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Cybernetics and programming

Features of applying lattice theory in digital signature schemes

Piskova Antonina Vladislavovna

graduate student, Department of Design and Security of Computer Systems, ITMO University

197101, Russia, Saint Petersburg, Kronverkskii prospekt, 49

Korobeinikov Anatolii Grigor'evich

Doctor of Technical Science

professor, Pushkov institute of terrestrial magnetism, ionosphere and radio wave propagation of the Russian Academy of Sciences St.-Petersburg Filial

199034, Russia, g. Saint Petersburg, ul. Mendeleevskaya, 1

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Abstract: The subject of the study is the scheme of digital signature, which is an important element in building secure systems used in most real-world security protocols. Reliability of existing schemes of electronic digital signature can be severely lowered in case of developments in classical cryptanalyst or progress in the development of quantum computers. A potential alternative approach is to construct the schemes based on the complexity of certain properties of the lattices, which are supposed to be intractable for quantum computers. Due to significant scientific advances in recent years, scheme based on lattice theory already used in practice and is a very viable alternative to number-theoretic cryptography. The study is based on the use of methods of lattice theory. This choice is dictated by the lack of solution of problem of finding the shortest vector or finding the nearest vector in polynomial time. The main conclusion of the paper is that the main area of future development in the schemes of the digital signature on the basis of lattice theory is their optimization and implementation of the Fiat-Shamir model in it. For example, Bliss scheme showed high performance and therefore it can be integrated into portable systems and devices.

Keywords: digital signature, RSA, post-quantum cryptography, Bliss scheme, cryptography, Fiat-Shamir transformation, lattice theory, Abelian group, Euclidean space, identification scheme
This article written in Russian. You can find full text of article in Russian here .

Korobeinikov A.G., Vorob'ev A. O., Sidorkina I. G., Pylin V. V. Analiz kriptograficheskoi stoikosti algoritmov asimmetrichnogo shifrovaniya informatsii//Izv.VUZOV. Priborostroenie. 2007. T. 50. № 8., str. 28-32.
Korobeinikov A.G., Kutuzov I.M. Algoritm obfuskatsii// NB: Kibernetika i programmirovanie. — 2013.-№ 3.-S.1-8. DOI: 0.7256/2306-4196.2013.3.9356. URL: http://e-notabene.ru/kp/article_9356.html
Thomas Poppelmann and Tim Guneysu. Towards Efficient Arithmetic for Lattice-Based Cryptography on Reconfigurable Hardware//LATINCRYPT. – 2012. – R. 139–158.
Ozgur Dagdelen, Marc Fischlin, Tommaso Gagliardoni. The Fiat-Shamir Transformation in a Quantum World // ASIACRYPT.-2013.-№2.-R. 62–81.
Vadim Lyubashevsky. Fiat-Shamir with Aborts: Applications to Lattice and Factoring-Based Signatures // ASIACRYPT.-2009. – R. 598–616.
Vadim Lyubashevsky. Lattice Signatures without Trapdoors // EUROCRYPT.-2012. – R. 738–755.
Leo Ducas and Daniele Micciancio. Improved Short Lattice Signatures in the Standard Model // CRYPTO.-2014. – R. 335–352
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