On the applications of Extremal Graph Theory to Coding Theory and Cryptography

Bollobás, 1978 Chistov, 2011, An improvement of the complexity bound for solving systems of polynomial equations, Zapisky nauchnych seminarov POMI, 390, 299 Dieudonné, 1970, La géométrie des groupes classiques, vol. 5 Gallager, 1962, Low-Density Parity-Check Codes, IRE Trans of Info Thy, 8, 21pp, 10.1109/TIT.1962.1057683 Ding, 2006, Multivariate Public Key Cryptosystems, Springer, Advances in Information Security, 25, 260 Guinand, 1997, Tanner Type Codes Arising from Large Girth Graphs, 5 Lazebnik, 1995, A new series of dense graphs of high girth, Bull. Amer. Math. Soc. (N. S.), 32, 73, 10.1090/S0273-0979-1995-00569-0 Lazard, 2009, Thirty years of Polynomial System Solving, and now?, J. Symb. Comput., 44, 222, 10.1016/j.jsc.2008.03.004 Lubotsky, 1989, Ramanujan graphs, J. Comb. Theory., 115, 62 Matsumoto, 1988, Public quadratic polynomial-tuples for efficient signatureverification and message-encryption, Eurocrypt, Springer-Verlag, 8, 419 Margulis, 1988, Explicit group-theoretical constructions of combinatorial schemes and their application to the design of expanders and concentrators, J. Probl. Inf. Transm., 24, 3946 Patarin, 1995, 248 M. Polak, V. Ustimenko, On LDPC Codes Corresponding to Infinite Family of Graphs A(k; K), Federated Conference on Computer Science and Information Systems 2012, in: Proceedings in the IEEE Xplore Digital Library, 567–570. Romańczuk, 2013, On Extremal Graph Theory, Explicit Algebraic Constructions of Extremal Graphs and Corresponding Turing Encryption Machines, vol. 427 Romańczuk Romańczuk, 2011, On the key exchange with new cubical maps based on graphs, Annales UMCS Informatica AI XI, 4, 11 Ustimenko, 2011 Ustimenko, 2011, On the key expansion of D(n;K)-based cryptographical algorithm, Annales UMCS Informatica AI XI, 2, 95 Ustimenko, 2013, On Extremal Graph Theory and Symbolic Computations, Dopovidi of the National Ukrainian Acad. Sci., 2, 15 Wróblewska, 2008, On some applications of graph based public key, Albanian J. Math., 2, 229