17 citations · 28 across the 7 of their papers we have counts for
15 papers
Cryptanalysis of protocols using (Simultaneous) Conjugacy Search Problem in certain Metabelian Platform Groups
Delaram Kahrobaei, Carmine Monetta, Ludovic Perret +2
There are many group-based cryptosystems in which the security relies on the difficulty of solving Conjugacy Search Problem (CSP) and Simultaneous Conjugacy Search Problem (SCSP) i…
A Closer Look at the Multilinear Cryptography using Nilpotent Groups
Delaram Kahrobaei, Antonio Tortora, Maria Tota
In a previous paper we generalized the definition of a multilinear map to arbitrary groups and introduced two multiparty key-exchange protocols using nilpotent groups. In this pape…
Multilinear Cryptography using Nilpotent Groups
Delaram Kahrobaei, Antonio Tortora, Maria Tota
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.
Engel groups with an identity
Pavel Shumyatsky, Antonio Tortora, Maria Tota
We give an affrmative answer to the question whether a residually finite Engel group satisfying an identity is locally nilpotent. More generally, for a residually finite group G wi…
On the primitivity of PRESENT and other lightweight ciphers
Riccardo Aragona, Marco Calderini, Antonio Tortora +1
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 ass…
A finiteness condition on centralizers in locally nilpotent groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
We give a detailed description of infinite locally nilpotent groups G such that the index |C_G (x) : <x>| is finite, for every non-normal cyclic subgroup <x> of G. We are also able…
A finiteness condition on centralizers in locally finite groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
We consider a finiteness condition on centralizers in a group G, namely that |C_G (x) : <x>| is finite for every non-normal cyclic subgroup <x> of G. For periodic groups, this is t…
On varieties of groups satisfying an Engel type identity
P. Shumyatsky, A. Tortora, M. Tota
Let m, n be positive integers, v a multilinear commutator word and w = v^m. Denote by v(G) and w(G) the verbal subgroups of a group G corresponding to v and w, respectively. We pro…
Some finiteness conditions on normalizers or centralizers in groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
We consider the following two finiteness conditions on normalizers and centralizers in a group G: (i) |N_G(H):H| is finite for every non-normal subgroup H of G, and (ii) |C_G(x):<x…
An Engel condition for orderable groups
P. Shumyatsky, A. Tortora, M. Tota
Let m,n be positive integers, v a multilinear commutator word and w=v^m. We prove that if G is an orderable group in which all w-values are n-Engel, then the verbal subgroup v(G) i…
Some restrictions on normalizers or centralizers in finite p-groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
We study three restrictions on normalizers or centralizers in finite p-groups, namely: (i) |N_G(H) : H| <= p^k for every H non-normal in G, (ii) |N_G(<g>) : <g>| <= p^k for every <…
A restriction on centralizers in finite groups
Gustavo A. Fernandez-Alcober, Leire Legarreta, Antonio Tortora +1
For a given m>=1, we consider the finite non-abelian groups G for which |C_G(g):<g>|<=m for every g in G\Z(G). We show that the order of G can be bounded in terms of m and the larg…
On locally graded groups with a word whose values are Engel
Pavel Shumyatsky, Antonio Tortora, Maria Tota
Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is a locally graded group in which all w-values are n-Engel, then the verbal subgroup…
On groups admitting a word whose values are Engel
Raimundo Bastos, Pavel Shumyatsky, Antonio Tortora +1
Let m, n be positive integers, v a multilinear commutator word and w = v^m. We prove that if G is a residually finite group in which all w-values are n-Engel, then the verbal subgr…
On groups with all subgroups subnormal or soluble of bounded derived length
Kivanc Ersoy, Antonio Tortora, Maria Tota
In this paper, we deal with locally graded groups whose subgroups are either subnormal or soluble of bounded derived length, say d. In particular, we prove that every locally (solu…