Related papers: Commutative-like Encryption: A New Characterizatio…
This paper presents a new chaining technique for the use of Hadamard transforms for encryption of both binary and non-binary data. The lengths of the input and output sequence need not be identical. The method may be used also for hashing.
The objective of this work is to survey several digital signatures proposed in the last decade using non-commutative groups and rings and propose a digital signature using non-commutative groups and analyze its security.
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 show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme of such type. In most cases, such schemes are built on…
Cryptography is an art and science of secure communication. Here the sender and receiver are guaranteed the security through encryption of their data, with the help of a common key. Both the parties should agree on this key prior to…
In this paper, we have proposed a modified cryptographic scheme based on the application of recursive matrices as key in ECC and ElGamal. For encryption, we consider mapping analogous to affine Hill cipher in which a plaintext matrix has…
We propose a new symmetric cryptographic scheme based on functional invariants defined over discrete oscillatory functions with hidden parameters. The scheme encodes a secret integer through a four-point algebraic identity preserved under…
In this paper I consider all possible properties from commutative algebra for polynomial composites and monoid domains. The aim is full characterization of these structures. I start with the examination of group, ring, modules properties,…
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…
Homomorphic encryption is a form of encryption which allows computation to be carried out on the encrypted data without the need for decryption. The success of quantum approaches to related tasks in a delegated computation setting has…
The goal of this chapter is to present a survey of homomorphic encryption techniques and their applications. After a detailed discussion on the introduction and motivation of the chapter, we present some basic concepts of cryptography. The…
We propose a symmetric key homomorphic encryption scheme based on the evaluation of multivariate polynomials over a finite field. The proposed scheme is somewhat homomorphic with respect to addition and multiplication. Further, we define a…
Cryptography plays a pivotal role in safeguarding sensitive information and facilitating secure communication. Classical cryptography relies on mathematical computations, whereas quantum cryptography operates on the principles of quantum…
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).…
This article will describe an optical encryption technical of images which it is proposed in an analogical and digital way. The development of the technical to a digital level, it is made to implementing algorithms (routines) in MATLAB. We…
In this paper we consider cryptographic applications of the arithmetic on the hyperoctahedral group. On an appropriate subgroup of the latter, we particularly propose to construct public key cryptosystems based on the discrete logarithm.…
We present an in-place implementation of the cryptographic permutation \textbf{Gimli}, a NIST round 2 candidate for lightweight cryptography, and provide an upper bound for the required quantum resource in depth and gate-counts. In…
A commutative algebra is exact if its multiplication endomorphisms are trace-free and is Killing metrized if its Killing type trace-form is nondegenerate and invariant. A Killing metrized exact commutative algebra is necessarily neither…
This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic…
In this article, we have proposed a generalized Lucas matrix (recursive matrix of higher order) having relation with generalized Fibonacci sequences and established many special properties in addition to that usual matrix algebra. Further,…