Related papers: Use of Signed Permutations in Cryptography
By resorting to basic features of topological knot theory we propose a (classical) cryptographic protocol based on the `difficulty' of decomposing complex knots generated as connected sums of prime knots and their mutants. The scheme…
We propose a new cryptosystem based on polycyclic groups. The cryptosystem is based on the fact that the word problem can be solved effectively in polycyclic groups, while the known solutions to the conjugacy problem are far less efficient.
We give a combinatorial description for the weak order on the hyperoctahedral group. This characterization is then used to analyze the order-theoretic properties of the shifted products of hyperoctahedral groups. It is shown that each…
Signed difference sets have interesting applications in communications and coding theory. A $(v,k,\lambda)$-difference set in a finite group $G$ of order $v$ is a subset $D$ of $G$ with $k$ distinct elements such that the expressions…
We describe an efficient quantum algorithm for computing discrete logarithms in semigroups using Shor's algorithms for period finding and discrete log as subroutines. Thus proposed cryptosystems based on the presumed hardness of discrete…
In this expository article we present an overview of the current state-of-the-art in post-quantum group-based cryptography. We describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic…
With the emerging of mobile communication technologies, we are entering the fifth generation mobile communication system (5G) era. Various application scenarios will arise in the 5G era to meet the different service requirements. Different…
This paper suggests a message authentication scheme, which can be efficiently used for secure digital signature creation. The algorithm used here is an adjusted union of the concepts which underlie projective geometry and group structure on…
To ensure the secure transmission of data, cryptography is treated as the most effective solution. Cryptographic key is an important entity in this procedure. In general, randomly generated cryptographic key (of 256 bits) is difficult to…
Homomorphic encryption has largely been studied in context of public key cryptosystems. But there are applications which inherently would require symmetric keys. We propose a symmetric key encryption scheme with fully homomorphic evaluation…
The point of this paper is to use affine automorphisms from algebraic geometry to build cryptographic multivariate mappings. We will construct groups G,H, both isomorphic to the cyclic group with a prime number of elements and multilinear…
Encryption schemes attempt to provide a means for entities to communicate confidentially over a public channel. Such schemes have been studied for centuries, and their use has become widespread. However, developments in the area of quantum…
A cryptarithm (or alphametic) is a mathematical puzzle in which numbers are represented with words in such a way that identical letters stand for equal digits and distinct letters for unequal digits. An alphametic puzzle is usually given in…
This paper proposes a new homomorphic functional encryption using modular multiplications over a hidden ring. Unlike traditional homomorphic encryption where users can only passively perform ciphertext addition or multiplication, the…
We study permutation groups of given minimal degree without the classical primitivity assumption. We provide sharp upper bounds on the order of a permutation group of minimal degree m and on the number of its elements of any given support.…
In order to study signed Eulerian numbers, we introduce permutations of a particular type, called parity-alternate permutations, because they take even and odd entries alternately. The objective of this paper is twofold. The first is to…
Homomorphic encryption (HE) is a privacy-preserving technique that enables computation directly over ciphertext. Unfortunately, a key challenge for HE is that implementations can be impractically slow and have limits on computation that can…
This paper studies how a system operator and a set of agents securely execute a distributed projected gradient-based algorithm. In particular, each participant holds a set of problem coefficients and/or states whose values are private to…
Due to implementation constraints the XOR operation is widely used in order to combine plaintext and key bit-strings in secret-key block ciphers. This choice directly induces the classical version of the differential attack by the use of…
A symmetric encryption method based on properties of quasicrystals is proposed. The advantages of the cipher are strict aperiodicity and everywhere discontinuous property as well as the speed of computation, simplicity of implementation and…