022e28a6-616a-4a68-ae8c-20bf07285f9120210319070454413wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL1991-876310.37394/23203http://wseas.org/wseas/cms.action?id=4073220202022020201510.37394/23203.2020.15http://wseas.org/wseas/cms.action?id=23195Post-Quantum Network Security:McEliece and Niederreiter Cryptosystems Analysis and Education IssuesAlekseiVambolDepartment of Computer Systems and Networks, National Aerospace University «KhAI», Kharkiv, UkraineVyacheslavKharchenkoDepartment of Computer Systems and Networks, National Aerospace University «KhAI», Kharkiv, UkraineOlexandrPotiiDepartment of Computer Systems and Networks, National Aerospace University «KhAI», Kharkiv, UkraineNikosBardisDepartment of Mathematics and Engineering Sciences, Hellenic Army Academy, Athens, GreeceThe paper is aimed at analyzing of the classical McEliece and Niederreiter cryptosystems as well as theQuasi-Cyclic MDPC McEliece cipher in a context of the post-quantum network security. Theoretical foundations ofthe aforesaid cryptographic schemes are considered. The characteristics of the given cryptosystems and otherasymmetric encryption schemes are analyzed. The cipher metrics, which are considered in the paper, includecryptographic strength, performance, public key size and length of ciphertext. The binary Goppa codes are describedin the context of their role for the cryptanalytic resistance of the classic McEliece and Niederreiter schemes. Thecrucial advantages and drawbacks of the aforementioned cryptosystems are analyzed. The prospects for applicationof these ciphers to the network security protocols are outlined. The investigations, which are aimed at finding waysto reduce the public key sizes and improve the energy efficiency of the given ciphers, are briefly described. A neweducational module “Introduction to Post-Quantum Cryptography” is presented1119202011192020627634https://www.wseas.org/multimedia/journals/control/2020/b245103-027.pdf10.37394/23203.2020.15.62https://www.wseas.org/multimedia/journals/control/2020/b245103-027.pdfETSI White Paper No. 8. “Quantum Safe Cryptography and Security”, European Telecommunications Standards Institute”, 2015, 49 p. 10.1109/mcsi.2017.31Vambol, Aleksei, et al. "McEliece and Niederreiter Cryptosystems Analysis in the Context of Post-Quantum Network Security." 2017 Fourth International Conference on Mathematics and Computers in Sciences and in Industry (MCSI). IEEE, 2017. S. Y. Yan, “Quantum Attacks on Public-Key Cryptosystems”, Springer, 2013, 214 p. E. Jochemsz, “Goppa Codes & the McEliece Cryptosystem”, Vrije Universiteit Amsterdam, 2002, 63 p. 10.1002/sec.274R. Lu, X. Lin, X. Liang, X. Shen, “An efficient and provably secure public key encryption scheme based on coding theory”, Security and Communication Networks, 2011, vol. 4, iss. 12, pp. 1440-1447. V. D. Goppa, “A New Class of Linear Correcting Codes”. Problems of Information Transmission, 1970, vol. 6, iss. 3, pp. 207-212. 10.1007/978-3-642-34129-8_45C. Löndahl, T. Johansson, “A New Version of McEliece PKC Based on Convolutional Codes”, Lecture Notes in Computer Science, 2012, vol. 7618, pp. 461-470. 10.1109/tit.1984.1056946M. Loeloeian, J. Conan, “A [55,16,19] binary Goppa code”, IEEE Transactions on Information Theory, 1984, vol. 30, iss. 5, p. 773. 10.1007/978-3-642-02384-2_6T. P. Berger, P.-L. Cayrel, P. Gaborit, A. Otmani, “Reducing Key Length of the McEliece Cryptosystem”, Lecture Notes in Computer Science, 2009, vol. 5580, pp. 77-97. 10.1016/j.dam.2005.03.017P. Fitzpatrick, J. A. Ryan, “Enumeration of in equivalent irreducible Goppa codes”, Discrete Applied Mathematics, 2006, vol. 154, iss. 2, pp. 399-412. M. Kratochvíl, “Implementation of cryptosystem based on error-correcting code”, Charles University in Prague, 2013, 60 p. P. Fahn, “Answers to Frequently Asked Questions about Today's Cryptography”, RSA Laboratories, 1996, 204 p. D. J. Bernstein, J. Buchmann, E. Dahmen, “Post-Quantum Cryptography”, Springer, 2009, 246 p. I. Woungang, S. Misra, S. C. Misra, “Selected Topics in Information and Coding Theory”, World Scientific, 2010, 724 p. “ETSI GR QSC 001: Quantum-Safe Cryptography (QSC); Quantum-safe algorithmic framework”, European Telecommunications Standards Institute, 2016, 42 p. 10.1109/isit.2013.6620590R. Misoczki, J.-P. Tillich, N. Sendrier, P. S. L. M. Barreto, “MDPC-McEliece: New McEliece variants from Moderate Density Parity-Check codes”, IEEE International Symposium on Information Theory (ISIT-2013), 2013, pp. 2069-2073. R. Daskalov, P. Hristov, “New one-generator quasi-cyclic codes over GF(7)”, Problems of Information Transmission, 2002, vol. 38, iss. 1, pp. 50-54. 10.1109/tit.2018.2804444C. Aguilar, O. Blazy, J.-C. Deneuville, P. Gaborit, G. Zemor, “Efficient Encryption from Random Quasi-Cyclic Codes”, CoRR abs/1612.05572, 2016, 28 p. R. G. Gallager, “Low-Density Parity-Check Codes”, M.I.T. Press, 1963, 90 p. H. Crapo, D. Senato, “Algebraic Combinatorics and Computer Science: A Tribute to Gian-Carlo Rota”, Springer Science & Business Media, 2001, 546 p. 10.1007/3-540-44586-2_2K. Kobara, H. Imai, “Semantically secure McEliece public-key cryptosystems - conversions for McEliece PKC”, PKC 2001: Public Key Cryptography, 2001, vol. 1992, pp. 19-35. 10.1007/978-3-662-53887-6_29Q. Guo, T. Johansson, P. Stankovski, “A Key Recovery Attack on MDPC with CCA Security Using Decoding Errors”, Lecture Notes in Computer Science, 2016, vol. 10031, pp. 789-815. M. Kindberg, “A usability study of post-quantum algorithms”, Lunds universitet, 2017, 68 p. 10.15587/1729-4061.2016.75250S. Yevseiev, K. Rzayev, O. Korol, Z. Imanova, “Development of McEliece modified asymmetric crypto-code system on elliptic truncated codes”, Eastern-European Journal of Enterprise Technologies, 2016, vol. 4, iss. 9 (82), pp. 18-26.