A group theoretical ElGamal cryptosystem based on a semidirect product of groups and a proposal for a signature protocol

2015 ◽  
pp. 97-113
Author(s):  
Anja Moldenhauer
Keyword(s):  
Semidirect Product ◽  
Elgamal Cryptosystem ◽  
Product Of Groups

scholarly journals The multiple holomorph of a semidirect product of groups having coprime exponents

2020 ◽  
Vol 115 (1) ◽  
pp. 13-21
Author(s):  
Cindy Tsang
Keyword(s):  
Semidirect Product ◽  
Product Of Groups

scholarly journals Supramenable groups and partial actions

2016 ◽  
Vol 37 (5) ◽  
pp. 1592-1606 ◽  
Author(s):  
EDUARDO P. SCARPARO
Keyword(s):  
Semidirect Product ◽  
Crossed Product ◽  
Probability Measures ◽  
Crossed Products ◽  
Hausdorff Spaces ◽  
Tracial States ◽  
Product Of Groups

We characterize supramenable groups in terms of the existence of invariant probability measures for partial actions on compact Hausdorff spaces and the existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a $\text{C}^{\ast }$-algebra by a semidirect product of groups into two iterated partial crossed products. However, we give conditions which ensure that such decomposition is possible.

scholarly journals Is a semidirect product of groups necessarily a group?

1993 ◽  
Vol 118 (3) ◽  
pp. 689-689 ◽  
Author(s):  
Gary F. Birkenmeier ◽  
C. Brad Davis ◽  
Kevin J. Reeves ◽  
Sihai Xiao
Keyword(s):  
Semidirect Product ◽  
Product Of Groups

Application of the Semidirect Product of Groups

1971 ◽  
Vol 12 (2) ◽  
pp. 314-314 ◽  
Author(s):  
Robert Geroch ◽  
E. T. Newman
Keyword(s):  
Semidirect Product ◽  
Product Of Groups

Text Encryption based on Huffman Coding and ElGamal Cryptosystem

2020 ◽  
Vol 14 ◽  
Author(s):  
Khoirom Motilal Singh ◽  
Laiphrakpam Dolendro Singh ◽  
Themrichon Tuithung
Keyword(s):  
Data Transfer ◽  
Huffman Coding ◽  
Large Integer ◽  
Text Data ◽  
Storage Devices ◽  
Scientific World ◽  
Elgamal Cryptosystem ◽  
Encryption Schemes ◽  
Transfer Operation ◽  
And Performance

Background: Data which are in the form of text, audio, image and video are used everywhere in our modern scientific world. These data are stored in physical storage, cloud storage and other storage devices. Some of it are very sensitive and requires efficient security while storing as well as in transmitting from the sender to the receiver. Objective: With the increase in data transfer operation, enough space is also required to store these data. Many researchers have been working to develop different encryption schemes, yet there exist many limitations in their works. There is always a need for encryption schemes with smaller cipher data, faster execution time and low computation cost. Methods: A text encryption based on Huffman coding and ElGamal cryptosystem is proposed. Initially, the text data is converted to its corresponding binary bits using Huffman coding. Next, the binary bits are grouped and again converted into large integer values which will be used as the input for the ElGamal cryptosystem. Results: Encryption and Decryption are successfully performed where the data size is reduced using Huffman coding and advance security with the smaller key size is provided by the ElGamal cryptosystem. Conclusion: Simulation results and performance analysis specifies that our encryption algorithm is better than the existing algorithms under consideration.

scholarly journals Nonsingular matrix as private key on ElGamal cryptosystem

2021 ◽  
Vol 1821 (1) ◽  
pp. 012018
Author(s):  
Maxrizal ◽  
Syafrul Irawadi
Keyword(s):  
Nonsingular Matrix ◽  
Private Key ◽  
Elgamal Cryptosystem

scholarly journals On the group of unit-valued polynomial functions

2021 ◽  
Author(s):  
Amr Ali Al-Maktry
Keyword(s):  
Commutative Ring ◽  
Semidirect Product ◽  
Polynomial Functions ◽  
Dual Numbers ◽  
Ring Of Integers ◽  
Group Of Units ◽  
Canonical Representations ◽  
Finite Commutative Ring

AbstractLet R be a finite commutative ring. The set $${{\mathcal{F}}}(R)$$ F ( R ) of polynomial functions on R is a finite commutative ring with pointwise operations. Its group of units $${{\mathcal{F}}}(R)^\times $$ F ( R ) × is just the set of all unit-valued polynomial functions. We investigate polynomial permutations on $$R[x]/(x^2)=R[\alpha ]$$ R [ x ] / ( x 2 ) = R [ α ] , the ring of dual numbers over R, and show that the group $${\mathcal{P}}_{R}(R[\alpha ])$$ P R ( R [ α ] ) , consisting of those polynomial permutations of $$R[\alpha ]$$ R [ α ] represented by polynomials in R[x], is embedded in a semidirect product of $${{\mathcal{F}}}(R)^\times $$ F ( R ) × by the group $${\mathcal{P}}(R)$$ P ( R ) of polynomial permutations on R. In particular, when $$R={\mathbb{F}}_q$$ R = F q , we prove that $${\mathcal{P}}_{{\mathbb{F}}_q}({\mathbb{F}}_q[\alpha ])\cong {\mathcal{P}}({\mathbb{F}}_q) \ltimes _\theta {{\mathcal{F}}}({\mathbb{F}}_q)^\times $$ P F q ( F q [ α ] ) ≅ P ( F q ) ⋉ θ F ( F q ) × . Furthermore, we count unit-valued polynomial functions on the ring of integers modulo $${p^n}$$ p n and obtain canonical representations for these functions.

Topological Left Amenability of Semidirect Products

1981 ◽  
Vol 24 (1) ◽  
pp. 79-85 ◽  
Author(s):  
H. D. Junghenn
Keyword(s):  
Large Class ◽  
Semidirect Product ◽  
Locally Compact ◽  
Semidirect Products ◽  
Topological Semigroups

AbstractLet S and T be locally compact topological semigroups and a semidirect product. Conditions are determined under which topological left amenability of S and T implies that of , and conversely. The results are used to show that for a large class of semigroups which are neither compact nor groups, various notions of topological left amenability coincide.

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