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Theoretical possibilities for combining various mathematical primitives within an electronic digital signature scheme.
Komarova Antonina Vladislavovna

Graduate student, St. Petersburg National Research University of Information Technologies, Mechanics and Optics

196244, Russia, Saint Petersburg, ul. Tipanova, d. 29

piter-ton@mail.ru
Korobeinikov Anatolii Grigor'evich

Doctor of Technical Science

Professor, Department of Design and Security of Computer Systems, St. Petersburg National Research University of Information Technologies, Mechanics

196631, Russia, g. Saint Petersburg, ul. Kronverkskii Prospekt, 49

korobeynikov_a_g@mail.ru
Menshchikov Aleksandr Alekseevich

Graduate student, St. Petersburg National Research University of Information Technologies, Mechanics and Optics

197101, Russia, Saint Petersburg, Kronverkskii prospekt, 49

menshikov@corp.ifmo.ru
Klyaus Tat'yana Konstantinovna

Graduate student, St. Petersburg National Research University of Information Technologies, Mechanics and Optics

197101, Russia, g. Saint Petersburg, Kronverskkii prospekt, 49

t_klyaus@corp.ifmo.ru
Negol's Aleksandr Valer'evich

Graduate student, St. Petersburg National Research University of Information Technologies, Mechanics and Optics

197101, Russia, g. Saint Petersburg, ul. Kronverkskii Prospekt, 49

dozory07@yandex.ru
Sergeeva Anastasiya Aleksandrovna

Graduate student, St. Petersburg National Research University of Information Technologies, Mechanics and Optics

197101, Russia, Saint Petersburg, Kronverkskii prospekt, 49

aasergeeva@corp.ifmo.ru
Abstract. The study is devoted to the algorithms and protocols of  an electronic digital signature, providing for the key information properties: its integrity, authenticity and accessibility. This article highlights the problems of modern cryptography and a possible way to solve them via creation of an electronic digital signature  that can withstand a quantum computer. The article concerns various mathematical primitives, which can increase the stability of existing cryptosystems when used together. This area of research is a new and promising one for the development of domestic cryptography. The theoretical methods of research used in this article include the theory of computational complexity, the theory of rings, fields and lattices, algorithmic aspects of lattice theory and their application in cryptography, in particular, the complexity of solving systems of linear Diophantine equations, the complexity of finding the shortest nonzero lattice vector And the vector of the lattice closest to the given vector, known approximate algorithms for these problems. We refer to experimental methods of research, such as carrying out statistical calculations and data analysis in the Mathlab mathematical environment, constructing elliptic curves in the mathematical environment of Mathcad, creating software implementations of the algorithm for generating a signature in Python, using precompiled modules from the NumPy library. It is planned to achieve the following results in the future: 1. The development of a methodology for constructing electronic digital signature schemes based on two independent computationally difficult problems; 2. The development of a polynomially complex electronic digital signature scheme based on fundamentally different mathematical primitives; 3. The estimation of the size of safe parameters of the developed EDS protocols; 4. The theoretical model of the growth of calculation time from the length of an electronic digital signature key.
Keywords: information security, elliptic curve, the lattice theory, cryptosystem, postquantum cryptography, the shortest vector problem, discrete logarithming, Pollard algorithm, information privacy, digital signature
DOI: 10.25136/2306-4196.2017.3.23364
Article was received: 10-07-2017

Review date: 23-06-2017

Publish date: 26-07-2017

This article written in Russian. You can find full text of article in Russian here.

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