A Simple Generalization of the ElGamal Cryptosystem to Non-Abelian Groups
نویسندگان
چکیده
منابع مشابه
A Simple Generalization of the Elgamal Cryptosystem to Non-abelian Groups
In this article we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the ElGamal cryptosystem over finite fields can be built using the proposed groups and a set of automorphisms of these groups. We also show that the security of this proposed MOR cryptosystem is equ...
متن کاملA simple generalization of the El-Gamal cryptosystem to non-abelian groups II
The MOR cryptosystem is a generalization of the ElGamal cryptosystem, where the discrete logarithm problem works in the automorphism group of a group G, instead of the group G itself. The framework for the MOR cryptosystem was first proposed by Paeng et al. [13]. Mahalanobis [10] used the group of unitriangular matrices for the MOR cryptosystem. That effort was successful: the MOR cryptosystem ...
متن کاملA simple generalization of El-Gamal cryptosystem to non-abelian groups
In this paper we study the MOR cryptosystem. We use the group of unitriangular matrices over a finite field as the non-abelian group in the MOR cryptosystem. We show that a cryptosystem similar to the El-Gamal cryptosystem over finite fields can be built using the proposed groups and a set of automorphisms of these groups. We also show that the security of this proposed MOR cryptosystem is equi...
متن کاملA Generalization of Circulant Matrices for Non-Abelian Groups
A circulant matrix of order n is the matrix of convolution by a fixed element of the group algebra of the cyclic group Zn. Replacing Zn by an arbitrary finite group G gives the class of matrices that we call G-circulant. We determine the eigenvalues of such matrices with the tools of representation theory and the non-abelian Fourier transform. Definition 1 An n by n matrix C is circulant if the...
متن کاملnon-divisibility for abelian groups
Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2008
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870802160883