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Article title METHODS OF ALGEBRAIC ANALYSIS FOR ASSESSMENT OF INFORMATION SECURITY
Authors L.K. Babenko, E.A. Maro
Section SECTION I. INFORMATION TECHNOLOGIE AND PROTECTION OF INFORMATION
Month, Year 09, 2016 @en
Index UDC 681.03.245
DOI 10.18522/2311-3103-2016-9-3750
Abstract This article describes the approach to algebraic analysis methods for the evaluation of data protection by cryptographic algorithms, as an example we have observed the symmetric block ciphers. As the base of research we have selected standards GOST 34.12-2015 (n = 64) and PRESENT. The basis of the algebraic analysis is the method of reduction system of equations to the Boolean formulas satisfiability (SAT) problem. We create a generation algorithms of Boolean systems of nonlinear equations for arbitrary substitution boxes and a different number of encryption rounds (based on a Feistel network and SP-network). We present a methodjlogy of algebraic analysis with a SAT-solver CryptoMiniSat, which allows pre-calculating the expected complexity of finding the sets of solutions of Boolean nonlinear equations systems by the methods of reduction to SAT-problem. Observed criteria for the evaluation of data protection based on the algebraic analysis of cryptographic algorithms are listed. Developed in the course of research algorithms and methodology may be further used to evaluate the security of arbitrary transformations on the basis of operations of replacement and addition modulo by algebraic analysis. During the modeling of the algebraic analysis we assessed data protection of reduced-rounds encryption algorithms (experiments were made using SageMath Cloud computing resources). For 8 rounds "Magma" algorithm (GOST 34.12-2015, n = 64) encryption key was calculated with 4 texts for 3029.56 4 seconds. For 4 rounds encryption PRESENT (ISO 29192-2: 2012) we have calculated 16 keys-sets with 8 texts for 3268.42 seconds.

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Keywords Evaluation of data protection; algebraic analysis; symmetric block encryption algorithms; GOST 34.12-2015; PRESENT; Boolean formulas satisfiability problem (SAT); solver CryptoMiniSat; algebraic normal form (ANF); conjunctive normal form (CNF).
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