Related papers: Cryptoanalysis of a tropical triad matrix semiring…

We consider a key-exchange protocol based on matrices over a tropical semiring which was recently proposed in \cite{grig19}. We show that a particular private parameter of that protocol can be recovered with a simple binary search,…

We present a cryptanalysis of a key exchange protocol based on the digital semiring. For this purpose, we find the maximal solution of a linear system over such semiring, and use the properties of circulant matrix to demonstrate that the…

We present a new key exchange protocol based on circulant matrices acting on matrices over a congruence-simple semiring. We describe how to compute matrices with the necessary properties for the implementation of the protocol. Additionally,…

We examine two public key exchange protocols proposed recently by Grigoriev and Shpilrain (arXiv:1811.06386), which use tropical algebra. We introduce a fast attack on the first protocol, and we show that the second protocol cannot be…

We address a cryptanalysis of two protocols based on the supposed difficulty of discrete logarithm problem on (semi) groups of matrices over a group ring. We can find the secret key and break entirely the protocols.

One-sided linear systems of the form ``$Ax=b$'' are well-known and extensively studied over the tropical (max-plus) semiring and wide classes of related idempotent semirings. The usual approach is to first find the greatest solution to such…

We use extensions of tropical algebras as platforms for very efficient public key exchange protocols.

We show that a previously introduced key exchange based on a congruence-simple semiring action is not secure by providing an attack that reveals the shared key from the distributed public information for any of such semirings

The tropical semiring is a semiring of extended real numbers, where the operations of `max' and `+' replace the usual addition and multiplication, respectively. Difference equations obtained from the ultradiscrete limit of discrete…

Several cryptographic protocols constructed based on less-known algorithmic problems, such as those in non-commutative groups, group rings, semigroups, etc., which claim quantum security, have been broken through classical reduction methods…

Tropical linear algebra has been recently put forward by Grigoriev and Shpilrain as a promising platform for implementation of protocols of Diffie-Hellman and Stickel type. Based on the CSR expansion of tropical matrix powers, we suggest a…

This paper introduces a new structure of commutative semiring, generalizing the tropical semiring, and having an arithmetic that modifies the standard tropical operations, i.e. summation and maximum. Although our framework is combinatorial,…

We consider a key exchange procedure whose security is based on the difficulty of computing discrete logarithms in a group, and where exponentiation is hidden by a conjugation. We give a platform-dependent cryptanalysis of this protocol.…

It was recently demonstrated that the Matrix Action Key Exchange (MAKE) algorithm, a new type of key exchange protocol using the semidirect product of matrix groups, is vulnerable to a linear algebraic attack if the matrices are over a…

In a recent paper [arXiv:2009.00716], Rahman and Shpilrain proposed a new key-exchange protocol MAKE based on external semidirect product of groups. The purpose of this paper is to show that the key exchange protocol is insecure. We were…

We show that two new key exchange protocols with security based on the triple DP may have security based on the MSCSP.

We use tropical algebras as platforms for a very efficient digital signature protocol. Security relies on computational hardness of factoring one-variable tropical polynomials; this problem is known to be NP-hard.

We employ tropical algebras as platforms for several cryptographic schemes that would be vulnerable to linear algebra attacks were they based on "usual" algebras as platforms.

In this paper, we introduce and analyze a normalization method for solving a system of linear equations over tropical semirings. We use a normalization method to construct an associated normalized matrix, which gives a technique for solving…

In the papers by Alvarez et al. and Pathak and Sanghi a non-commutative based public key exchange is described. A similiar version of it has also been patented (US7184551). In this paper we present a polynomial time attack that breaks the…