Related papers: Tropical cryptography
In this paper we develop a combinatorial abstraction of tropical linear programming. This generalizes the search for a feasible point of a system of min-plus-inequalities. It is based on the polyhedral properties of triangulations of the…
Sometimes it is possible to embed an algebraic trapdoor into a block cipher. Building on previous research, in this paper we investigate an especially dangerous algebraic structure, which is called a hidden sum and which is related to some…
We develop a generalized framework for invariant-based cryptography by extending the use of structural identities as core cryptographic mechanisms. Starting from a previously introduced scheme where a secret is encoded via a four-point…
Complex algebraic varieties become easy piecewise-linear objects after passing to the so-called tropical limit. Geometry of these limiting objects is known as tropical geometry. In this short survey we take a look at motivation and…
This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…
These notes outline some basic notions of Tropical Geometry and survey some of its applications for problems in classical (real and complex) geometry. To appear in the Proceedings of the Madrid ICM.
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…
Physical implementations of cryptographic algorithms leak information, which makes them vulnerable to so-called side-channel attacks. The problem of secure computation in the presence of leakage is generally known as leakage resilience. In…
Most currently used cryptographic tools for protecting data are based on certain computational assumptions, which makes them vulnerable with respect to technological and algorithmic developments, such as quantum computing. One existing…
Under the emerging network coding paradigm, intermediate nodes in the network are allowed not only to store and forward packets but also to process and mix different data flows. We propose a low-complexity cryptographic scheme that exploits…
A cryptographic algorithm is proposed based on fully quantum mechanical keys and ciphers. Encryption and decryption are carried out via an appropriate measurement process on entangled states as governed by a quantum mechanical, asymmetrical…
We introduce tropical complexes, as an enrichment of the dual complex of a degeneration with additional data from non-transverse intersection numbers. We define cycles, divisors, and linear equivalence on tropical complexes, analogous both…
Tropicalization is a procedure for associating a polyhedral complex in Euclidean space to a subvariety of an algebraic torus. We study the question of which graphs arise from tropicalizing algebraic curves. By using Baker's specialization…
We construct cryptographic trilinear maps that involve simple, non-ordinary abelian varieties over finite fields. In addition to the discrete logarithm problems on the abelian varieties, the cryptographic strength of the trilinear maps is…
We examine the security of existing radio navigation protocols and attempt to define secure, scalable replacements.
Tropical algebraic geometry is the geometry of the tropical semiring $(\mathbb{R},\min,+)$. Its objects are polyhedral cell complexes which behave like complex algebraic varieties. We give an introduction to this theory, with an emphasis on…
In this paper we model a class of stream and block ciphers as systems of (ordinary) explicit difference equations over a finite field. We call this class "difference ciphers" and we show that ciphers of application interest, as for example…
In this paper, we present a generic attack for ciphers, which is in essence a collision attack on the secret keys of ciphers .
Cryptography is the discipline that allows securing of the exchange of information. In this internship, we will focus on a certain branch of this discipline, secure computation in a network. The main goal of this internship, illustrated in…
Based on our previous work on truly concurrent process algebras APTC, we use it to verify the security protocols. This work (called Secure APTC, abbreviated SAPTC) have the following advantages in verifying security protocols: (1) It has a…