Related papers: Cryptoanalysis of a tropical triad matrix semiring…
In this paper, we propose to use a twisted dihedral group algebra for public-key cryptography. For this, we introduce a new $2$-cocycle $\alpha_{\lambda}$ to twist the dihedral group algebra. Using the ambient space…
Cryptography protects users by providing functionality for the encryption of data and authentication of other users. This technology lets the receiver of an electronic message verify the sender, ensures that a message can be read only by…
This paper proposes an efficient secret key cryptosystem based on polar codes over Binary Erasure Channel. We introduce a method, for the first time to our knowledge, to hide the generator matrix of the polar codes from an attacker. In…
Tropicalisation (with trivial coefficients) is a process that turns a polynomial equation into a combinatorial predicate on subsets of the set of variables. We show that for each minuscule representation of a simple reductive group, there…
The aim of this article is to solve the system $XA=Y$ where $A=(a_{ij})\in M_{m\times n}(S)$, $Y\in S^{m}$ and $X$ is an unknown vector of size $n$, being $S$ an additively idempotent semiring. If the system has solutions then we completely…
We prove general Cramer type theorems for linear systems over various extensions of the tropical semiring, in which tropical numbers are enriched with an information of multiplicity, sign, or argument. We obtain existence or uniqueness…
Inspired by Bitcoin, many different kinds of cryptocurrencies based on blockchain technology have turned up on the market. Due to the special structure of the blockchain, it has been deemed impossible to directly trade between traditional…
The widespread use of wireless sensor networks (WSNs) that are consisted of resource-constrained sensor nodes in communication with gateways in open-space environments and industries has highlighted the need for a secure yet fast…
We study tropical commuting matrices from two viewpoints: linear algebra and algebraic geometry. In classical linear algebra, there exist various criteria to test whether two square matrices commute. We ask for similar criteria in the realm…
Generalizing supertropical algebras, we present a "layered" structure, "sorted" by a semiring which permits varying ghost layers, and indicate how it is more amenable than the "standard" supertropical construction in factorizations of…
In contrast to the situation in classical linear algebra, not every tropically non-singular matrix can be factored into a product of tropical elementary matrices. We do prove the factorizability of any tropically non-singular 2x2 matrix…
Recently, Tsai et al. (Laser Phys. Lett. 17, 075202, 2020) proposed a lightweight authenticated semi-quantum key distribution protocol for a quantum participant to share a secret key with a classical participant. However, this study points…
We explore several facets of tropical subrepresentations of a linear representation of a group over the tropical semifield $\mathbb{T}$. A key role in the study of tropical subrepresentations is played by two types of modules over a…
We introduce a faithful tropical linear representation of the Chinese monoid, and thus prove that this monoid admits all the semigroup identities satisfied by tropical triangular matrices.
The purpose of this paper is fourfold. The first is to develop the theory of tropical differential algebraic geometry from scratch; the second is to present the tropical fundamental theorem for differential algebraic geometry, and show how…
In this paper, we present a lattice-theoretic characterization for valuated matroids, which is an extension of the well-known cryptomorphic equivalence between matroids and geometric lattices ($=$ atomistic semimodular lattices). We…
The aim of this technical report is to complement the work in [To et al. 2014] by proposing a Group Key Exchange protocol so that the Querier and TDSs (and TDSs themselves) can securely create and exchange the shared key. Then, the security…
Recently, a quantum key exchange protocol has been described, which served as basis for securing an actual bank transaction by means of quantum cryptography [quant-ph/0404115]. Here we show, that the authentication scheme applied is…
The symmetrized tropical semiring is an extension of the tropical semifield, initially introduced to solve tropical linear systems using Cramer's rule. It is equivalent to the real tropical hyperfield, which has been used in the study of…
We discuss the use of elliptic curves in cryptography on high-dimensional surfaces. In particular, instead of a Diffie-Hellman key exchange protocol written in the form of a bi-dimensional row, where the elements are made up with 256 bits,…