A Simple Generalization of the Elgamal Cryptosystem to Non-abelian Groups
نویسنده
چکیده
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 equivalent to the ElGamal cryptosystem over finite fields.
منابع مشابه
A 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 ...
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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...
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The MOR cryptosystem [9] is a natural generalization of the El-Gamal cryptosystem to non-abelian groups. Using a p-group, a cryptosystem was built in [4]. It seems resoanable to assume the cryptosystem is as secure as the El-Gamal cryptosystem over finite fields. A natural question arises can one make a better cryptosystem using p-groups? In this paper we show that the answer is no.
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