Related papers: Tropical cryptography
We study some basic algorithmic problems concerning the intersection of tropical hypersurfaces in general dimension: deciding whether this intersection is nonempty, whether it is a tropical variety, and whether it is connected, as well as…
By allowing intermediate nodes to perform non-trivial operations on packets, such as mixing data from multiple streams, network coding breaks with the ruling store and forward networking paradigm and opens a myriad of challenging security…
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 take a critical look at the relationship between the security of cryptographic schemes in the Random Oracle Model, and the security of the schemes that result from implementing the random oracle by so called "cryptographic hash…
We introduce a simple, practical approach with probabilistic information-theoretic security to solve one of quantum key distribution's major security weaknesses: the requirement of an authenticated classical channel to prevent…
The significance of quantum computation for cryptography is discussed. Following a brief survey of the requirements for quantum computational hardware, an overview of the ion trap quantum computation project at Los Alamos is presented. The…
We introduce cyclic diagram monoids, a generalisation of classical diagram monoids that adds elements of arbitrary period by including internal components, with a view towards cryptography. We classify their simple representations and…
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…
We describe triples and systems, expounded as an axiomatic algebraic umbrella theory for classical algebra, tropical algebra, hyperfields, and fuzzy rings.
The Chow polytope of an algebraic cycle in a torus depends only on its tropicalisation. Generalising this, we associate a Chow polytope to any abstract tropical variety in a tropicalised toric variety. Several significant polyhedra…
We consider an application to the discrete log problem using completely regular semigroups which may provide a more secure symmetric cryptosystem than the classic system based on groups. In particular we describe a scheme that would appear…
This work presents a new tool to verify the correctness of cryptographic implementations with respect to cache attacks. Our methodology discovers vulnerabilities that are hard to find with other techniques, observed as exploitable leakage.…
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…
This paper will discuss the Logjam attack on TLS. The Logjam attack allows, under certain conditions, to defeat the security provided by TLS. This is done by manipulating server and client into using weak and deprecated export grade crypto,…
We analyze the security and reliability of a recently proposed class of public-key cryptosystems against attacks by unauthorized parties who have acquired partial knowledge of one or more of the private key components and/or of the…
In this survey, we discuss linear series on tropical curves and their relation to classical algebraic geometry, describe the main techniques of the subject, and survey some of the recent major developments in the field, with an emphasis on…
In the not so unlikely scenario of total compromise of computers accessible to a group of users, they might be tempted to resort to human-computable paper-and-pencil cryptographic methods aided by a classic Tabula Recta, which helps to…
This thesis delves into the geometry of abstract tropical curves, exploring their complete linear system and associated tropical submodules. We establish a lower bound on the dimension of tropical submodules in terms of the Baker-Norine…
We present applications of tropical geometry to some integrable piecewise-linear maps, based on the lecture given by one of the authors (R. I.) at the workshop "Tropical Geometry and Integrable Systems" (University of Glasgow, July 2011),…
We define a formal framework for the study of algebras of type Max-plus, Min-Plus, tropical algebras, and more generally algebras over a commutative idempotent semi-field. This work is motivated by the increasingly diversified use of these…