相关论文: The discrete logarithm problem in the group of non…
The Ring Learning-With-Errors (LWE) problem, whose security is based on hard ideal lattice problems, has proven to be a promising primitive with diverse applications in cryptography. There are however recent discoveries of faster algorithms…
We study the discrete logarithm problem for the multiplicative group and for elliptic curves over a finite field by using a lifting of the corresponding object to an algebraic number field and global duality. We introduce the…
This paper introduces a novel cryptographic approach based on the continuous logarithm in the complex circle, designed to address the challenges posed by quantum computing. By leveraging its multi-valued and spectral properties, this…
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…
Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols…
We present a new group law defined on a subset of the projective plane $\mathbb{F}P^2$ over an arbitrary field $\mathbb{F}$, which lends itself to applications in Public Key Cryptography, in particular to a Diffie-Hellman-like key agreement…
In this paper, we study a security problem of protecting secrets in distributed systems. Specifically, we employ discrete-event systems to describe the structure and behaviour of distributed systems, in which global secret information is…
Solving the discrete logarithm problem (DLP) with quantum computers is a fundamental task with important implications. Beyond Shor's algorithm, many researchers have proposed alternative solutions in recent years. However, due to current…
We study the complexity of securely evaluating arithmetic circuits over finite rings. This question is motivated by natural secure computation tasks. Focusing mainly on the case of two-party protocols with security against malicious…
We give an exposition of the hidden subgroup problem for dihedral groups from the point of view of the standard hidden subgroup quantum algorithm for finite groups. In particular, we recall the obstructions for strong Fourier sampling to…
The Hidden Subgroup Problem (HSP) is a computational problem which includes as special cases integer factorization, the discrete logarithm problem, graph isomorphism, and the shortest vector problem. The celebrated polynomial-time quantum…
By analogy with the developed cryptographic theory of discrete logarithm problems, we define several hard problems in Entropoid based cryptography, such as Discrete Entropoid Logarithm Problem (DELP), Computational Entropoid Diffie-Hellman…
We survey the state of the art on the algorithmic analysis of discrete linear dynamical systems, focussing in particular on reachability, model-checking, and invariant-generation questions, both unconditionally as well as relative to…
Confidentiality and Integrity are two paramount objectives in the evaluation of information and communication technology. In this paper, we propose an arithmetic approach for designing asymmetric key cryptography. Our method is based on the…
The capability of discretization of matrix elements in the problem of quadratic functional minimization with linear member built on matrix in N-dimensional configuration space with discrete coordinates is researched. It is shown, that…
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…
Iterative clustering algorithms help us to learn the insights behind the data. Unfortunately, this may allow adversaries to infer the privacy of individuals with some background knowledge. In the worst case, the adversaries know the…
In this paper, we propose to use a skew dihedral group ring given by the group $D_{2n}$ and the finite field $\mathbb{F}_{q^2}$ for public-key cryptography. Using the ambient space $\mathbb{F}_{q^{2}}^{\theta} D_{2n}$ and a group…
This article presets a review of the achievements rapidly developing field of cryptography - public-key cryptography based on the lattice theory. Paper contains the necessary basic concepts and the major problems of the lattice theory, as…
Ever since the link between nonlinear science and cryptography became apparent, the problem of applying chaotic dynamics to the construction of cryptographic systems has gained a broad audience and has been the subject of thousands of…