Geodesic
A key exchange protocol based on the ring $B_n(R, P)$
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 1, pp. 52-57
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

A key exchange protocol over a special class of formal matrices $B_n(R,P)$ was proposed. The potential of this design for constructing key exchange protocols using suitable associative rings and ideals over them was shown.
Keywords: key exchange protocol, ring of formal matrices. 
@article{UZKU_2024_166_1_a3,
     author = {M. F. Nasrutdinov},
     title = {A key exchange protocol based on the ring $B_n(R, P)$},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
     pages = {52--57},
     year = {2024},
     volume = {166},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2024_166_1_a3/}
}
TY  - JOUR
AU  - M. F. Nasrutdinov
TI  - A key exchange protocol based on the ring $B_n(R, P)$
JO  - Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
PY  - 2024
SP  - 52
EP  - 57
VL  - 166
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/UZKU_2024_166_1_a3/
LA  - ru
ID  - UZKU_2024_166_1_a3
ER  - 
%0 Journal Article
%A M. F. Nasrutdinov
%T A key exchange protocol based on the ring $B_n(R, P)$
%J Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki
%D 2024
%P 52-57
%V 166
%N 1
%U http://geodesic.mathdoc.fr/item/UZKU_2024_166_1_a3/
%G ru
%F UZKU_2024_166_1_a3
M. F. Nasrutdinov. A key exchange protocol based on the ring $B_n(R, P)$. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 166 (2024) no. 1, pp. 52-57. http://geodesic.mathdoc.fr/item/UZKU_2024_166_1_a3/

[1] Shannon C.E., “A mathematical theory of communication”, Bell Syst. Tech. J., 27:3 (1948), 379–423 | DOI

[2] Diffie W., Hellman M.E., “New directions in cryptography”, IEEE Trans. Inf. Theory, 22:6 (1976), 644–654 | DOI

[3] Yashchenko V.V., Introduction to Cryptography, 4th enlarged ed., MTsNMO, M., 2014, 347 pp. (In Russian)

[4] Roman'kov V.A., Algebraic Cryptography: A Monograph, Izd. Omsk. Gos. Univ., Omsk, 2013, 136 pp. (In Russian)

[5] Myasnikov A., Shpilrain V., Ushakov A., Non-Commutative Cryptography and Complexity of Group-Theoretic Problems, Mathematical Surveys and Monographs, 177, Am. Math. Soc., Providence, RI, 2011, 385 pp. | DOI

[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., 25:5 (2014), 347–361 | DOI

[7] Bergman G.M., “Some examples in PI ring theory”, Isr. J. Math., 18:3 (1974), 257–277 | DOI

[8] Climent J.-J., Navarro P.R., Tortosa L., “On the arithmetic of the endomorphisms ring End${(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})}$”, Appl. Algebra Eng., Commun. Comput., 22:2 (2011), 91–108 | DOI

[9] Climent J.-J., Navarro P.R., Tortosa L., “Key exchange protocols over noncommutative rings. The case of End${(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})}$”, Int. J. Comput. Math., 89:13–14 (2012), 1753–1763 | DOI

[10] Kamal A.A., Youssef A.M., “Cryptanalysis of a key exchange protocol based on the endomorphisms ring End${(\mathbb{Z}_{p} \times \mathbb{Z}_{p^2})}$”, Appl. Algebra Eng., Commun. Comput, 23:3 (2012), 143–149 | DOI

[11] Climent J.-J., López-Ramos J.A., Navarro P.R., Tortosa L., “Key agreement protocols for distributed secure multicast over the ring $E_p^{(m)}$”, WIT Trans. Inf. Commun. Technol, 45 (2013), 13–24 | DOI

[12] Zhang Y., “Cryptanalysis of a key exchange protocol based on the ring $E_p^{(m)}$”, Appl. Algebra Eng., Commun. Comput, 29:2 (2018), 103–112 | DOI

[13] Nasrutdinov M.F., Tronin S.N., “On some class of formal matrix ring”, Lobachevskii J. Math., 43:3 (2022), 677–681 | DOI