scholarly journals Variations of orthomorphisms and pseudo-hadamard transformations on nonabelian groups

2019 ◽  
pp. 24-27
Author(s):  
B.A. Pogorelov ◽  
M. A. Pudovkina
Keyword(s):  
Nonabelian Groups

scholarly journals Conjugacy Systems Based on Nonabelian Factorization Problems and Their Applications in Cryptography

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lize Gu ◽  
Shihui Zheng
Keyword(s):  
Performance Analysis ◽  
Quantum Algorithm ◽  
Integer Factorization ◽  
Algebraic Structures ◽  
Cryptographic Primitives ◽  
Factorization Problem ◽  
Integer Factorization Problem ◽  
Modern Cryptography ◽  
Nonabelian Groups

To resist known quantum algorithm attacks, several nonabelian algebraic structures mounted upon the stage of modern cryptography. Recently, Baba et al. proposed an important analogy from the integer factorization problem to the factorization problem over nonabelian groups. In this paper, we propose several conjugated problems related to the factorization problem over nonabelian groups and then present three constructions of cryptographic primitives based on these newly introduced conjugacy systems: encryption, signature, and signcryption. Sample implementations of our proposal as well as the related performance analysis are also presented.

scholarly journals Minimum product set sizes in nonabelian groups of order pq

2009 ◽  
Vol 129 (6) ◽  
pp. 1234-1245 ◽  
Author(s):  
Alan Deckelbaum
Keyword(s):  
Nonabelian Groups

CONJUGATE GRAPHS OF FINITE GROUPS

2012 ◽  
Vol 04 (02) ◽  
pp. 1250035 ◽  
Author(s):  
A. ERFANIAN ◽  
B. TOLUE
Keyword(s):  
Simple Group ◽  
Finite Groups ◽  
Nonabelian Group ◽  
Nonabelian Simple Group ◽  
Vertex Set ◽  
Thompson’S Conjecture ◽  
Central Factors ◽  
Nonabelian Groups

In this paper we introduce the conjugate graph [Formula: see text] associated to a nonabelian group G with vertex set G\Z(G) such that two distinct vertices join by an edge if they are conjugate. We show if [Formula: see text], where S is a finite nonabelian simple group which satisfy Thompson's conjecture, then G ≅ S. Further, if central factors of two nonabelian groups H and G are isomorphic and |Z(G)| = |Z(H)|, then H and G have isomorphic conjugate graphs.

Automorphism group of nonabelian groups of order p3

2014 ◽  
Author(s):  
Nor Haniza Sarmin ◽  
Yasamin Barakat
Keyword(s):  
Automorphism Group ◽  
Nonabelian Groups

scholarly journals Tight frames generated by finite nonabelian groups

2008 ◽  
Vol 48 (1-3) ◽  
pp. 11-27 ◽  
Author(s):  
Richard Vale ◽  
Shayne Waldron
Keyword(s):  
Tight Frames ◽  
Nonabelian Groups

Quantum algorithms for Simon's problem over nonabelian groups

2009 ◽  
Vol 6 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Gorjan Alagic ◽  
Cristopher Moore ◽  
Alexander Russell
Keyword(s):  
Quantum Algorithms ◽  
Nonabelian Groups

scholarly journals Nonabelian Groups with $(96,20,4)$ Difference Sets

10.37236/927 ◽  
2007 ◽  
Vol 14 (1) ◽  
Author(s):  
Omar A. AbuGhneim ◽  
Ken W. Smith
Keyword(s):  
Difference Sets ◽  
Difference Set ◽  
Existence Problem ◽  
Normal Subgroups ◽  
Nonabelian Groups

We resolve the existence problem of $(96,20,4)$ difference sets in 211 of 231 groups of order $96$. If $G$ is a group of order $96$ with normal subgroups of orders $3$ and $4$ then by first computing $32$- and $24$-factor images of a hypothetical $(96,20,4)$ difference set in $G$ we are able to either construct a difference set or show a difference set does not exist. Of the 231 groups of order 96, 90 groups admit $(96,20,4)$ difference sets and $121$ do not. The ninety groups with difference sets provide many genuinely nonabelian difference sets. Seven of these groups have exponent 24. These difference sets provide at least $37$ nonisomorphic symmetric $(96,20,4)$ designs.

scholarly journals Characterization of finite abelian and minimal nonabelian groups

2010 ◽  
Vol 45 (1) ◽  
pp. 55-62
Author(s):  
Yakov Berkovich
Keyword(s):  
Nonabelian Groups

scholarly journals On lacunary sets for nonabelian groups

1978 ◽  
Vol 25 (2) ◽  
pp. 167-176 ◽  
Author(s):  
A. H. Dooley
Keyword(s):  
Necessary Conditions ◽  
Abelian Groups ◽  
Sidon Sets ◽  
Compact Abelian Groups ◽  
Nonabelian Groups

AbstractResults concerning a class of lacunary sets are generalized from compact abelian to compact nonabelian groups. This class was introduced for compact abelian groups by Bozejko and Pytlik; it includes the p-Sidon sets of Edwards and Ross. A notion of test family is introduced and is used to give necessary conditions for a set to be lacunary. Using this, it is shown that (2) has no infinite p-Sidon sets for 1 ≤p<2.

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