Related papers: Tropical cryptography II: extensions by homomorphi…
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.
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 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 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 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,…
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 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…
In this article, we describe a key exchange protocol based on right transversals. We also describe it for general extension associated to right loops.
The purpose of the paper is to give new key agreement protocols (a multi-party extension of the protocol due to Anshel-Anshel-Goldfeld and a generalization of the Diffie-Hellman protocol from abelian to solvable groups) and a new…
This paper is a compressed summary of some principal definitions and concepts in the approach to the black box algebra being developed by the authors. We suggest that black box algebra could be useful in cryptanalysis of homomorphic…
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…
We propose public-key cryptosystems with public key a system of polynomial equations, algebraic or differential, and private key a single polynomial or a small-size ideal. We set up probabilistic encryption, signature, and signcryption…
In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This…
In the last few years there has been a growing interest towards methods for statistical inference and learning based on computational geometry and, notably, tropical geometry, that is, the study of algebraic varieties over the min-plus…
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 study the geometry of tropical extensions of hyperfields, including the ordinary, signed and complex tropical hyperfields. We introduce the framework of 'enriched valuations' as hyperfield homomorphisms to tropical extensions, and show…
We propose a public key encryption cryptosystem based on solutions of linear equation systems with predefinition of input parameters through shared secret computation for factorizable substitutions. The existence of multiple equivalent…
In this paper we study the convergence of the max-consensus protocol. Tropical algebra is used to formulate the problem. Necessary and sufficient conditions for convergence of the max-consensus protocol over fixed as well as switching…
This paper presents results on generalized public key cryptography with exponentials modulo primes and composite numbers where the mapping is not one-to-one and the uniqueness is achieved by additional side information. Such transformations…
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…