Submit your papersSubmit Now
For Enquiries: [email protected]
IIARD LogoIIARD

Theory and Application of Computational Algebra on Coding

Danjuma Samaila, Hannatu Ibrahim, Paul I. Dalatu

Abstract

This research presents the theory and application of computational algebra on coding. Starting on the level of develop error detection and correction codes, lading to Improved data integrity in various applications, we then further explore the mathematics foundations and practical of computational algebra techniques in the field of coding theory. And also, polynomial interpolation, matrix factorization, and integer factorization. We then consider coding theory in cryptography, block and linear codes, as well as the level of encoding with cyclic codes, Elliplic curve cryptography and factorization develop secure encryption and decryption method distinction between private-key and public-key cryptography, McEliece cryptosystem, Reed-solomon codes structure. We consider the Generic decoding attacks, structural attacks, Digital signature schemes based on error-correcting codes, Description of the Xinmei scheme, Resistance of the Alabbadi- wickes scheme against attacks

References

AlabbaadI. M, and Wicker.S.B, Digital signature scheme Based on error-correcting codes, proceedings of 1993 IEEE International symposium on information theory, 1993,pp,199. Alabbadi.M,and Wicker. S.B, Susceptibility of digital signature schemes based on error-correcting codes to universal forgery,error (Moscow, 1993), springer, Berlin, 1994 pp. 6-12. Berson.T.A,Failure of the McEliece public-key cryptosystem under message resend and related – message attack, Advances in cryptology CRYPTO 97, Lcture notes in computer science 1294 (B.S kalislai jr, ed),springer-verlage, 1997, pp 213 220. Beelen,P.H.T, Algebraic geometry and coding theory, ph.D thesis Eindhoven university of technology, 2001. Billet.O,Ding.J,(2016) Overview of cryptanalysis Techniqus in multivariate public key cryptography, inbook:Grobner Bases, coding and cryptography, Editors: M.sala, T. mora L.perrel, S. Sakata and C Traverso springer-verlag Berlin Heidelberg, pp. 263-283 (2009). Baigneres, Thomas, et al (2006). A Classical introduction to cryptography exercise book. New York;springer, ISBN 0387279342. Berlekamp E.R, McEliece R.J,And Tilborg H.C.A ,(1978). On the inherent intranctability of certain coding problems “in IEEE Transactions on information theory. Fujisaki.E and Okamoto.T, (1999). How to enhance the security of public-key encryption at minimum cost, public key cryptography, Gold wasser,S. Micali, and Tong.P, (1982) Why and how to establish a private code on or public network,23rd annual symposium on foundations of computer science chilago, IEEE, New York, pp 134-144. Gong.G and Lam.C,C,Y, (2002). Recursive sequences over elliptic curves, sequences and their Application SETA 01, springer London, pp 182-196o. Gong.G, Berson.T, and Stinson.D. (2000). Elliptic curve pse udorandom sequence generators, selected areas in cryptography (Kingston, oN,1999 ). Grantham.J, (2001), frobenius pseudoprimes, math, comp. 70, no 234873891. Glowinski. R, and kuznetsov. Y,On the solution of the Dirichlet problem for liner elliptic operators by a distributed lagrande multiplier method, comples Rendus de l Academie des sciences- series ⌠- mathematics 327 (2002) HalL C. L,. Goldberg l. and Schneier.B, (1999).Reaction attacks against several public-key cryptosystems proceedings of information and communication security, ICLCS 99, springer-verlag pp2-13 Hallgren S, (1994). Linear congruential generators over elliptic curves, Tech.Report CS -94-143, Dept. of comp. sc., carnene Mellon univ., Hamming, R.W (1986) Coding and information Theory 2nd edition prentice Hall. Hamming.R.W, Error detecting and error correcting codes, Bell, system Technical journal 29 147- 160 Hardly.G.H and Wright E.M, (1979). An introduction to the theory of numbers fifth ed. The clarendon press. OxFord university press New York, Hardy.D.W AND Walker C.L, (2003). Applied Algebra codes ciphers and Discrete algorithms pearson Education inc. Hill R, (1986). A first course in coding Theory, oxford university press, New York, ed. Judson T.W and Thomas W. Judson, (1997). and Abstract Algebra Theory and applications Remixed’. Kabatianskii. G, Krouk., and Smeets. B, (1997).A. digital signature scheme based on random error- correcting codes, cryptography and coding (cirencester) springer,Berlin pp 161-167 IJCSMT Kasami,T.Fujiwara,and Lin.S An approximation to the weight distribution of binary linear codes, IEEE Trans.inform.Theory no 6769-780. Kafun.D, (1967). The code breakers the story of secret writing, McEillan publishing company, New York, NY, usA. Harn.L and Wang.D.C,(1992). cryptoananlysists and modification of digital signature scheme based on error-correcting codes, Electronic letters no 2157-15. Kahn, David A, (1996) The code breakers; the comprehensive history of secret communication from an cient times to the internet; the story of secret writing New York scribner,ISBN 0684837309. Kahn. D, (1967) The code breakere the story of secret writing MacMillan, New York, Alightly revised edition has recently appeared. Kragler.R, contour integration: a procedure still missing in mathematica, lecture atnxv11 mathematica-Tag, (18 febr. 2016) WIAS\Berlin (2016) Mac F. Williams and Sloane.N (1977). The Theory of Error Correcting Codes, North. Holl And publishing company,Amsterdam. McEliece A, R.J. (1978). public key cryptography in; DSN progress Report 42-44. McEliece Knapsack.R.J, (1986). Type cryptosystems Algebraic Coding Theory. In problems of control and information Theory 15.2 (159-166) Niederrerter knapsack .H, (1986). Type cryplosystems and Algebraic Coding Theory”in problems of control and information theory. Peterson, W.W (1961). Error-Correcting Codes, The M.I.T Press Cambridge mass. Peretz.Y, on muoliariable encryption schemes, based on simultaneous algebraic RICCati equations over finite fields, finite fields and Their Application,39, pp.1-35 (2016) Quick math, (2007), Automatic math solutions 1999-2007 cited. Reed I. S and Solomon, G (1960). polynomial codes over certain finite fields, J. SOC.Indust. Appl.Math., Rothe,Jory,(2005) .complexity theory and cryptology,an introduction to crypto complexity. New York springer.ISBN 3540221476. ElGamal T, A (1984) Public key cryptosystem and a sidnature scheme based on discrete logarithms, Advances in cryptology (santa Barbara, calit, 1984), springer,Berlin, 1985. Sidelnikov .V.M, And Shestakov S.O,(1992). On insecurity of cryptosystems based on generalized Reed-solomon codes in Discrete math APPL 2.4. Stinson, Dougles, R. (2002). Cryptography: theory and practice, Boca Raton:CRC Press, ISBN 1584882069. Shen.W, Tang.S,ToT, a fast multivariable public key cryptosystm with Basic secure Trapdoor, cryptology eprint Archive, Report 2013|771. Lacr . org (2013). Tao.C, A Diene, S. Jang and J. Ding, simple matrix scheme for Encryption, p Qcrypto 2013, LNCS 7932, PP. 231-242 (2013). VAN LINT, J.H (1999). Introdution to coding theory springer-verlag, Berlin,third ed., Wicker S.B and Bhargava, V.K.E (1994). Reed-Solomon Codes And Applications, IEEE Press,Piscataway,first. Wicker, S.B (1995). Error Control systems for digital Communication and storage, prentice- Hall,upper saddle River,first ed. Wolf. C. B, preneel, Taxonomy of public-key schemes based on the problem of multivariate Quadratic Equations, cryptology eprint Archive, Report 2005\077, http:ll eprint (2005) Wikipedia, (2007). Contributors public-key cryptography. The Free Encyclopedia; last revision 8 may 129350176. IJCSMT Wikipeolia, (2007). Contributors:linear Code The Free Encyclopedia; last revision 19 Aprit 12464759

More Articles from INTERNATIONAL JOURNAL OF COMPUTER SCIENCE AND MATHEMATICAL THEORY

Advances in Algorithmic Contract Scoring for Pre-Negotiation Yield Optimization and Risk Retention

Author: Ngozi Samuel Uzougbo, Michael Ominyi, Cyril Chimelie Anichukwueze, Blessing, Chika Jones

DevTest flow: Designing a Scalable Continuous Testing Pipeline for High-Velocity Software Delivery

Author: Lawal Ahmed Oladimeji, Achori Busayo, Akeju BusayoZainab, Saka Samson, Damilare, Mbah Demian Chidi, Runsewe Similoluwa Mayowa, Oladiti Luqman, Abiodun