scholarly journals Public Key Protocols over Twisted Dihedral Group Rings

Symmetry ◽  
2019 ◽  
Vol 11 (8) ◽  
pp. 1019
Author(s):  
María Dolores Gómez Olvera ◽  
Juan Antonio López Ramos ◽  
Blas Torrecillas Jover
Keyword(s):  
Information Security ◽  
Group Ring ◽  
Key Management ◽  
Dihedral Group ◽  
Complexity Analysis ◽  
Public Key ◽  
Group Rings ◽  
Decomposition Problem ◽  
Hard Problems ◽  
Twisted Group Ring

Key management is a central problem in information security. The development of quantum computation could make the protocols we currently use unsecure. Because of that, new structures and hard problems are being proposed. In this work, we give a proposal for a key exchange in the context of NIST recommendations. Our protocol has a twisted group ring as setting, jointly with the so-called decomposition problem, and we provide a security and complexity analysis of the protocol. A computationally equivalent cryptosystem is also proposed.

Units in Group Rings of the Infinite Dihedral Group

1991 ◽  
Vol 34 (1) ◽  
pp. 83-89 ◽  
Author(s):  
Maciej Mirowicz
Keyword(s):  
Group Ring ◽  
Integral Domain ◽  
Dihedral Group ◽  
Group Rings ◽  
Finitely Generated ◽  
Group Of Units ◽  
Group D

AbstractThis paper studies the group of units U(RD∞) of the group ring of the infinite dihedral group D∞ over a commutative integral domain R. The structures of U(Z2D∞) and U(Z3D∞) are determined, and it is shown that U(ZD∞) is not finitely generated.

A key exchange protocol using matrices over group ring

2019 ◽  
Vol 12 (05) ◽  
pp. 1950075
Author(s):  
Indivar Gupta ◽  
Atul Pandey ◽  
Manish Kant Dubey
Keyword(s):  
Group Ring ◽  
Complexity Analysis ◽  
Discrete Logarithm ◽  
Key Exchange ◽  
Group Rings ◽  
Secret Key ◽  
Key Exchange Protocol ◽  
Diffie Hellman ◽  
Shared Secret ◽  
Invertible Matrices

The first published solution to key distribution problem is due to Diffie–Hellman, which allows two parties that have never communicated earlier, to jointly establish a shared secret key over an insecure channel. In this paper, we propose a new key exchange protocol in a non-commutative semigroup over group ring whose security relies on the hardness of Factorization with Discrete Logarithm Problem (FDLP). We have also provided its security and complexity analysis. We then propose a ElGamal cryptosystem based on FDLP using the group of invertible matrices over group rings.

scholarly journals Twisted group rings which are semi-prime Goldie rings

1975 ◽  
Vol 16 (1) ◽  
pp. 1-11 ◽  
Author(s):  
A. Reid
Keyword(s):  
Group Ring ◽  
Quotient Ring ◽  
Factor Group ◽  
Polynomial Rings ◽  
Group Rings ◽  
Twisted Group ◽  
Twisted Group Ring ◽  
Quotient Rings

In this paper we examine when a twisted group ring,Rγ(G), has a semi-simple, artinian quotient ring. In §1 we assemble results and definitions concerning quotient rings, Ore sets and Goldie rings and then, in §2, we defineRγ(G). We prove a useful theorem for constructing a twisted group ring of a factor group and establish an analogue of a theorem of Passman. Twisted polynomial rings are discussed in §3 and I am indebted to the referee for informing me of the existence of [4]. These are used as a tool in proving results in §4.

scholarly journals Twisted group rings and a problem of Faith

1973 ◽  
Vol 9 (1) ◽  
pp. 11-19 ◽  
Author(s):  
John H. Cozzens
Keyword(s):  
Group Ring ◽  
Type Theorem ◽  
Arbitrary Field ◽  
Group Rings ◽  
One Dimensional ◽  
Simple Modules ◽  
Isomorphism Classes ◽  
Twisted Group ◽  
Homological Characterization ◽  
Twisted Group Ring

A homological characterization is given of when a twisted group ring relative to an automorphism of an arbitrary field has all of its simple right modules injective (= a right V-ring). This answers a question raised by Osofsky. A “Hilbert Theorem 90” type theorem determines the cardinality of the isomorphism classes of one-dimensional simple modules.

Determining Units in Some Integral Group Rings

1990 ◽  
Vol 33 (2) ◽  
pp. 242-246 ◽  
Author(s):  
E. G. Goodaire ◽  
E. Jespers ◽  
M. M. Parmenter
Keyword(s):  
Finite Group ◽  
Group Ring ◽  
Dihedral Group ◽  
Group Rings ◽  
Integral Group ◽  
Basic Information ◽  
Integral Group Rings ◽  
Special Cases ◽  
A Finite Group ◽  
Made In

In this brief note, we will show how in principle to find all units in the integral group ring ZG, whenever G is a finite group such that and Z(G) each have exponent 2, 3, 4 or 6. Special cases include the dihedral group of order 8, whose units were previously computed by Polcino Milies [5], and the group discussed by Ritter and Sehgal [6]. Other examples of noncommutative integral group rings whose units have been computed include , but in general very little progress has been made in this direction. For basic information on units in group rings, the reader is referred to Sehgal [7].

Implementation Color-Images Cryptography Using RSA Algorithm

2017 ◽  
Vol 7 (11) ◽  
pp. 181
Author(s):  
Ali Saleh Al Najjar
Keyword(s):  
Information Security ◽  
Image Encryption ◽  
Color Images ◽  
Public Key ◽  
Open Channels ◽  
Image Security ◽  
Rsa Algorithm ◽  
The Media ◽  
Encrypted Images ◽  
Difficult Issue

Absolute protection is a difficult issue to maintain the confidentiality of images through their transmission over open channels such as internet or networks and is a major concern in the media, so image Cryptography becomes an area of attraction and interest of research in the field of information security. The paper will offer proposed system that provides a special kinds of image Encryption image security, Cryptography using RSA algorithm for encrypted images by HEX function to extract HEX Code and using RSA public key algorithm, to generate cipher image text. This approach provides high security and it will be suitable for secured transmission of images over the networks or Internet.

Public-Key Encryption

2017 ◽  
Author(s):  
Keith M. Martin
Keyword(s):  
Elliptic Curve ◽  
Public Key Cryptography ◽  
Public Key ◽  
Public Key Encryption ◽  
Hybrid Encryption ◽  
Public Key Cryptosystems ◽  
Encryption And Decryption ◽  
Encryption Schemes ◽  
Hard Problems ◽  
Set Up

In this chapter, we introduce public-key encryption. We first consider the motivation behind the concept of public-key cryptography and introduce the hard problems on which popular public-key encryption schemes are based. We then discuss two of the best-known public-key cryptosystems, RSA and ElGamal. For each of these public-key cryptosystems, we discuss how to set up key pairs and perform basic encryption and decryption. We also identify the basis for security for each of these cryptosystems. We then compare RSA, ElGamal, and elliptic-curve variants of ElGamal from the perspectives of performance and security. Finally, we look at how public-key encryption is used in practice, focusing on the popular use of hybrid encryption.

Performance and Scalability Assessment for Non-Certificate-Based Public Key Management in VANETs

2012 ◽  
Vol 6 (1) ◽  
pp. 33-56 ◽  
Author(s):  
Pei-Yuan Shen ◽  
Maolin Tang ◽  
Vicky Liu ◽  
William Caelli
Keyword(s):  
Key Management ◽  
Vehicular Ad Hoc Networks ◽  
Ad Hoc ◽  
Comprehensive Evaluation ◽  
Public Key ◽  
Secure Messaging ◽  
Evaluation Of Performance ◽  
Management Regime ◽  
Verification Process ◽  
Hoc Networks

Current research in secure messaging for Vehicular Ad hoc Networks (VANETs) focuses on employing a digital certificate-based Public Key Cryptosystem (PKC) to support security. However, the security overhead of such a scheme creates a transmission delay and introduces a time-consuming verification process to VANET communications. This paper proposes a non-certificate-based public key management for VANETs. A comprehensive evaluation of performance and scalability of the proposed public key management regime is presented, which is compared with a certificate-based PKC by employing a number of quantified analyses and simulations. In this paper, the authors demonstrate that the proposal can maintain security and assert that it can improve overall performance and scalability at a lower cost, compared with certificate-based PKC. The proposed scheme adds a new dimension to key management and verification services for VANETs.

scholarly journals Group ring based public key cryptosystems

2021 ◽  
pp. 1-22
Author(s):  
Gaurav Mittal ◽  
Sunil Kumar ◽  
Shiv Narain ◽  
Sandeep Kumar
Keyword(s):  
Group Ring ◽  
Public Key ◽  
Public Key Cryptosystems
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