DEVELOPMENT OF AUTHENTICATION CODES OF MESSAGES ON THE BASIS OF UMAC WITH CRYPTO-CODE MCELIECE’S SCHEME

Year 2019, Volume: 3 Issue: 2, 153 - 170, 31.08.2019

Serhii Yevseiev , Olha Korol Alla Gavrilova

Abstract

The development of decentralized
systems and blockchain technology have expanded the range of
cryptocurrency-based banking services. The main difference from the
hierarchical structures of the organizations of the banking sector (national
and commercial banks) is the formation of valid nodes ensuring the confirmation
of transactions based on the checking and verification of digital signatures
and MAC codes. The Bitcoin protocols use the SHA-256 algorithm to form MAC
codes, however, the rapid growth of the system leads to significant time costs
not only for mining, but also for validation of the formed blocks. The further
development of decentralized systems, increase the number of wall-distributors
and full nodes forces us to look for new ways to solve a temporary problem
based on using different approaches to providing authentication in
decentralized systems. The paper discusses the algorithm for generating UMAC
message authentication codes using a McEliece’s crypto-code scheme based on the
use of universal hashing functions. A reduced UMAC model (mini-UMAC) and a
method for statistical analysis of the collision characteristics of the
generated message authentication codes are proposed. Using the reduced UMAC
model, collisional characteristics of authentication codes are investigated, it
is shown that the use of cryptographic transformation (using the AES algorithm)
at the final stage of UMAC leads to a violation of the universal hashing
characteristics.

Keywords

mini-UMAC with a McEliece’s crypto-code scheme, authentication, universal function, authenticity codes

References

• Reference1 Black J. “UMAC: Fast and provably secure message authenticationˮ, Advances in Cryptology / J. Black, S. Halevi H., Krawczyk, T. Krovetz, P. Rogaway. – CRYPTO '99, LNCS vol. 1666, PP. 216-233, Springer-Verlag, 1999.Reference2 T. Krovetz, P. Rogaway. Fast universal hashing with small keys and no preprocessing, work in progress, 2000. – URL: http://www.cs.ucdavis.edu/~rogaway/umacReference3 T. Krovetz, J. Black, S. Halevi, A. Hevia, H. Krawczyk, P. Rogaway. UMAC -Message authentication code using universal hashing. IETF Internet Draft, draft-krovetz-umac-00.txt. – URL: www.cs.ucdavis.edu/~rogaway/umac, 2000.Reference4 Krovetz T. UMAC-Message authentication code using universal hashing. IETF Internet Draft, draft-krovetz-umac-02.txt. – URL: www.cs.ucdavis.edu/~rogaway/umac, 2004. Reference5 Final report of European project number IST-1999-12324, named New European Schemes for Signatures, Integrity, and Encryption, April 19, 2004 – Version 0.15 (beta), Springer-Verlag. Reference6 Krovetz T. UMAC-Message authentication code using universal hashing, 2006. – URL: http://www.cs.ucdavis.edu/~rogaway/umac Reference7 Krovetz T. Software-Optimized Universal Hashing and Message Authentication. Dissertation submitted in partial satisfaction of the requirements for the degree of doctor of philosophy. University Of California Davis. September 2000. – 269 p.Reference8 Carter J. L. Universal classes of hash functions / J.L. Carter, M.N. Wegman // Computer and System Scince – 1979 – №18 – pp. 143–154Reference9 Wegman M. N. New hash functions and their use in authentication and set equality / M. N.Wegman, J. L. Carter / Computer and System Scince – 1981 – № 22 – pp. 265–279 Reference10 O. G. Korol Investigation of properties of modular transformations and methods of hashing information on their basis / O. G. Korol, L. T. Parhuts, S. P. Yevseiev // Information Processing Systems. – 2013. – № 4(111). – pp. 106–110. Reference11 O. G. Korol. The method of universal hashing on the basis of modular transformations / O. G. Korol, S. P. Yevseiev // Information processing systems. Information Technology and Computer Engineering. – 2011. – № 7(97). – pp. 131–132Reference12 O. G. Korol. Mechanisms and protocols for protecting information in computer networks and systems / O. G. Korol, S. P. Yevseiev, A. V. Dorokhov // Scientific Journal of the Ministry of Defense of Republic of Serbia. Military Technical Gazette, Belgrade, 2011. – №. 4. – pp. 15–30. Reference13 Korol O.G. Results of the statistical test security hash algorithms-candidates tender to select standard hash algorithm SHA-3 / O. G. Korol, S. P. Yevseiev // News of higher technical educational institutions of Azerbaijan. – 2012. – № 2. – pp. 73–78.Reference14 Status Report on the First Round of the SHA-3 Cryptographic Hash Algorithm Competitionhttp Andrew Regenscheid, Ray Perlner, Shu-jen Chang, John Kelsey, Mridul Nandi, Souradyuti Paul. [Електронний ресурс] – Режим доступу: www.nist.gov/index.html.Reference15 Raphael Chung-Wei Phan, “Mini Advanced Encryption Standard (Mini-AES): A testbed for Cryptanalysis Studentsˮ, Cryptologia, XXVI (4), October 2002. – pp. 283–306Reference16 A Description of Baby Rijndael // ISU CprE/Math 533; NTU ST765-U. – 2003Reference17 Raphael Chung-Wei Phan, “Mini Advanced Encryption Standard (Mini-AES): A testbed for Cryptanalysis Studentsˮ, Cryptologia, XXVI (4), October 2002. – pp. 283–306Reference18 I. V. Lisitskaya, T. A. Grinenko, and S. Yu. Bessonov, “Analysis of the differential and linear properties of ciphers rijndael, serpent, threefish with 16-bit inputs and outputs”, East European Journal of Advanced Technologies, pp. 50-54. 2015Reference19 S. P. Yevseiev, S. E. Ostapov, and R. V. Korolev, “Use of mini-versions for evaluation of the stability of block-symmetric ciphersˮ, Scientific and Technical Journal “Information Securityˮ, vol.23, no. 2, pp. 100–108, 2017Reference20 S. Yevseiev, O. Y. Yokhov, and O. G. Korol. Data Gaining in Information Systems. Monograph. Kharkiv, Ukraine: pub. KhNUE, 2013Reference21 S. Yevseiev, H. Rzayev, and A. Tsyganenko, “Analysis of the software implementation of direct and inverse transformations using the non-binary balanced coding method”, Science and Technology Journal “Security Without Information”, vol. 22, no. 2, pp. 196–203, 2016Reference22 S. Yeseiev, “The use of flawed codes in crypto-code systems”, Information processing systems, №, 5 (151) pp. 109–121, 2017Reference23 S. Yevseiev, I. Bilodid. “The use of unprofitable codes in hybrid crypto-code designsˮ, Fifth International Scientific and Technical Conference “Problems of Informatizationˮ, Cherkasy – Baku – Bielsko-Biala – Poltava, 2017, p. 11Reference24 R. Hryshchuk, S. Yevseiev, A. Shmatko Construction methodology of information security system of banking information in automated banking systems: monograph, 284 p., Vienna.: Premier Publishing s. r. o., 2018