相关论文: The discrete logarithm problem in the group of non…

We construct three public key knapsack cryptosystems. Standard knapsack cryptosystems hide easy instances of the knapsack problem and have been broken. The systems considered in the article face this problem: They hide a random (possibly…

Most common public key cryptosystems and public key exchange protocols presently in use, such as the RSA algorithm, Diffie-Hellman, and elliptic curve methods are number theory based and hence depend on the structure of abelian groups. The…

We present a polynomial-time reduction of the discrete logarithm problem in any periodic (a.k.a. torsion) semigroup (SGDLP) to the same problem in a subgroup of the same semigroup. It follows that SGDLP can be solved in polynomial time by…

This is a study of the MOR cryptosystem using the special linear group over finite fields. The automorphism group of the special linear group is analyzed for this purpose. At our current state of knowledge, I show that the MOR cryptosystem…

This paper is devoted to the study of the dynamics of a discrete system related to some self stabilizing protocol on a ring of processors.

We present a polynomial-time quantum algorithm for the Hidden Subgroup Problem over $\mathbb{D}_{2^n}$. The usual approach to the Hidden Subgroup Problem relies on harmonic analysis in the domain of the problem, and the best known algorithm…

Most cryptosystems are defined over finite algebraic structures where arithmetic operations are performed modulo natural numbers. This applies to private key as well as to public key ciphers. No secure cryptosystems defined over the field…

Discretizing Helmholtz problems via finite elements yields linear systems whose efficient solution remains a major challenge for classical computation. In this paper, we investigate how variational quantum algorithms could address this…

In the recently emerging field of group-based cryptography, the Conjugacy Search Problem (CSP) has gained traction as a non-commutative replacement of the Discrete Log Problem (DLP). The problem of finding a secure class of nonabelian…

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,…

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient.…

In this paper, we present a new diverse class of post-quantum group-based Digital Signature Schemes (DSS). The approach is significantly different from previous examples of group-based digital signatures and adopts the framework of group…

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 this paper a three fuzzy vault schemes which integrated with discrete logarithmic encryption scheme are proposed. In the first scheme, the message m is encoded with discrete logarithmic encryption scheme using randomly generated identity…

The Lagrange problem is established in the discrete field theory subject to constraints with values in a Lie group. For the admissible sections that satisfy a certain regularity condition, we prove that the critical sections of such…

In this paper we introduce a rank $2$ lattice over a polynomial ring arising from the public key of the BIKE cryptosystem. The secret key is a sparse vector in this lattice. We study properties of this lattice and generalize the recovery of…

The discreteness problem for finitely generated subgroups of $PSL(2,\mathbb{R})$ and $PSL(2,\mathbb{C})$ is a long-standing open problem. In this paper we consider whether or not this problem is decidable by an algorithm. Our main result is…

We consider the setting of a master server who possesses confidential data (genomic, medical data, etc.) and wants to run intensive computations on it, as part of a machine learning algorithm for example. The master wants to distribute…

The spectral problem for matrices with a block-hierarchical structure is often considered in context of the theory of complex systems. In the present article, a new class of matrices with a block-rectangular non-symmetric hierarchical…

We consider systems of stochastic differential equations of the form \[ \d X_t^i = \sum_{j=1}^d A_{ij}(X_{t-}) \d Z_t^j\] for $i=1,\dots,d$ with continuous, bounded and non-degenerate coefficients. Here $Z_t^1,\dots,Z_t^d$ are independent…