Related papers: A Closer Look at the Tropical Cryptography
We use extensions of tropical algebras as platforms for very efficient public key exchange protocols.
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 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.
This article analyzes a key exchange protocol based on the triad tropical semiring, recently proposed by Jackson, J. and Perumal, R. We demonstrate that the triad tropical semiring is isomorphic to a circulant matrix over tropical numbers.…
We suggest the usage of algebraic subsets instead of subgroups in public-key cryptography. In particular, we present the subset version of two protocols introduced by Shpilrain and Ushakov with some examples in ascending HNN-extensions of…
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…
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…
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.
This paper shows that an eavesdropper can always recover efficiently the private key of one of the two parts of the public key cryptography protocol introduced by Shpilrain and Ushakov in [9]. Thus an eavesdropper can always recover the…
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…
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…
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…
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…
In 2010, Grigoriev and Shpilrain, introduced some graph-based authentication schemes. We present a cryptanalysis of some of these protocols, and introduce some new schemes to fix the problems.
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…
Chebyshev polynomials have been recently proposed for designing public-key systems. Indeed, they enjoy some nice chaotic properties, which seem to be suitable for use in Cryptography. Moreover, they satisfy a semi-group property, which…
The security of neural cryptography is investigated. A key-exchange protocol over a public channel is studied where the parties exchanging secret messages use multilayer neural networks which are trained by their mutual output bits and…
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…
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…
General cryptographic schemes are presented where keys can be one-time or ephemeral. Processes for key exchange are derived. Public key cryptographic schemes based on the new systems are easily established. Authentication and signature…