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Modification and Optimization of Pollards's Factorization ρ-Method by Means of Recursive Algorithm of Number Calculation Factorization
IEEE, 2019.
Смирнов И. А., Разумов П. В., Болдырихин Н. В., Черкесова Л. В., Ревякина Е. А., Поркшеян В. М., Сафарьян О. А., Лободенко А. Г.
Investigations of cryptographic algorithms for
today are very actually in connection with cybernetic attacks
threat and necessity of information protection at the
enterprises of various levels including the strategic
appointment. The project implementation of John Pollard’s
factorization ρ–method in the programming language C ++ is
presented, which works faster than the standard algorithm by
27%. It can facilitate greatly the deciphering operation and
cryptographic analysis of various ciphers such as RSA cipher
Stepan L. Kuznetsov, , in: Automated Reasoning: 13th International Joint Conference, IJCAR 2026, Lisbon, Portugal, July 26–29, 2026, Proceedings, Part II. (LNCS, volume 16689)Vol. 16689.: Cham: Springer, 2026. P. 161–177.
Kleene algebras are an algebraic abstraction of regular expressions, one of the central notions in computer science. While the equational theory of Kleene algebras is known to be decidable, reasoning from finite sets of hypotheses (Horn theory) quickly becomes undecidable. This happens even for simple classes of hypotheses which themselves do not involve Kleene star. ...
Added: July 26, 2026
Kudinov A., Мясников К. М., Математика и теоретические компьютерные науки 2025 Т. 3 № 2 С. 58–84
The paper proves that for weakly transitive logics with the universal modality, whose formula satisfiability problem is in PSPACE, adding the connectedness axiom does not increase the complexity. Furthermore, an explicit algorithm solving this problem is presented. ...
Added: October 14, 2025
Blank M., Discrete and Continuous Dynamical Systems 2025 Vol. 45 No. 11 P. 4186–4201
Appeals to randomness in various number-theoretic constructions appear regularly in modern scientific publications. Such famous names as V.I. Arnold, M. Katz, Ya.G. Sinai, and T. Tao are just a few examples. Unfortunately, all of these approaches rely on various, although often very non-trivial and elegant, heuristics. A new analytical approach is proposed to address the ...
Added: May 23, 2025
Михайловский А. С., Платоновские исследования 2024 Т. 21 № 2 С. 223–261
The most famous episode in the intellectual biography of Thomas Hobbes is the socalled “Euclidean illumination”, a half-mythical story of Hobbes’s relatively late and accidental discovery of Euclidean Elements. The short remark on the beauty of Euclidean method in late prosaic Hobbesian autobiography (1672–1675) has a much more detailed counterpart in the first edition of ...
Added: December 5, 2024
Черкесова Л. В., Сафарьян О. А., Смирнов И. А., Молодой исследователь Дона 2018 Т. 3 (12) С. 111–121
The paper presents the project implementation of ρ-factor Pollard factorization in C ++, which works faster than the standard algorithm by 27%, which can significantly facilitate the work in deciphering and cryptanalysis of various ciphers such as RSA ...
Added: May 9, 2023
Stepan L. Kuznetsov, Journal of Logic and Computation 2023 Vol. 33 No. 6 P. 1437–1462
We prove undecidability and pinpoint the place in the arithmetical hierarchy for commutative action logic, i.e. the equational theory of commutative residuated Kleene lattices (action lattices), and infinitary commutative action logic, the equational theory of *-continuous commutative action lattices. Namely, we prove that the former is Σ01�10-complete and the latter is Π01�10-complete. Thus, the situation is the ...
Added: March 7, 2023
Faliszewski P., Karpov A., Obraztsova S., Autonomous Agents and Multi-Agent Systems 2022 Vol. 36 Article 18
We analyze the complexity of several NP-hard election-related problems under the assumptions that the voters have group-separable preferences. We show that under this assumption our problems typically remain NP-hard, but we provide more efficient algorithms if additionally the clone decomposition tree is of moderate height. We also show a polynomial-time algorithm for sampling group-separable elections uniformly at ...
Added: March 14, 2022
Bille A., Victor Buchstaber, Spodarev E., Journal of Mathematical Chemistry 2021 Vol. 59 No. 1 P. 264–288
After Curl, Kroto and Smalley were awarded 1996 the Nobel Prize in chemistry, fullerenes have been subject of much research. One part of that research is the prediction of a fullerene’s stability using topological descriptors. It was mainly done by considering the distribution of the twelve pentagonal facets on its surface, calculations mostly were performed ...
Added: June 16, 2021
Kuznetsov S., , in: Logic, Language, and Security. Essays Dedicated to Andre Scedrov on the Occasion of His 65th BirthdayIssue 12300.: Cham: Springer, 2020. P. 3–16.
Infinitary action logic is an extension of the multiplicative-additive Lambek calculus with Kleene iteration, axiomatized by an 𝜔-rule. Buszkowski and Palka (2007) show that this logic is \(\Pi^0_1\)-complete. As shown recently by Kuznetsov and Speranski, the extension of infinitary action logic with the exponential modality is much harder: \(\Pi^1_1\)-complete. The raise of complexity is of ...
Added: November 25, 2020
Shitov Y., SIAM Review 2017 Vol. 59 No. 4 P. 794–800
Using elementary linear algebra, we develop a technique that leads to solutions of two widely known problems on nonnegative matrices. First, we give a short proof of the result by Vavasis stating that the nonnegative rank of a matrix is NP-hard to compute. This proof is essentially contained in the paper by Jiang and Ravikumar, ...
Added: November 9, 2017
Matveenko V., , in: Supplementary Proceedings of the Sixth International Conference on Analysis of Images, Social Networks and Texts (AIST-SUP 2017), Moscow, Russia, July 27-29, 2017Vol. 1975.: Aachen: CEUR-WS.org, 2017. Ch. 31 P. 293–300.
Commonly in network analysis a graph (network) is represented by its adjacency matrix, and the latter may have an enormous order. We show that in many situations (generalizing the case of regular graph) a much smaller matrix (referred as type adjacency matrix) may be used instead. We introduce concepts of the types of nodes and ...
Added: November 7, 2017
Zakharyaschev M., BRESOLIN D., KURUCZ A. et al., , in: ACM Transactions on Computational Logic (TOCL)Vol. 18. Issue 3.: NY: ACM, 2017. P. 1–39.
We investigate the satisfiability problem for Horn fragments of the Halpern-Shoham interval temporal logic depending on the type (box or diamond) of the interval modal operators, the type of the underlying linear order (discrete or dense), and the type of semantics for the interval relations (reflexive or irreflexive). For example, we show that satisfiability of ...
Added: September 17, 2017
Zakharov V., Новикова Т. А., , in: Proceedings of the 28th International Workshop on Unification, UNIF 2014. Technical report no. 14-06 in RISC Report Series.: Linz: Research Institute for Symbolic Computation (RISC), Johannes Kepler University Linz, 2014. P. 55–61.
It is generally accepted that to unify a pair of substitutions 1 and 2 means to find out
a pair of substitutions 0 and 00 such that the compositions 10 and 200 are the same.
Actually, unification is the problem of solving linear equations of the form 1X = 2Y in
the semigroup of substitutions. But some other ...
Added: October 13, 2015
Zakharov V.A., Kuzurin N. N., Varnovsky N. P. et al., Programming and Computer Software 2015 Vol. 41 No. 6 P. 361–372
Program obfuscation is a semantic-preserving transformation aimed at bringing a program into a form that impedes understanding of its algorithm and data structures or prevents extracting certain valuable information from the text of the program. Since obfuscation may find wide use in computer security, information hiding and cryptography, security requirements to program obfuscators have become ...
Added: October 13, 2015
Antonopoulos T., Gorogiannis N., Haase C. et al., , in: Lecture Notes in Computer Science. 17th International Conference, FOSSACS 2014, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2014, Grenoble, France, April 5-13, 2014, Proceedings.: Berlin: Springer, 2014. Ch. 27 P. 411–425.
We establish foundational results on the computational complexity of deciding entailment in Separation Logic with general inductive predicates whose underlying base language allows for pure formulas, pointers and existentially quantified variables. We show that entailment is in general undecidable, and ExpTime-hard in a fragment recently shown to be decidable by Iosif et al. Moreover, entailment ...
Added: March 24, 2015
Savateev Y., Annals of Pure and Applied Logic 2012 Vol. 163 P. 775–788
In this paper we prove that the derivability problems for product-free Lambek calculus and product-free Lambek calculus allowing empty premises are NP-complete. Also we introduce a new derivability characterization for these calculi. ...
Added: October 20, 2014
Savateev Y., Известия РАН. Серия математическая 2011 Т. 75 № 3 С. 189–222
We use proof-nets to study the algorithmic complexity of the derivability problem for some fragments of the Lambek calculus. We prove the NP-completeness of this problem for the unidirectional fragment and the product-free fragment, and also for versions of these fragments that admit empty antecedents. ...
Added: October 20, 2014