A key exchange protocol based on the ring Bn(R, P)
https://doi.org/10.26907/2541-7746.2024.1.52-57
Abstract
A key exchange protocol over a special class of formal matrices Bn(R, P) was proposed. The potential of this design for constructing key exchange protocols using suitable associative rings and ideals over them was shown.
References
1. Shannon C.E. A mathematical theory of communication. Bell Syst. Tech. J., 1948, vol. 27, no. 3, pp. 379–423. doi: 10.1002/j.1538-7305.1948.tb01338.x.
2. Diffie W., Hellman M.E. New directions in cryptography. IEEE Trans. Inf. Theory, 1976, vol. 22, no. 6, pp. 644–654. doi: 10.1109/TIT.1976.1055638.
3. Yashchenko V.V. Vvedenie v kriptografiyu [Introduction to Cryptography]. 4<sup>th</sup> enlarged ed. Moscow, MTsNMO, 2014. 347 p. (In Russian)
4. Roman’kov V.A. Algebraicheskaya kriptografiya : monografiya [Algebraic Cryptography : A Monograph]. Omsk, Izd. Omsk. Gos. Univ., 2013. 136 p. (In Russian)
5. Myasnikov A., Shpilrain V., Ushakov A. Non-Commutative Cryptography and Complexity of Group-Theoretic Problems. Ser.: Mathematical Surveys and Monographs. Vol. 177. Providence, RI, Am. Math. Soc., 2011. 385 p. doi: 10.1090/surv/177.
6. Climent J.-J., Navarro P.R., Tortosa L. An extension of the noncommutative Bergman’s ring with a large number of noninvertible elements. Appl. Algebra Eng., Commun. Comput., 2014, vol. 25, no. 5, pp. 347–361. doi: 10.1007/s00200-014-0231-6.
7. Bergman G.M. Some examples in PI ring theory. Isr. J. Math., 1974, vol. 18, no. 3, pp. 257–277. doi: 10.1007/BF02757282.
8. Climent J.-J., Navarro P.R., Tortosa L. On the arithmetic of the endomorphisms ring End(BbbZ p times BbbZ p2). Appl. Algebra Eng., Commun. Comput., 2011, vol. 22, no. 2, pp. 91–108. doi: 10.1007/s00200-011-0138-4.
9. Climent J.-J., Navarro P.R., Tortosa L. Key exchange protocols over noncommutative rings. The case of End(BbbZ p times BbbZ p2). Int. J. Comput. Math., 2012, vol. 89, nos. 13–14, pp. 1753–1763. doi: 10.1080/00207160.2012.696105.
10. Kamal A.A., Youssef A.M. Cryptanalysis of a key exchange protocol based on the endomorphisms ring End(BbbZ p times BbbZ p2). Appl. Algebra Eng., Commun. Comput., 2012, vol. 23, no. 3, pp. 143–149. doi: 10.1007/s00200-012-0170-z.
11. Climent J.-J., L´opez-Ramos J.A., Navarro P.R., Tortosa L. Key agreement protocols for distributed secure multicast over the ring E(m) p. WIT Trans. Inf. Commun. Technol., 2013, vol. 45, pp. 13–24. doi: 10.2495/DATA130021.
12. Zhang Y. Cryptanalysis of a key exchange protocol based on the ring E(m) p. Appl. Algebra Eng., Commun. Comput., 2018., vol. 29, no. 2, pp. 103–112. doi: 10.1007/s00200-017-0332-0.
13. Nasrutdinov M.F., Tronin S.N. On some class of formal matrix ring. Lobachevskii J. Math., 2022, vol. 43, no. 3, pp. 677–681. doi: 10.1134/S1995080222060269.
Review
For citations:
Nasrutdinov M.F. A key exchange protocol based on the ring Bn(R, P). Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(1):52-57. (In Russ.) https://doi.org/10.26907/2541-7746.2024.1.52-57
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