Algebra and Discrete Mathematics. - № 2 (23). - 2017
http://hdl.handle.net/123456789/4602
Tue, 03 Oct 2023 18:23:11 GMT2023-10-03T18:23:11ZOn new multivariate cryptosystems with nonlinearity gap
http://hdl.handle.net/123456789/4681
On new multivariate cryptosystems with nonlinearity gap
Ustimenko, V.
The pair of families of bijective multivariate maps
of kind Fn and Fn
−1
on affine space Kn over finite commutative ring
K given in their standard forms has a nonlinearity gap if the degree
of Fn is bounded from above by independent constant d and degree
of F
−1
is bounded from below by c
n, c > 1. We introduce examples
of such pairs with invertible decomposition Fn = G1
nG2
n . . . Gk
n,
i.e. the decomposition which allows to compute the value of F
n−1
in given point p = (p1, p2, . . . , pn) in a polynomial time O(n
2
).
The pair of families Fn, F
′
n of nonbijective polynomial maps of
affine space Kn such that composition FnF
′
n leaves each element
of K∗n
unchanged such that deg(Fn) is bounded by independent
constant but deg(F
′
n
) is of an exponential size and there is a decom-
position G1
nG2
n . . . Gk
n of Fn which allows to compute the reimage
of vector from F(K∗n
) in time 0(n
2
). We introduce examples of
such families in cases of rings K = Fq and K = Zm.
Ustimenko V. On new multivariate cryptosystems with nonlinearity gap / V. Ustimenko // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp. 331 - 348
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/123456789/46812017-01-01T00:00:00ZOn groups with biprimary subgroups of even order
http://hdl.handle.net/123456789/4678
On groups with biprimary subgroups of even order
Sokhor, I.
We investigate groups in which maximal sub-
groups of even order are primary or biprimary. We also research
soluble groups with restriction on a number of prime devisors of some
proper subgroup orders. We give applications of received results to
cofactors of proper subgroups.
Sokhor I. On groups with biprimary subgroups of even order / I.Sokhor // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp. 312 - 330
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/123456789/46782017-01-01T00:00:00ZA note on Hall S-permutably embedded subgroups of finite groups
http://hdl.handle.net/123456789/4675
A note on Hall S-permutably embedded subgroups of finite groups
Sinitsa, D.A.
Let G be a finite group. Recall that a subgroup A
of G is said to permute with a subgroup B if AB = BA. A subgroup
A of G is said to be S-quasinormal or S-permutable in G if A
permutes with all Sylow subgroups of G. Recall also that HsG is
the S-permutable closure of H in G, that is, the intersection of all
such S-permutable subgroups of G which contain H. We say that
H is Hall S-permutably embedded in G if H is a Hall subgroup of
the S-permutable closure HsG of H in G.
We prove that the following conditions are equivalent: (1) every
subgroup of G is Hall S-permutably embedded in G; (2) the nilpotent
residual GN of G is a Hall cyclic of square-free order subgroup of
G; (3) G = D ⋊ M is a split extension of a cyclic subgroup D of
square-free order by a nilpotent group M, where M and D are both
Hall subgroups of G.
Sinitsa D.A. A note on Hall S-permutably embedded subgroups of finite groups / D.A.Sinitsa // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp.305- 311
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/123456789/46752017-01-01T00:00:00ZProfinite closures of the iterated monodromy groups associated with quadratic polynomials
http://hdl.handle.net/123456789/4669
Profinite closures of the iterated monodromy groups associated with quadratic polynomials
Samoilovych, I.
In this paper we describe the profinite closure
of the iterated monodromy groups arising from the arbitrary post-
critically finite quadratic polynomial.
Samoilovych I. Profinite closures of the iterated monodromy groups associated with quadratic polynomials / I. Samoilovych // Algebra and Discrete Mathematics. - 2017. - Vol. 23. - Number 2. - Рp. 285 - 304
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/123456789/46692017-01-01T00:00:00Z