Related papers: Cryptoanalysis of a tropical triad matrix semiring…
We consider multidimensional optimization problems that are formulated in the framework of tropical mathematics to minimize functions defined on vectors over a tropical semifield (a semiring with idempotent addition and invertible…
Tropical mathematics often is defined over an ordered cancellative monoid $\tM$, usually taken to be $(\RR, +)$ or $(\QQ, +)$. Although a rich theory has arisen from this viewpoint, cf. [L1], idempotent semirings possess a restricted…
We provide geometric methods and algorithms to verify, construct and enumerate pairs of words (of specified length over a fixed $m$-letter alphabet) that form identities in the semigroup $\ut{n}$ of $n\times n$ upper triangular tropical…
Here we concerned with quantum key distribution - a way to establish common cryptographic key between several parties. The work proposes a combination between quantum key distribution and systematic polar coding (an error correction…
In this paper we give an elementary proof of the Fundamental Theorem of Algebra for polynomials over the rational tropical semi-ring. We prove that, tropically, the rational numbers are algebraically closed. We provide a simple algorithm…
The Quantum Key Distribution protocol can encode a single quantum state and implements an information-theoretically secure key distribution protocol in communication. In the actual QKD experimental system, there are usually two encoding…
Supertropical monoids are a structure slightly more general than the supertropical semirings, which have been introduced and used by the first and the third authors for refinements of tropical geometry and matrix theory in [IR1]-[IR3], and…
Polar codes are a new class of error correcting linear block codes, whose generator matrix is specified by the knowledge of transmission channel parameters, code length and code dimension. Moreover, regarding computational security, it is…
Recent study on certificateless authenticated key agreement focuses on bilinear pairing-free certificateless authenticated key agreement protocol. Yet it has got limitations in the aspect of computational amount. So it is important to…
Known key exchange schemes offering information-theoretic (unconditional) security are complex and costly to implement. Nonetheless, they remain the only known methods for achieving unconditional security in key exchange. Therefore, the…
An algorithm is presented which implements a probabilistic attack on the key-exchange protocol based on permutation parity machines. Instead of imitating the synchronization of the communicating partners, the strategy consists of a Monte…
Authenticated Key Exchange (AKE) protocols represent an important cryptographic mechanism that enables several parties to communicate securely over an open network. Elashry, Mu and Susilo proposed in 2015 an Identity Based Authenticated Key…
In the distributed environment, authentication and key exchange mechanisms play a major role. In general, for authentication, the client and the server mutually exchange a common cryptographic key. In earlier, passwords were stored on a…
We present an improved post-quantum version of Sakalauskas matrix power function key agreement protocol, using rectangular matrices instead of the original square ones. Sakalauskas matrix power function is an efficient and secure way to…
We introduce a scheme-theoretic enrichment of the principal objects of tropical geometry. Using a category of semiring schemes, we construct tropical hypersurfaces as schemes over idempotent semirings such as $\mathbb{T} = (\mathbb{R}\cup…
We investigate the post-quantum security of the encrypted key exchange(EKE) protocols based on some basic physical parameters of ion-trap quantum computer, and show that the EKE protocol with a 40-bit password will be secure against a…
We construct a nontrivial identity which holds in the semigroup of tropical 3-by-3 matrices.
We present in this paper an algorithm for exchanging session keys, coupled with a hashing encryption module. We show schemes designed for their potential invulnerability to classical and quantum attacks. In turn, if the parameters included…
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…
We introduce the \emph{linear centralizer method}, and use it to devise a provable polynomial time solution of the Commutator Key Exchange Problem, the computational problem on which, in the passive adversary model, the security of the…