MATHEMATICAL MODEL OF AUTHENTICATION OF A TRANSMITTED MESSAGE BASED ON A MCELIECE SCHEME ON SHORTED AND EXTENDED MODIFIED ELLIPTIC CODES USING UMAC MODIFIED ALGORITHM
DOI:
https://doi.org/10.28925/2663-4023.2019.5.4051Keywords:
decentralized systems; blockchain technology; post-quantum cryptosystems; McEliece crypto code design; elliptic curves; UMAC algorithmAbstract
The subject of the research is a mathematical model of authentication of the transmitted message based on the McEliese scheme on shortened and elongated modified elliptic codes using the modified UMAC algorithm. The aim of this work is to develop such a scheme for the information exchange over Internet communication channels, which would ensure the proper level of verification and integrity of the transmitted information, taking into account the prevention of an increase in the costs of the actions taken. Tasks: analysis of existing ways to increase the resistance to hacking of transmitted messages over telecommunication networks; analysis of a message transfer scheme using blockchain technology; formalized description of a mathematical model for providing clear text authentication using a modified UMAC algorithm, as the formation of key data, a crypto-code construction (CCC) is used on the McEliese scheme on modified elliptic codes (MEС); development of data encryption and decryption algorithms using CCC based on McEliese on the MEC and UMAC algorithm. Аn approach was proposed to verify the authentication and verification of the information packet during transmission and reception via telecommunication channels, which allows using already known hashing methods to compare generated codegrams and transmitted messages for their correspondence, which increases the level of cryptographic stability of the transmitted data and the reliability of the received data. The developed schemes of algorithms for generating codеgrams and their decryption using the proposed approach make it possible to gradually demonstrate the implementation of procedures for generating codegrams and their hash codes using both shortening and lengthening the code. Further research should prove from a practical point of view the effectiveness of using this approach when transmitting a message regarding the preservation of its integrity and authenticity. Therefore, it is necessary to develop a test system that should implement the proposed approach, as well as evaluate the results obtained.
Downloads
References
А. Veneduhin, “Post-Quantum Cryptography: NIST 4 Program [Postkvantovaya kriptografiya: programma NIST 4]”, Bezopasnost, Kriptologiya, Sayt dxdt.ru: zanimatelniy internet-zhurnal. [Online]. Access mode: https://dxdt.ru/2019/02/04/8687/ [04 fев., 2019]. (in Russian)
А.V. Korolkov, “On some applied aspects of quantum cryptography in the context of the development of quantum computing and the advent of quantum computers [O nekotoryh prikladnyh aspektah kvantovoq kriptografii v kontekste razvitiya kvantobyh bychisleniy I poyavleniya kvantovyh komputerov]”, Voprosy kiberbezopasnosti, М.: ZAO “Nauchno-proizvodstvennoe obyedineniye “Eshelon", № 1(9), pp. 6–13, 2015 (in Russian).
S.P. Yevseev, H.N. Rzaev, О.G. Korol, and Z.B. Imanova, “Development of a modified asymmetric McElise crypto-code system on shortened elliptic codes [Razrabotka modificirovannoy nesimmetrichnoy kripto-kodovoy sistemy Mak-Elisa ukorochennyh ellipticheskih kodah]”, Vostochno-Evropeyskiy zhurnal peredovyh tehnologiy, № 4/9 (82), pp. 158-165, 2016 (in Russian)/
Serhii Yevseiev, Olha Korol, and Alla Havrylova, “Development of authentication codes of messages on the basis of UMAC with crypto-code McEliece’s scheme on elliptical codes”, Materials of VIІth International Scientific and Technical Conference “Information protection and information systems security”: report theses, May 30 –31, 2019, Lviv: Lviv Polytechnic Publishing House, pp. 86 – 87, 1 electron. opt. disk (DVD), 2019 (in English).
А.А. Kuznetsov, О.G. Korol, and S.P. Yevseev, “Investigation of collision properties of message authentication codes UMAC [Issledovanie kollizionnyh svoystv kodov autentifikacii soobsheniy UMAC]”, Prikladnaya radioelektronika: nauch.-tehn. zhurnal, vol. 11, № 2, pp. 171–183, 2012 (in Russian).
А.А. Kuznetsov, О.G. Korol, and V.V. Bosko, “A model for generating message authentication codes using universal hashing functions [Model formirovaniya kodov autentifikacii soobsheniy s ispolzovaniem universalnyh heshiruushih funkciy]”, Zahyst informacii v informaciyno-telekomunikaciynyh systеmah, 2016, pp. 117 – 125 (in Russian).
Olga Korol, Lubomyr Parhuts, and Sergey Yevseev, “Development of a model and method for the cascade formation of MAC using modular transformations [Razrabotka modeli i metoda kaskadnogo formirovaniya MAC s ispolzovaniem modularnyh preobrazovaniy]”, Zahiist informatsii, lypen-veresen, t. 15, №3, pp. 186 – 196, 2013 (in Russian).
Y.L. Onanchenko, and А.V. Lysenko, “Analysis of known decoding methods for non-binary block codes [Analiz izvestnyh metodov dekodirovaniya nedvoichnyh blokovyh kodov]”, Visnyk SumDU, Seria Tehnichni nauki, № 3, pp. 100 – 105, 2008 (in Russian).
К.Y. Batenko, and А.N. Prokudin, “Post-quantum digital signature algorithm based on the Merkle tree and GOST RF 34.11–12 “Stribog” [Post-kvantoviy algoritm elektronno-cifrovoy podpisi na osnove dereva Merkla b GOST RF 34.11-12 “Stribog”]”, Molodoy ucheniy, №23, pp. 100-103, 2017. [Online]. Access mode: https://moluch.ru/archive/157/44376/ [30 aug., 2019] (in Russian).
А.А. Kuznetsov, А.I. Pushkarev, I.I. Svatovskiy, and А.V. Shevtsov, “Asymmetric cryptosystems on algebraic codes for the post-quantum period [Nesimmetrichnye kriptosistemy na algebraicheskih kodah dlya postkvantovogo perioda]”, Radiotehnika, 2016, rel. 186, pp. 70 – 90 (in Russian).
P. Kravchenko, B. Skryabin, and О. Dubinina, Blockchain and decentralized systems: textbook. manual for students of higher. Education: in 3 parts [Blokcheyn i decentralizovannye sistemy: ucheb. Posobie dlya studentov vyssh. obrazovaniya: d 3 chastyah], Kharkov: PROMART, part. 1, 2018 (in Russian).
Maryna Yesina, Olga Akolzina, and Ivan Gorbenko, “Conditions and opportunities of Blockchain applying”, Materials of VIІth International Scientific and Technical Conference “Information protection and information systems security”: report theses, May 30–31, 2019, Lviv: Lviv Polytechnic Publishing House, 1 electron. opt. disk (DVD), pp. 46–47, 2019 (in English).
