Related papers: A note on using finite non-abelian $p$-groups in t…
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…
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…
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…
This paper studies the MOR cryptosystem, using the automorphism group of the extra-special $p$-group of exponent $p$, for an odd prime $p$. Similar results can be obtained for extra-special $p$-groups of exponent $p^2$ and for the even…
In this paper we study the MOR cryptosystem using finite classical Chevalley groups over a finite field of odd characteristic. In the process we develop an algorithm for these Chevalley groups in the same spirit as the row-column operation…
In this paper, we propose two cryptosystems based on group rings and existing cryptosystem. First one is Elliptic ElGamal type group ring public key cryptosystem whose security is greater than security of cryptosystems based on elliptic…
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…
In this paper, we extend the ElGamal cryptosystem to the third group of units of the ring $\Z_{n}$, which we prove to be more secure than the previous extensions. We describe the arithmetic needed in the new setting. We also provide some…
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.…
An important problem of modern cryptography concerns secret public-key computations in algebraic structures. We construct homomorphic cryptosystems being (secret) epimorphisms f:G --> H, where G, H are (publically known) groups and H is…
The theory of finite simple groups is a (rather unexplored) area likely to provide interesting computational problems and modelling tools useful in a cryptographic context. In this note, we review some applications of finite non-abelian…
We develop a public key cryptosystem based on invariants of diagonalizable groups and investigate properties of such cryptosystem first over finite fields, then over number fields and finally over finite rings. We consider the security of…
The article explores the creation of a cryptosystem using a halidon group ring of a dihedral group. Due to the non-abelian nature of the group, constructing the cryptosystem is more challenging compared to an abelian group. The logic used…
This paper introduces a newly developed private key cryptosystem and a public key cryptosystem. In the first one, each letter is encrypted with a different key. Therefore, it is a kind of a one-time pad. The second one is inspired by the…
Post-quantum cryptography (PQC) attempts to find cryptographic protocols resistant to attacks using for instance Shor's polynomial time algorithm for numerical field problems like integer factorization (IFP) or the discrete logarithm (DLP).…
Cryptographic systems are derived using units in group rings. Combinations of types of units in group rings give units not of any particular type. This includes cases of taking powers of units and products of such powers and adds the…
We present a study on the use of Pell hyperbolas in cryptosystems with security based on the discrete logarithm problem. Specifically, after introducing the group's structure over generalized Pell conics (and also giving the explicit…
An improved design of a cryptosystem based on small Ree groups is proposed. We have changed the encryption algorithm and propose to use a logarithmic signature for the entire Ree group. This approach improves security against sequential key…
The advent of large-scale quantum computers implies that our existing public-key cryptography infrastructure has become insecure. That means that the privacy of many mobile applications involving dynamic peer groups, such as multicast…
Consider the classical ElGamal digital signature scheme based on the modular relation $\alpha^m\equiv y^r\, r^s\ [p]$. In this work, we prove that if we can compute a natural integer $i$ such that $\alpha^i\ mod\ p$ is smooth and divides…