Metric for comparing graphs with ordered vertices based on the maximum common subgraph

The work is devoted to methods for comparing and classifying graphs. This trend is known as "graph matching". An overview of metrics for comparing graphs based on the maximum common subgraph is given. A modification of the distance based on the maximum common subgraph, which takes into account the ordering of the vertices, is proposed. It is shown that this function satisfies all the properties of the metric (non-negativity, identity, symmetry, triangle inequality).

The maximum number of vertices of primitive regular graphs of orders 2, 3, 4 with exponent 2

In 2015, the results were obtained for the maximum number of vertices nk in regular graphs of a given order k with a diameter 2: n2 = 5, n3 = 10, n4 = 15. In this paper, we investigate a similar question about the largest number of vertices npk in a primitive regular graph of order k with exponent 2. All primitive regular graphs with exponent 2, except for the complete one, also have diameter d = 2. The following values were obtained for primitive regular graphs with exponent 2: np2 = 3, np3 = 4, np4 = 11.

On the nonexistence of certain orthogonal arrays of strength four

Дано решение открытой проблемы олимпиады по криптографии NSUCRYPTO-2018: показано, что не существует ортогональных массивов OA (16L, 11, 2, 4) с L = 6 и 7. Этот результат позволяет определить минимальные веса некоторых корреляционно-иммунных булевых функций высокого порядка.

THE ATTACKERS POWER BOUNDARIES FOR TRACEABILITY OF ALGEBRAIC GEOMETRIC CODES ON SPECIAL CURVES

Broadcast encryption is a data distribution protocol which can prevent malefactor parties from unauthorized accessing or copying the distributed data. It is widely used in distributed storage and network data protection schemes. To block the socalled coalition attacks on the protocol, classes of error-correcting codes with special properties are used, namely c-FP and c-TA properties. We study the problem of evaluating the lower and the upper boundaries on coalition power, within which the algebraic geometry codes possess these properties. Earlier, these boundaries were calculated for single-point algebraic-geometric codes on curves of the general form. Now, we clarified these boundaries for single-point codes on curves of a special form; in particular, for codes on curves on which there are many equivalence classes after factorization by equality of the corresponding points coordinates relation.

ON LOGIC NETWORKS ALLOWING SHORT SINGLE FAULT DETECTION TESTS UNDER ARBITRARY FAULTS OF GATES

It is proved that one can implement any non-constant Boolean function in n variables by an irredundant logic network in the basis {&, ⊕, ¬}, containing not more than one dummy input variable and allowing a single fault detection test with length not more than 2n + 3 regarding arbitrary faults of logic gates.

Detection of malware using an artificial neural network based on adaptive resonant theory

The process of detecting malicious code by anti-virus systems is considered. The main part of this process is the procedure for analyzing a file or process. Artificial neural networks based on the adaptive-resonance theory are proposed to use as a method of analysis. The graph2vec vectorization algorithm is used to represent the analyzed program codes in numerical format. Despite the fact that the use of this vectorization method ignores the semantic relationships between the sequence of executable commands, it allows to reduce the analysis time without significant loss of accuracy. The use of an artificial neural network ART-2m with a hierarchical memory structure made it possible to reduce the classification time for a malicious file. Reducing the classification time allows to set more memory levels and increase the similarity parameter, which leads to an improved classification quality. Experiments show that with this approach to detecting malicious software, similar files can be recognized by both size and behavior.

DETECTING SERVER-SIDE ENDPOINTS IN WEB APPLICATIONS BASED ON STATIC ANALYSIS OF CLIENT-SIDE JavaScript CODE

The problem of server-side endpoint detection in the context of blackbox security analysis of dynamic web applications is considered. We propose a method to increase coverage of server-side endpoint detection using static analysis of client-side JavaScript code to find functions which generate HTTP requests to the server-side of the application and reconstruct parameters for those functions. In the context of application security testing, static analysis allows to find such functions even in dead or unreachable JavaScript code, which cannot be achieved by dynamic crawling or dynamic code analysis. Evaluation of the proposed method and its implementation has been done using synthetic web application with endpoints vulnerable to SQL injections, and the same application was used to compare the proposed method with existing solutions. Evaluation results show that adding JavaScript static analysis to traditional dynamic crawling of web applications may significantly improve server-side endpoint coverage in blackbox application security analysis.

THE GENERAL COMPLEXITY OF THE PROBLEM TO RECOGNIZE HAMILTONIAN PATHS

Generic-case approach to algorithmic problems has been offered by A. Miasnikov, V. Kapovich, P. Schupp, and V. Shpilrain in 2003. This approach studies an algorithm behavior on typical (almost all) inputs and ignores the rest of inputs. In this paper, we study the generic complexity of the problem of recognition of Hamiltonian paths in finite graphs. A path in graph is called Hamiltonian if it passes through all vertices exactly once. We prove that under the conditions P 6= NP and P = BPP for this problem there is no polynomial strongly generic algorithm. A strongly generic algorithm solves a problem not on the whole set of inputs, but on a subset, the sequence of frequencies of which exponentially quickly converges to 1 with increasing size. To prove the theorem, we use the method of generic amplification, which allows to construct generically hard problems from the problems hard in the classical sense. The main component of this method is the cloning technique, which combines the inputs of a problem together into sufficiently large sets of equivalent inputs. Equivalence is understood in the sense that the problem is solved similarly for them.

GROUP AUTHENTICATION SCHEME BASED ON ZERO-KNOWLEDGE PROOF

In this paper, we address the problem of mutual authentication in user groups in decentralized messaging systems without trusted third party. We propose a mutual authentication algorithm for groups using zero-knowledge proof. Using the algorithm, which is based on trust chains existing in decentralized network, users are able to authenticate each other without establishing a shared secret over side channel. The proposed algorithm is based on Democratic Group Signature protocol (DGS) and Communication-Computation Efficient Group Key algorithm for large and dynamic groups (CCEGK). We have performed security analysis of the proposed mutual authentication scheme against several attacks including Sybil attack and have made complexity estimation for the algorithm. The algorithm is implemented in an experimental P2P group messaging application, and using this implementation we estimate overhead of the authentication scheme and convergence time for several initial configurations of user groups and trust chains.