Symmetric encryption scheme based on quasigroup using chained mode of operation
*Satish KumarCorresponding authorsatish.kumar.rs.mat18@itbhu.ac.inDepartment of Mathematical Sciences Indian Institute of Technology (BHU)Varanasi, Uttar Pradesh, 221005, IndiaView full profile → , Harshdeep Singhharshdeep.sag@gov.inDefence R & D Organization Metcalfe HouseDelhi, 110054, IndiaView full profile → , Indivar Guptaindivar_gupta@yahoo.comDefence R & D Organization Metcalfe HouseDelhi, 110054, IndiaView full profile → , Ashok Ji Guptaagupta.apm@itbhu.ac.inDepartment of Mathematical Sciences Indian Institute of Technology (BHU)Varanasi, Uttar Pradesh, 221005, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 12 Dec 2023
- Published Online:
- 18 Dec 2024
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JDMSC-1917
- Pages:
- 2337–2364
Abstract
Keywords
Subject Classifications
References
[1] F. H. Al-Rubbiay, “Cipher block chaining-based color medical image encryption for secure transmission,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 26 (2023).
[2] V. A. Artamonav, S. Chakrabarti, S. K. Tiwari, and V. T. Markov, “Algebraic properties of subquasigroups and construction of finite quasigroups,” Algebra and Logic, vol. 61, pp. 251-270 (2022).
[3] L. E. Bassham III, A. L. Rukhin, J. Soto, J. R. Nechvatal, M. E. Smid, E. B. Barker, S. D. Leigh, M. Levenson, M. Vangel, D. L. Banks, et al., “SP 800-22 rev. 1a. A statistical test suite for random and pseudorandom number generators for cryptographic applications,” National Institute of Standards & Technology (2010).
[4] M. Battey and A. Parakh, “An efficient quasigroup block cipher,” Wireless Personal Communications, vol. 73, pp. 63-76 (2013).
[5] M. Bellare, A. Desai, E. Jokiph, and P. Rogaway, “A concrete security treatment of symmetric encryption,” Proceedings 38th Annual Symposium on Foundations of Computer Science, IEEE, pp. 394-403 (1997).
[6] M. Bellare and P. Rogaway, “Entity authentication and key distribution,” Advances in Cryptology - CRYPTO-93. CRYPTO 1993, Lecture Notes in Computer Science, pp. 232-249 (1994).
[7] J. C. H. Castro, J. M. Sierra, A. Seznec, A. Izquierdo, and A. Ribagorda, “The strict avalanche criterion randomness test,” Mathematics and Computers Simulation, vol. 68, pp. 1-7 (2005).
[8] D. Chauhan, I. Gupta, P. R. Mishra, and R. Verma, “An ultra-lightweight block cipher with string transformations,” Cryptologia, pp. 1-7 (2023).
[9] W. L. Chee, “Public key cryptography based on Moufang loops,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 25, pp. 2411-2427 (2022).
[10] E. Couselo, S. Gonzalez, V. Markov, and A. Nechav, “Recursive MDS-codes and recursive differentiable quasigroups,” Discrete Math. Appl., vol. 8, pp. 217-246 (1998).
[11] L. Berardi, S. Jain, and B. K. Dass, “Bound for solid burst error correction with Lee weight,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 8, pp. 225-235 (2005).
[12] B. Biagio, B. K. Dass, and S. Jain, “High-density-burst error detection,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 7, pp. 5-21 (2004).
[13] B. K. Dass, “Burst Error Locating Linear Codes,” Journal of Information and Optimization Sciences, vol. 3, pp. 77-80 (1982).
[14] B. K. Dass, N. Sharma, and R. Verma, “MDS and I-perfect poset block codes,” Finite Fields and Their Applications, vol. 62, 101620 (2020).
[15] J. Dénes, “Latin squares and non-binary encoding,” Proc. Conf. Information Theory, CNRS, Paris, pp. 215-221 (1979).
[16] J. Dénes and A. D. Keedwell, “Some applications of non-associative algebraic systems in cryptology,” Pure Mathematics and Applications, vol. 12, pp. 147-195 (2001).
[17] J. Dénes and A. D. Keedwell, “Latin squares: New developments in the theory and applications,” Elsevier, vol. 46 (1991).
[18] A. Desai, “New paradigms for constructing symmetric encryption schemes secure against chosen-ciphertext attack,” Annual International Cryptology Conference, pp. 394-412 (2000).
[19] D. Dolev, C. Dwork, and M. Naor, “Non-malleable cryptography,” Proceedings of the Twenty-Third Annual ACM Symposium on Theory of Computing, pp. 542-552 (1991).
[20] L. Euler, “Recherches sur une espece de carrés magiques,” Commentationes Arithmeticae Collectae, vol. 2, pp. 302-361 (1849).
[21] D. Gligoroski, S. Markovski, and L. Kocarev, “Edon-R, An Infinite Family of Cryptographic Hash Functions,” Int. J. Netw. Secur., vol. 8, no. 3, pp. 293-300 (2009).
[22] D. Gligoroski, S. Markovski, and L. Kocarev, “Error-Correcting Codes Based on Quasigroups,” 16th International Conference on Computer Communications and Networks, pp. 165-172 (2007).
[23] D. Gligoroski, S. Markovski, and S. J. Knapskog, “A public key block cipher based on multivariate quadratic quasigroups,” arXiv preprint arXiv:0808.0247 (2008).
[24] A. Joshi and A. K. Mohapatra, “A novel lightweight authentication protocol for body area networks based on elliptic-curve cryptography,” Journal of Information and Optimization Sciences, vol. 41, pp. 1645-1672 (2020).
[25] J. Katz and Y. Lindell, Introduction to Modern Cryptography, CRC Press (2020).
[26] A. D. Keedwell and J. Dénes, Latin Squares and Their Applications, Elsevier (2015).
[27] S. Kumar, I. Gupta, and A. J. Gupta, “A study of public key cryptosystems based on quasigroups,” Cryptologia, pp. 511-540 (2022).
[28] S. Kumar, H. Singh, I. Gupta, and A. J. Gupta, “MDS codes based on orthogonality of quasigroups,” Applicable Algebra in Engineering, Communication and Computing (2023).
[29] M. Marcus and H. Minc, “Permanents,” The American Mathematical Monthly, vol. 77, pp. 577-591 (1965).
[30] S. Markovski, V. Dimitrova, Z. Trajcheska, M. Petkovska, M. Kostadinoski, and D. Buhov, “Block cipher defined by matrix presentation of quasigroups,” Cryptology ePrint Archive (2021).
[31] S. Markovski, D. Gligoroski, and S. Andova, “Using quasigroups for one-one secure encoding,” Proc. VIII Conf. Logic and Computer Science, ‘LIRA’, vol. 97, pp. 157-162 (1997).
[32] S. Markovski, A. Mileva, S. Samardziska, and B. Jakimovski, NaSHA, in First SHA-3 Candidate Conference, February 25-28, K.U. Leuven, Belgium (2009).
[33] G. Mittal, S. Kumar, and S. Kumar, “Novel public-key cryptosystems based on NTRU and algebraic structure of group rings,” Journal of Information and Optimization Sciences, vol. 42, pp. 1507-1521 (2021).
[34] R. Moufang, “Zur Struktur von Alternativkörpern,” Mathematische Annalen, vol. 10, pp. 416-430 (1935).
[35] E. Ochodková and V. Snášel, “Using quasigroups for secure encoding of file systems,” Proceedings of the International Scientific NATO PfP/PWP Conference Security and Information Protection, pp. 175-181 (2001).
[36] G. Shafi and S. Micali, “Probabilistic encryption,” Journal of Computer and System Sciences, vol. 28, pp. 270-299 (1984).
[37] J. Yu Shao and Wan-di Wei, “A formula for the number of Latin squares,” Discrete Mathematics, vol. 110, pp. 293-296 (1992).
[38] V. Shcherbacov, Elements of Quasigroup Theory and Applications, CRC Press (2017).
[39] D. R. Stinson, Cryptography: Theory and Practice, CRC Press (2005).
[40] S. K. Tiwari, A. Awasthi, S. Chakrabarti, and S. Yadav, “INRU: A quasigroup-based lightweight block cipher,” arXiv preprint arXiv:2112.07411 (2011).
[41] J. A. Tsimi and P. B. Gabriel Cedric, “On the generalized modal q-valent Reed-Muller codes,” Journal of Information and Optimization Sciences, vol. 42, pp. 1885-1906 (2021).
[42] J. A. Tsimi and R. C. Youdom, “The modal q-valent extensions of BCH codes,” Journal of Information and Optimization Sciences, vol. 42, pp. 1723-1764 (2021).




