scholarly journals Walks on graphs as symmetric or asymmetric tools to encrypt data

2002 ◽  
Vol 20 (1) ◽  
pp. 34 ◽  
Author(s):  
V. A. Ustimenko ◽  
Y. M. Khmelevsky
Keyword(s):  
Real Life ◽  
Theoretical Method ◽  
General Idea ◽  
Simple Groups ◽  
Prototype Model ◽  
Encryption Scheme ◽  
Symmetric Encryption ◽  
Encrypt Data ◽  
Rank 2 ◽  
Groups Of Lie Type

New results on graph theoretical method of encryption will be presented. The general idea is to treat vertices of a graph as messages, and walks of a certain length as ecnryption tools. We will construct one-time pad algorithms with a certain resistance to attacks when the adversary knows plaintext and ciphertext. Special linguistic graphs of high girth whose vertices (messages) and walks (encoding tools) could be both naturally identified with vectors over the finite field, and with the so-called parallelotopic graphs, which turn out to be efficient tools for symmetric encryption. We will formulate criteria when parallelotopic graph (or the more general graph of tactical configuration) is a graph of absolutely optimal encryption scheme, producing asymptotic one-time pad algorithm. We will show how to convert one-time pads, which are related to geometries of rank 2 of simple groups of Lie type, to a real-life encryption scheme involving potentially infinite text and flexible passwords. We will discuss families of linguistic and parallelotopic graphs of increasing girth as the source for the generation of asymmetric cryptographic functions and related open key algorithms. We will construct new families of such graphs via group theoretical and geometrical technique. The software for symmetric and asymmetric ecnryption (prototype model of the package) is ready for demonstration.

Local identification of spherical buildings and finite simple groups of Lie type

2013 ◽  
Vol 154 (3) ◽  
pp. 527-547 ◽  
Author(s):  
ULRICH MEIERFRANKENFELD ◽  
GERNOT STROTH ◽  
RICHARD M. WEISS
Keyword(s):  
Finite Group ◽  
Short Proof ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Group Of Lie Type ◽  
Parabolic Structure ◽  
Arbitrary Finite Group ◽  
Rank 2 ◽  
Groups Of Lie Type

AbstractWe give a short proof of the uniqueness of finite spherical buildings of rank at least 3 in terms of the structure of the rank 2 residues and use this result to prove a result making it possible to identify an arbitrary finite group of Lie type from knowledge of its “parabolic structure” alone. Our proof also involves a connection between loops, “Latin chamber systems” and buildings.

scholarly journals Finite simple exceptional groups of Lie type in which all subgroups of odd index are pronormal

2020 ◽  
Vol 23 (6) ◽  
pp. 999-1016
Author(s):  
Anatoly S. Kondrat’ev ◽  
Natalia V. Maslova ◽  
Danila O. Revin
Keyword(s):  
Simple Groups ◽  
Finite Simple Groups ◽  
Exceptional Groups ◽  
Odd Index ◽  
Groups Of Lie Type

AbstractA subgroup H of a group G is said to be pronormal in G if H and {H^{g}} are conjugate in {\langle H,H^{g}\rangle} for every {g\in G}. In this paper, we determine the finite simple groups of type {E_{6}(q)} and {{}^{2}E_{6}(q)} in which all the subgroups of odd index are pronormal. Thus, we complete a classification of finite simple exceptional groups of Lie type in which all the subgroups of odd index are pronormal.

A Novel Iterated Function System-Based Model for Coloured Image Encryption

2021 ◽  
Vol 12 (2) ◽  
pp. 1-10
Author(s):  
Amine Rahmani
Keyword(s):  
Image Encryption ◽  
Iterated Function System ◽  
Mathematical Concept ◽  
Logistic Equation ◽  
Encryption Scheme ◽  
Symmetric Encryption ◽  
New Model ◽  
Proposed Model ◽  
Iterated Function ◽  
Chaotic Cryptography

Chaotic cryptography has been a well-studied domain over the last few years. Many works have been done, and the researchers are still getting benefit from this incredible mathematical concept. This paper proposes a new model for coloured image encryption using simple but efficient chaotic equations. The proposed model consists of a symmetric encryption scheme in which it uses the logistic equation to generate secrete keys then an affine recursive transformation to encrypt pixels' values. The experimentations show good results, and theoretic discussion proves the efficiency of the proposed model.

A Study of the State of the Art in Synthetic Emotional Intelligence in Affective Computing

2020 ◽  
pp. 1199-1212
Author(s):  
Syeda Erfana Zohora ◽  
A. M. Khan ◽  
Arvind K. Srivastava ◽  
Nhu Gia Nguyen ◽  
Nilanjan Dey
Keyword(s):  
Emotional Intelligence ◽  
Affective Computing ◽  
Ethical Issues ◽  
State Of The Art ◽  
Real Life ◽  
Life Time ◽  
The State ◽  
Point Of View ◽  
General Idea ◽  
Tremendous Amount

In the last few decades there has been a tremendous amount of research on synthetic emotional intelligence related to affective computing that has significantly advanced from the technological point of view that refers to academic studies, systematic learning and developing knowledge and affective technology to a extensive area of real life time systems coupled with their applications. The objective of this paper is to present a general idea on the area of emotional intelligence in affective computing. The overview of the state of the art in emotional intelligence comprises of basic definitions and terminology, a study of current technological scenario. The paper also proposes research activities with a detailed study of ethical issues, challenges with importance on affective computing. Lastly, we present a broad area of applications such as interactive learning emotional systems, modeling emotional agents with an intention of employing these agents in human computer interactions as well as in education.

scholarly journals IDCrypt: A Multi-User Searchable Symmetric Encryption Scheme for Cloud Applications

IEEE Access ◽  
2018 ◽  
Vol 6 ◽  
pp. 2908-2921 ◽  
Author(s):  
Guofeng Wang ◽  
Chuanyi Liu ◽  
Yingfei Dong ◽  
Peiyi Han ◽  
Hezhong Pan ◽  
...  
Keyword(s):  
Encryption Scheme ◽  
Symmetric Encryption ◽  
Searchable Symmetric Encryption ◽  
Cloud Applications

scholarly journals On the Steinberg Character of a Finite Simple Group of Lie Type

1971 ◽  
Vol 12 (1) ◽  
pp. 1-14 ◽  
Author(s):  
Bhama Srinivasan
Keyword(s):  
Algebraic Group ◽  
Linear Algebraic Group ◽  
Simple Groups ◽  
Closed Field ◽  
Finite Simple Groups ◽  
Reductive Algebraic Group ◽  
Simple Algebraic Group ◽  
Simply Connected ◽  
Groups Of Lie Type ◽  
Steinberg Character

Let K be an algebraically closed field of characteristic ρ >0. If G is a connected, simple connected, semisimple linear algebraic group defined over K and σ an endomorphism of G onto G such that the subgroup Gσ of fixed points of σ is finite, Steinberg ([6] [7]) has shown that there is a complex irreducible character χ of Gσ with the following properties. χ vanishes at all elements of Gσ which are not semi- simple, and, if x ∈ G is semisimple, χ(x) = ±n(x) where n(x)is the order of a Sylow p-subgroup of (ZG(x))σ (ZG(x) is the centraliser of x in G). If G is simple he has, in [6], identified the possible groups Gσ they are the Chevalley groups and their twisted analogues over finite fields, that is, the ‘simply connected’ versions of finite simple groups of Lie type. In this paper we show, under certain restrictions on the type of the simple algebraic group G an on the characteristic of K, that χ can be expressed as a linear combination with integral coefficients of characters induced from linear characters of certain naturally defined subgroups of Gσ. This expression for χ gives an explanation for the occurence of n(x) in the formula for χ (x), and also gives an interpretation for the ± 1 occuring in the formula in terms of invariants of the reductive algebraic group ZG(x).

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