We investigate the average-case complexity of a generalization of the compact knapsack
problem to arbitrary rings: given m (random) ring elements a 1,..., am∈ R and a (random) …

Diophantine equations are equations containing two or more unknowns, such that only the
integer solutions are required. To find solutions of these equations numerically, we can be …

The paper introduces particle swarm optimisation as a viable strategy to find numerical
solution of Diophantine equation, for which there exists no general method of finding …

The paper attempts to find numerical solutions of Diophantine equations, a challenging
problem as there are no general methods to find solutions of such equations. It uses the …

Knapsack-based cryptosystems had been viewed as the most attractive and the most
promising asymmetric cryptographic algorithms for a long time due to their NP-completeness …

Researching post-quantum cryptography is now an important task in cryptography. Although
various candidates of post-quantum cryptosystems (PQC) have been constructed, sizes of …

In this paper we propose a new public key cryptosystem based on diophantine equations
which we call of degree increasing type. We use an analogous method to the “Algebraic …

The paper introduces a connectionist network approach to find numerical solutions of
Diophantine equations as an attempt to address the famous Hilbert's tenth problem. The …

The one-dimensional cellular automata (CA) system detailed herein uses a hybrid
mechanism to attain reversibility, and this approach is adapted to create a novel block cipher …

This thesis describes a method of deciphering messages encrypted with rotor machines
utilising a Genetic Algorithm to search the keyspace. A tness measure based on the phi test …