1,720,974 research outputs found
A new method for solving the elliptic curve discrete logarithm problem
No full textThe elliptic curve discrete logarithm problem is considered a securecryptographic primitive. The purpose of this paper is to propose a paradigmshift in attacking the elliptic curve discrete logarithm problem. In thispaper, we will argue that initial minors are a viable way to solve thisproblem. This paper will present necessary algorithms for this attack. We havewritten a code to verify the conjecture of initial minors using Schurcomplements. We were able to solve the problem for groups of order up to.Comment: 13 pages; revised for publicatio
The ElGamal Cryptosystem OVER CIRCULANT MATRICES
Get PDFCan one use the discrete logarithm problem in matrix groups, to build
a better and secure cryptosystem? We argue, it is indeed the case. This makes the group of circulant matrices suitable and attractive for lightweight cryptography
The Diffie–Hellman key exchange protocol, its generalization and nilpotent groups
No full textIn this paper we study a key exchange protocol similar to the Diffie-Hellman key exchange protocol, using abelian subgroups of the automor-phism group of a non-abelian nilpotent group. We also generalize group no. 92 of the Hall-Senior table [16] to an arbitrary prime p and show that, for those groups, the group of central automorphisms is commutative. We use these for the key exchange we are studying. 1
Diffie-Hellman Key Exchange Protocol, Its Generalization and Nilpotent Groups
Get PDFThis dissertation has two chapters. In the first chapter we talk about the discrete logarithm problem, more specifically we concentrate on the Diffie-Hellman key exchange protocol. We survey the current state of security for the Diffie-Hellman key exchange protocol. We also motivate the reader to think about the Diffie-Hellman key exchange in terms of group automorphisms. In the second chapter we study..
Diffie-Hellman Key Exchange Protocol And Non-Abelian Nilpotent Groups
Get PDFIn this paper we study a key exchange protocol similar to Diffie-Hellman key exchange protocol using abelian subgroups of the automorphism group of a non-abelian nilpotent group. We also generalize group no.92 of Hall-Senior table [15], for arbitrary prime p and show that for those groups, the group of central automorphisms commute. We use these for the key exchange we are studying
A simple generalization of the {E}l{G}amal cryptosystem to non-abelian groups II
Get PDFIn this paper I study the MOR cryptosystem using the special linear
group over finite fields. At our current state of knowledge, I show
that the MOR cryptosystem is more secure than the ElGamal
cryptosystem over finite fields
The discrete logarithm problem in the group of non-singular circulant matrices
Get PDFThe discrete logarithm problem is one of the backbones in public key
cryptography. In this paper we study the discrete logarithm problem in
the group of circulant matrices over a finite field. This gives rise
to secure and fast public key cryptosystems
A simple generalization of El-Gamal cryptosystem to non-abelian groups
Get PDFAbstract. In this paper we propose the group of unitriangular matrices over a finite field as a non-abelian group and composition of inner, diagonal and central automorphisms as a group of automorphisms for the MOR cryptosystem.
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