Restructuring of Discrete Logarithm Problem and ElGamal Cryptosystem by Using the Power Fibonacci Sequence Module M

A simple generalization of the ElGamal cryptosystem to non-abelian groups II

This is a study of the MOR cryptosystem using the special linear group over finite fields. The automorphism group of the special linear group is analyzed for this purpose. At our current state of knowledge, I show that the MOR cryptosystem has better security than the ElGamal cryptosystem over finite fields.

The Discrete Logarithm problem in the ElGamal cryptosystem over the abelian group U(n) Where n= p^m,or 2p^m

This study is mainly about the discrete logarithm problem in the ElGamal cryptosystem over the abelian group U(n) where n is one of the following forms p^m, or 2p^m where p is an odd large prime and m is a positive integer. It is another good way to deal with the ElGamal Cryptosystem using that abelian group U(n)={x: x is a positive integer such that x<n and gcd(n,x)=1} in the setting of the discrete logarithm problem . Since I show in this paper that this new study maintains equivalent (or better) security with the original ElGamal cryptosystem(invented by Taher ElGamal in 1985)[1], that work…

Image Encryption and Decryption in A Modification of ElGamal Cryptosystem in MATLAB

The need of exchanging messages and images secretly over unsecure networks promoted the creation of cryptosystems to enable receivers to interpret the exchanged information. In this paper, a particular public key cryptosystem called the ElGamal Cryptosystem is presented considered with the help MATLAB Program to be used over Images. Since the ElGamal cryptosystem over a primitive root of a large prime is used in messages encryption in the free GNU Privacy Guard software, recent versions of PGP, and other cryptosystems. This paper shows a modification of the this cryptosystem by applying it ove…

将ElGamal密码系统扩展到$\Z_{n}$的第三单位群

Extending the ElGamal Cryptosystem to the Third Group of Units of $\Z_{n}$

本文扩展ElGamal密码系统至环的第三单位群，证明其更安全，并描述所需算术及数值模拟验证安全性和效率。

The ElGamal cryptosystem over circulant matrices

In this paper we study extensively the discrete logarithm problem in the group of non-singular circulant matrices. The emphasis of this study was to find the exact parameters for the group of circulant matrices for a secure implementation. We tabulate these parameters. We also compare the discrete logarithm problem in the group of circulant matrices with the discrete logarithm problem in finite fields and with the discrete logarithm problem in the group of rational points of an elliptic curve.

The MOR cryptosystem and finite $p$-groups

The ElGamal cryptosystem is the most widely used public key cryptosystem. It uses the discrete logarithm problem as the cryptographic primitive. The MOR cryptosystem is a similar cryptosystem. It uses the discrete logarithm problem in the automorphism group as the cryptographic primitive. In this paper, we study the MOR cryptosystem for finite $p$-groups. The study is complete for $p^\prime$-automorphisms. For $p$-automorphisms there are some interesting open problems.