwise versions of a search based on the WLO and their implementations are discussed. They are compared with the usual exhaustive search applied in computing the algebraic degree. For Boolean functions of n variables, the bitwise implementation of the search by WLO has total time complexity O(n.2^n). When such a function is given by its truth table vector and its algebraic degree is computed by the bitwise versions of the algorithms discussed, the total time complexity is Θ((9n-2).2^n-7)=Θ(n.2^n). All algorithms discussed have time complexities of the same type, but with big differences in the constants hidden in the Θ-notation. The experimental results after numerous tests confirm the theo...
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The problem "Given a Boolean function f of n variables by its truth table vector. Find (if e... more The problem "Given a Boolean function f of n variables by its truth table vector. Find (if exists) a vector α∈{0,1}^n of maximal (or minimal) weight, such that f(α)= 1." is considered here. It is closely related to the problem of fast computing the algebraic degree of Boolean functions. It is an important cryptographic parameter used in the design of S-boxes in modern block ciphers, PRNGs in stream ciphers, at Reed-Muller codes, etc. To find effective solutions to this problem we explore the orders of the vectors of the n-dimensional Boolean cube {0,1}^n in accordance with their weights. The notion of "k-th layer" of {0,1}^n is involved in the definition and examination of the "weight order" relation. It is compared with the known relation "precedes". Several enumeration problems concerning these relations are solved and the corresponding comments were added to 3 sequences in the On-line Encyclopedia of Integer Sequences (OEIS). One special or...
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2021 International Conference Automatics and Informatics (ICAI)
The Reed-Muller transform is widely used in discrete mathematics and cryptography, in particular ... more The Reed-Muller transform is widely used in discrete mathematics and cryptography, in particular for computing the algebraic normal form of Boolean functions. This is a good reason to look for ways to optimize the implementation of the algorithm. Here we present different ways for optimization based on the bitwise representation of the true table vector of a Boolean function. We compare the implementation of the standard algorithm with the implementation using AVX2 and AVX512 instruction sets and the corresponding extended registers and parallel implementation using GPUs with CUDA and OpenMP. The experimental results show that various degree of speedup can be achieved depending on the used platforms and approaches.
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The algebraic normal forms (ANFs) of Boolean functions are used in computing the algebraic degree... more The algebraic normal forms (ANFs) of Boolean functions are used in computing the algebraic degree of S-boxes, which is one of the most important cryptographic criteria. It should be computed by fast algorithms so that more S-boxes are generated and the best of them are selected. Here we continue our previous work for fast computing the ANFs of Boolean functions. We represent and investigate the full version of bitwise implementation of the ANF Transform. The obtained algorithm has a time-complexity Θ((9n−2).2n−7) and Θ(2n−6) space complexity. The experimental results show that it is more than 20 times faster in comparison to the well-known byte-wise ANF Transform.
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arXiv: Combinatorics, 2017
The aim of the paper is to enumerate all closed knight paths of length n over a square board of s... more The aim of the paper is to enumerate all closed knight paths of length n over a square board of size n+1. The closed knight paths of length 4, 6 and 8 are classified up to equivalence. We determine that there are exactly 3 equivalence classes of closed knight paths of length 4, exactly 25 equivalence classes of closed knight paths of length 6 and exactly 478 equivalence classes of closed knight paths of length 8.
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Papers by Valentin Bakoev