Related papers: Cryptoanalysis of a tropical triad matrix semiring…
In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. It is based on the polyhedral properties of triangulations of the…
Encryption has increasingly been used in all applications for various purposes, but it also brings big challenges to network security. In this paper, we take first steps towards addressing some of these chal- lenges by introducing a novel…
The growth of tropical geometry has generated significant interest in the tropical semiring in the past decade. However, there are other semirings in tropical algebra that provide more information, such as the symmetrized (max, +),…
We offer a public key exchange protocol in the spirit of Diffie-Hellman, but we use (small) matrices over a group ring of a (small) symmetric group as the platform. This "nested structure" of the platform makes computation very efficient…
We establish necessary and sufficient conditions for a semigroup identity to hold in the monoid of $n\times n$ upper triangular tropical matrices, in terms of equivalence of certain tropical polynomials. This leads to an algorithm for…
In 2019, V. A. Roman'kov introduced the concept of marginal sets for groups. He developed a theory of marginal sets and demonstrated how these sets can be applied to improve some key exchange schemes. In this paper, we extend his ideas and…
We develop a tropical analogue of the classical double description method allowing one to compute an internal representation (in terms of vertices) of a polyhedron defined externally (by inequalities). The heart of the tropical algorithm is…
We cryptanalyse a matrix-based key transport protocol due to Baumslag, Camps, Fine, Rosenberger and Xu from 2006. We also cryptanalyse two recently proposed matrix-based key agreement protocols, due to Habeeb, Kahrobaei and Shpilrain, and…
In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our…
The tropicalization of a linear space over a non-archimedean field is a tropical linear space. In this paper, we present a method for computing the tropicalization of any lattice over a valuation ring. The resulting tropical semimodule is…
The problem of solving tropical linear systems, a natural problem of tropical mathematics, has already proven to be very interesting from the algorithmic point of view: it is known to be in $NP\cap coNP$ but no polynomial time algorithm is…
The idealized Kish-Sethuraman (KS) cipher is theoretically known to offer perfect security through a classical information channel. However, realization of the protocol is hitherto an open problem, as the required mathematical operators…
In this paper we present a new primitive for a key exchange protocol based on multivariate non-commutative polynomial rings, analogous to the classic Diffie-Hellman method. Our technique extends the proposed scheme of Boucher et al. from…
A tropical (or min-plus) semiring is a set $\mathbb{Z}$ (or $\mathbb{Z \cup \{\infty\}}$) endowed with two operations: $\oplus$, which is just usual minimum, and $\odot$, which is usual addition. In tropical algebra the vector $x$ is a…
We show that many known schemes of the public key exchange protocols in the algebraic cryptography, that use two-sided multiplications, are the specific cases of the general scheme of such type. In most cases, such schemes are built on…
We offer a public key exchange protocol based on a semidirect product of two cyclic (semi)groups of matrices over Z_p. One of the (semi)groups is additive, the other one multiplicative. This allows us to take advantage of both operations on…
Akiyama et al. (Int. J. Math. Indust., 2019) proposed a post-quantum key exchange protocol that is based on the hardness of solving a system of multivariate non-linear polynomial equations but has a design strategy different from ordinary…
In this paper, we will present a new key exchange cryptosystem based on linear algebra, which take less operations but weaker in security than Diffie-Hellman's one.
In this note, we propose a novel technique to reduce the algorithmic complexity of neural network training by using matrices of tropical real numbers instead of matrices of real numbers. Since the tropical arithmetics replaces…
In this paper, we present methods for solving a system of linear equations, $ AX=b $, over tropical semirings. To this end, if possible, we first reduce the order of the system through some row-column analysis, and obtain a new system with…