Secure encryption from cyclic codes
1Kocaeli Üniversitesi
Sigma Journal of Engineering and Natural Sciences 2022, Vol. 40, Issue 2, pp. 380-389; doi.org/10.14744/sigma.2022.00040
Abstract
Encryption is the process of scrambling a message and can provide a means of securing information. Information security is becoming more important in data storage and transmission. It is known that most encryption method in the literature. In this paper we propose two new encryption schemes by using cyclic codes. Our method is based on the One Time Pad system. We use the properties of cyclic codes to provide its security.
Keywords: Encryption; One Time Pad System; Cyclic Code; Skew Cyclic Code*
References
- Abualrub T, Seneviratne P. Skew codes over ring. [15] Klitz E, Masny D, Pietrzak K. Simple chosen- Hong Kong: Proc Int Multiconference Eng Comput ciphertext security from low-noise LPN. In Hugo Sci; 2010. Available at: http://www.iaeng.org/pub- Krawezyk, editor. Public-Key Cryptography – lication/IMECS2010/IMECS2010_pp846-847.pdf. PKC 2014. PKC 2014. Lecture Notes in Computer Accessed May 26, 2022. Science. Berlin, Heidelberg: Springer; 2014. [CrossRef]
- Ajtai M, Dwork C. A public-key cryptosystem [16] Kuklova Z. Coding theory, cryptography and cryp- with worst-case/average-case equivalence. 1997. tographic protocols-exercises with solutions (given Available at: http://citeseerx.ist.psu.edu/viewdoc/ in 2006). Bachelor Thesis. Brno: Masaryk University, download?doi=10.1.1.45.5652&rep=rep1&type= Faculty of Informatics; 2007. pdf. Accessed May 26, 2022. [17] Ling S, Xing C. Coding theory: A first course. UK:
- Alekhnovich M. More on average case vs approxi- Cambridge University Press; 2004. [CrossRef] mation complexity. Proc 44th Annuel IEEE Sym [18] McEliece RJ. A public-key cryptosystem based Foun Comput Sci 2003. Available at: https://www. on algebraic Coding theory. DSN Prog Rep cs.toronto.edu/~toni/Courses/PCP/handouts/ 1978:114–116. misha.pdf. Accessed May 26, 2022. [19] Misoezki R, Barreto PSLM. Compact McEliece
- Aguiler-Melchor C, Blazy O, Deneuville JC, Gaborit keys from goppa codes. In Michael J. Jacobson Jr, P, Zemor G. Efficient Encryption from random Rijmen V, Safavi-Naini R, editors. Selected areas in Quasi-Cyclic codes. IEEE Trans Info Theory cryptography. Heidelberg: Springer; 2009:376–392. 2018;64:3927–3943. [CrossRef] [CrossRef] Sigma J Eng Nat Sci, Vol. 40, No. 2, pp. 380–389, June, 2022 389
- Misoezki R, Tillich JP, Sendries N, Barreto PSLM. [23] Qian J. Quantum codes from cyclic codes over MDPC-McEliece: New mceliece variants from mod- 2 + v2 . J Inf Comput Sci 2013;10:1715–1722. [CrossRef] erate density parity-check codes. 2013. Available at: https://eprint.iacr.org/2012/409.pdf. Accessed May [24] Regev O. New lattice based cryptographic contruc- 26, 2022. [CrossRef] tions. In Proceedings of the 35th ACM Symposium
- Petrenko V, Ryabtsev S, Pavlov A, Apurin A. on Theory of Computing. J ACM 2004;51:899–942. [CrossRef] Development of an encryption method based on [25] Yao T, Shi M, Solé P. Skew cyclic codes over cyclic codes. Proceedings of the 21st International q + uq + vq + uvq* ,. J Algebra Comb Discrete Workshop on Computer Science and Information Struct App 2015;2:163–168. [CrossRef] Technologies. Atlantis Press 2019. [CrossRef]
- Prange E. The use of information sets in decod- Codes Over 2 + v2 ,. IEEE Trans Inf Theory ing cyclic codes. IRE Trans Inf Theory 1962;8:5–9. [CrossRef] 2010;56:1680–1684. [CrossRef]
Share and Cite
ÇALKAVUR, S.; GÜZELTEPE, M. Secure encryption from cyclic codes. Sigma Journal of Engineering and Natural Sciences 2022, Vol. 40, pp. 380-389. https://doi.org/10.14744/sigma.2022.00040
Export: