Geodesic
Schemes of public distribution of a~key based on a~noncommutative operation
Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 148-157.

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We study properties of two schemes of public distribution of a key suggested by V. M. Sidelnikov which are based on a noncommutative operation. As a noncommutative operation we consider the operations belonging to the family suggested by M. A. Cherepnev, namely, the operations in the rings of integers of cyclotomic fields based on the power residue symbol. In the paper, a cryptanalysis of both schemes is performed for a particular noncommutative operation. We show that for an arbitrary operation of the mentioned above family the first scheme in not resistant. For the second scheme, we prove a theorem on the equivalence of its breaking to a solution of some problem of a computational algebraic number theory. 
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V. V. Nazarov. Schemes of public distribution of a~key based on a~noncommutative operation. Diskretnaya Matematika, Tome 18 (2006) no. 4, pp. 148-157. http://geodesic.mathdoc.fr/item/DM_2006_18_4_a13/

[1] Sidelnikov V. M., Cherepnev M. A., Yaschenko V. V., “Sistemy otkrytogo raspredeleniya klyuchei na osnove nekommutativnykh polugrupp”, DAN SSSR, 332 (1993), 566–567 | Zbl

[2] Cherepnev M. A., “Skhemy otkrytogo raspredeleniya klyucha na osnove nekommutativnoi gruppy”, Diskretnaya matematika, 15:2 (2003), 47–51 | Zbl

[3] Cherepnev M. A., “Skhemy otkrytogo raspredeleniya klyucha na osnove nekommutativnoi operatsii”, Tez. dokl. XIII Mezhdunarodnoi konf. «Problemy teoreticheskoi kibernetiki», Kazan, 2002, 190