Overgroups of order 2n additive regular groups of a residue ring and of a vector space
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Boris A. Pogorelov
und
Marina A. Pudovkina
Abstract
The additive groups of the residue ring ℤ2n and of the vector space Vn over the field GF(2), as well as the group Gn generated by these additive groups, share common imprimitivity systems and enter as subgroups into the Sylow 2-subgroup of the symmetric group S(ℤ2n). These groups are used in cryptography as an encryption tool with the operations of addition in Vn and ℤ2n. The permutation structure of the subgroups of the group Gn is presented. The kernels of homomorphisms which correspond to various systems of imprimitivity, the normal subgroups, and some modular representations of the group Gn over the field GF(2) are described.
Originally published in Diskretnaya Matematika (2016)27, No3, 74–94 (in Russian).
References
[1] Cusick T. W., Stănică P., Cryptographic Boolean Functions and Applications, Elsevier, 2009, 232 pp.10.1016/B978-0-12-374890-4.00009-4Suche in Google Scholar
[2] Pogorelov B. A., Pudovkina M. A., “Orbital derivatives on residue rings. Part I. General properties”, Matematicheskie Voprosy Kriptograii, 5:4 (2014), 99–127 (in Russian).10.4213/mvk137Suche in Google Scholar
[3] Pogorelov B. A., Pudovkina M. A., “Orbital derivatives on residue rings. Part II. Probabilistic and combinatorial properties”, Matematicheskie Voprosy Kriptograii, 6:1 (2015), 117–133 (in Russian).10.4213/mvk154Suche in Google Scholar
[4] Sachkov V. N., Introduction to Combinatorial Methods of Discrete Mathematics, M.: MCCME, 2004 (in Russian), 424 pp.Suche in Google Scholar
[5] Grossman E., “Group theoretic remark on cryptographic system based on two types of additions”, Tech. Rept. 4742, Math. Sci. Dept., 1974.Suche in Google Scholar
© 2016 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Research Article
- Characterization of almost perfect nonlinear functions in terms of subfunctions
- Research Article
- Estimates for distribution of the minimal distance of a random linear code
- Research Article
- The distributions of interrecord fillings
- Research Article
- Galois theory for clones and superclones
- Research Article
- Overgroups of order 2n additive regular groups of a residue ring and of a vector space
Artikel in diesem Heft
- Frontmatter
- Research Article
- Characterization of almost perfect nonlinear functions in terms of subfunctions
- Research Article
- Estimates for distribution of the minimal distance of a random linear code
- Research Article
- The distributions of interrecord fillings
- Research Article
- Galois theory for clones and superclones
- Research Article
- Overgroups of order 2n additive regular groups of a residue ring and of a vector space
