Image encryption using sequence generated by cyclic group Kandar, Shyamalendu; Chaudhuri, Dhaibat; Bhattacharjee, Apurbaa ...
Journal of information security and applications,
February 2019, 2019-02-00, Volume:
44
Journal Article
Peer reviewed
•A permutation based non-chaotic image encryption technique.•Have used properties of cyclic group to define a sequence (or permutation of a sequence) which is used to perform pixel and bit level ...permutation.•Experimental results against different statistical and differential attacks prove the immunity of the proposed method.•Comparative analysis with some state of the art methods provides the scheme a strong base in the field of image encryption.
Image encryption using permutation is gaining its popularity over general encryption schemes like AES, DES, RSA etc., due to its high security, less time complexity using reasonable computational overheads. Mainly chaotic functions are employed in permutation based techniques to define a sequence, based on which the pixels or bits of an image are permuted. In parallel, researches are also carried out to define permutation using non chaotic techniques. In this paper, a novel non-chaotic image encryption technique is proposed. The properties of cyclic group are used as the backbone of the proposed method and using these properties some sequences/permutations are defined. These permutations are used for row/column level permutation of pixels and bit-level permutation. Iterative pixel addition operation with bit shifting using a ‘Transform array’ transforms the pixel value of the bit permuted image. Experimental results show that the proposed scheme is secure against statistical and differential attacks and provide a secure and efficient way for digital image encryption.
Number of terms in the group determinant Yamaguchi, Naoya; Yamaguchi, Yuka
Examples and counterexamples,
November 2023, 2023-11-00, 2023-11-01, Volume:
3
Journal Article
Peer reviewed
Open access
In this paper, we prove that when the number of terms in the group determinant of order odd prime p is divided by p, the remainder is 1. In addition, we give a table of the number of terms in kth ...power of the group determinant of the cyclic group of order n for n≤10 and k≤6, and also give a table of one for every group of order at most 15. These tables raise some questions for us about the number of terms in the group determinants.
Let n≥3. In this paper we deal with the conjugacy problem in the Artin braid group quotient Bn/Pn,Pn. To solve it we use systems of equations over the integers arising from the action of Bn/Pn,Pn ...over the abelianization of the pure Artin braid group Pn/Pn,Pn. Using this technique we also realize explicitly infinite virtually cyclic subgroups in Bn/Pn,Pn.
On Schur rings over infinite groups III Bastian, Nicholas; Misseldine, Andrew
Journal of algebraic combinatorics,
12/2023, Volume:
58, Issue:
4
Journal Article
Peer reviewed
Open access
In the paper, we develop further the properties of Schur rings over infinite groups, with particular emphasis on the virtually cyclic group
Z
×
Z
p
, where
p
is a prime. We provide structure theorems ...for primitive sets in these Schur rings. In the case of Fermat and safe primes, a complete classification theorem is proven, which states that all Schur rings over
Z
×
Z
p
are traditional. We also draw analogs between Schur rings over
Z
×
Z
p
and partitions of difference sets over
Z
p
.
A subset C of the vertex set of a graph Γ is called a perfect code in Γ if every vertex of Γ is at distance no more than 1 to exactly one vertex of C. A subset C of a group G is called a perfect code ...of G if C is a perfect code in some Cayley graph of G. In this paper we give sufficient and necessary conditions for a subgroup H of a finite group G to be a perfect code of G. Based on this, we determine the finite groups that have no nontrivial subgroup as a perfect code, which answers a question by Ma, Walls, Wang and Zhou.
On an example of Nagarajan Giokas, Annie; Singh, Anurag K.
Journal of algebra,
01/2024, Volume:
638
Journal Article
Peer reviewed
K. R. Nagarajan constructed an example of a formal power series ring of dimension two, over a field of characteristic two, with the action of a cyclic group of order two, such that the ring of ...invariants is not noetherian. We point out how Nagarajan's example readily extends to each positive prime characteristic, and also to a characteristic zero example: There exists a formal power series ring of dimension two, over a field of characteristic zero, with an action of the infinite cyclic group, such that the ring of invariants is not noetherian. Both the positive characteristic and the characteristic zero examples are sharp in multiple ways.
Determining eigenvalues, determinants, and inverse for a general matrix is computationally hard work, especially when the size of the matrix is large enough. But, if the matrix has a special type of ...entry, then there is an opportunity to make it much easier by giving its explicit formulation. In this article, we derive explicit formulas for determining eigenvalues, determinants, and inverses of circulant matrices with entries in the first row of those matrices in any formation of a sequence of numbers. The main method of our study is exploiting the circulant property of the matrix and associating it with cyclic group theory to get the results of the formulation. In every discussion of those concepts, we also present some computation remarks.
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