Related papers: The MOR cryptosystem and finite $p$-groups
Let $G_1$ be a cyclic multiplicative group of order $n$. It is known that the Diffie-Hellman problem is random self-reducible in $G_1$ with respect to a fixed generator $g$ if $\phi(n)$ is known. That is, given $g, g^x\in G_1$ and having…
In 1998 [8], Patarin proposed an efficient cryptosystem called Little Dragon which was a variant a variant of Matsumoto Imai cryptosystem C*. However Patarin latter found that Little Dragon cryptosystem is not secure [8], [3]. In this paper…
With the development of Shor's algorithm, some nondeterministic polynomial (NP) time problems (e.g. prime factorization problems and discrete logarithm problems) may be solved in polynomial time. In recent years, although some homomorphic…
In this paper we propose a signature scheme based on two intractable problems, namely the integer factorization problem and the discrete logarithm problem for elliptic curves. It is suitable for applications requiring long-term security and…
When deploying wireless sensor networks (WSNs) in public environments it may become necessary to secure their data storage and transmission against possible attacks such as node-compromise and eavesdropping. The nodes feature only small…
Finding low-weight multiples of a binary polynomial is a difficult problem arising in the context of stream ciphers cryptanalysis. The classical algorithm to solve this problem is based on a time memory trade-off. We will present an…
Since their introduction in 2004, Polynomial Modular Number Systems (PMNS) have become a very interesting tool for implementing cryptosystems relying on modular arithmetic in a secure and efficient way. However, while their implementation…
We present a new method for constructing genus 2 curves over a finite field with a given number of points on its Jacobian. This method has important applications in cryptography, where groups of prime order are used as the basis for…
The privacy concern in federated clustering has attracted considerable attention in past decades. Many privacy-preserving clustering algorithms leverage cryptographic techniques like homomorphic encryption or secure multiparty computation,…
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…
We introduce a generalized Anshel-Anshel-Goldfeld (AAG) key establishment protocol (KEP) for magmas. This leads to the foundation of non-associative public-key cryptography (PKC), generalizing the concept of non-commutative PKC. We show…
The secure instantiation of the random oracle is one of the major open problems in modern cryptography. We investigate this problem using concepts and methods of algorithmic randomness. In modern cryptography, the random oracle model is…
In September 2019, voters for the election at the Parliament of the city of Moscow were allowed to use an Internet voting system. The source code of it had been made available for public testing. In this paper we show two successful attacks…
In this paper, algorithms for multivariate public key cryptography and digital signature are described. Plain messages and encrypted messages are arrays, consisting of elements from a fixed finite ring or field. The encryption and…
This paper presents a means with time complexity of at worst O(n^3) to compute the discrete logarithm on cyclic finite groups of integers modulo p. The algorithm makes use of reduction of the problem to that of finding the concurrent zeros…
We consider the problem of efficiently computing a discrete Morse complex on simplicial complexes of arbitrary dimension and very large size. Based on a common graph-based formalism, we analyze existing data structures for simplicial…
A finite abelian $p$-group having an automorphism $x$ such that $1+\ldots+x^{p-1}=0$, can be viewed as a module over an appropriate discrete valuation ring $\mathcal{O}$ containing $\mathbb{Z}_p$ (the ring of $p$-adic integer). This yields…
Edge computing alleviates the computation burden of data-driven control in cyber-physical systems (CPSs) by offloading complex processing to edge servers. However, the increasing sophistication of cyberattacks underscores the need for…
We theoretically propose a symmetric encryption scheme based on Restricted Boltzmann Machines that functions as a probabilistic Enigma device, encoding information in the marginal distributions of visible states while utilizing bias…
Encrypted control is a promising method for the secure outsourcing of controller computation to a public cloud. However, a feasible method for security proofs of control has not yet been developed in the field of encrypted control systems.…