Zobrazeno 1 - 10
of 32
pro vyhledávání: '"Antonio Tortora"'
Publikováno v:
International Journal of Group Theory, Vol 14, Iss 2, Pp 59-73 (2023)
The homomorphic encryption allows us to operate on encrypted data, making any action less vulnerable to hacking. The implementation of a fully homomorphic cryptosystem has long been impracticable. A breakthrough was achieved only in 2009 thanks to Ge
Externí odkaz:
https://doaj.org/article/e96ce213cab6496f844fb56090b5094d
Autor:
Antonio Tortora, Maria Tota
Publikováno v:
International Journal of Group Theory, Vol 9, Iss 4, Pp 251-260 (2020)
The eighth edition of the international series of Groups St Andrews conferences was held at the University of Bath in 2009 and one of the theme days was dedicated to Engel groups. Since then much attention has been devoted to a verbal generalization
Externí odkaz:
https://doaj.org/article/1e8a213698334ddc8b70bd54a7df64b5
Autor:
Marialaura Noce, Antonio Tortora
Publikováno v:
International Journal of Group Theory, Vol 8, Iss 3, Pp 9-14 (2019)
Let $Gamma$ be the first Grigorchuk group. According to a result of Bar-thol-di, the only left Engel elements of $Gamma$ are the involutions. This implies that the set of left Engel elements of $Gamma$ is not a subgroup. The n
Externí odkaz:
https://doaj.org/article/9c9a32fa23964b1ba198c847644a2cce
Autor:
Costantino Delizia, Antonio Tortora
Publikováno v:
International Journal of Group Theory, Vol 1, Iss 2, Pp 19-24 (2012)
Let n be an integer. A group G is said to be n-abelian if the map phi_n that sends g to g^n is an endomorphism of G. Then (xy)^n=x^ny^n for all x,y in G, from which it follows [x^n,y]=[x,y]^n=[x,y^n]. It is also easy to see that a group G is n-abelia
Externí odkaz:
https://doaj.org/article/5e8276aa71f74beb9a695f525f7fdf5e
Publikováno v:
International Journal of Computer Mathematics: Computer Systems Theory. 7:63-67
In Kahrobaei et al. [Multilinear cryptography using nilpotent groups, Proceedings of Elementary Theory of Groups and Group Rings, and Related Topics conference. Conference held at Fairfield University and at the Graduate Center, CUNY, New York, NY, U
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bca6a5af616c51bdfda7b6c84f45a3ed
https://doi.org/10.1080/23799927.2021.2006314
https://doi.org/10.1080/23799927.2021.2006314
Let w be a group-word. For a group G, let G w {G_{w}} denote the set of all w-values in G and w ( G ) {w(G)} the verbal subgroup of G corresponding to w. The word w is semiconcise if the subgroup [ w ( G ) , G ] {[w(G),G]} is finite whenever
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::6eccf212c961a9ca37d2c854472aaa98
http://hdl.handle.net/11386/4738742
http://hdl.handle.net/11386/4738742
In this paper we generalize the definition of a multilinear map to arbitrary groups and develop a novel idea of multilinear cryptosystem using nilpotent group identities.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::04908b0c906a11ebaef86f31fe6dd110
http://arxiv.org/abs/1902.08777
http://arxiv.org/abs/1902.08777
Autor:
Antonio Tortora, Luise-Charlotte Kappe
Publikováno v:
Communications in Algebra. 45:3994-4001
A group in which all cyclic subgroups are 2-subnormal is called a 2-Baer group. The topic of this paper are generalized 2-Baer groups, i.e., groups in which the non-2-subnormal cyclic subgroups generate a proper subgroup of the group. If this subgrou
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::72a2566745c6f14c1b3cbcb94fdee7ad
https://doi.org/10.1080/00927872.2016.1252385
https://doi.org/10.1080/00927872.2016.1252385
We give an affirmative answer to the question whether a residually finite Engel group satisfying an identity is locally nilpotent. More generally, for a residually finite group [Formula: see text] with an identity, we prove that the set of right Enge
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cea5310728e59c363c240f0b2b57eabe
http://arxiv.org/abs/1805.12411
http://arxiv.org/abs/1805.12411
We provide two sufficient conditions to guarantee that the round functions of a translation-based cipher generate a primitive group. Furthermore, under the same hypotheses, and assuming that a round of the cipher is strongly proper and consists of [F
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f64e56f75f46af929cbbb310cc24b6e7
http://hdl.handle.net/11591/402848
http://hdl.handle.net/11591/402848