Related papers: Tropical cryptography
We develop a theory of toroidal vertex algebras and their modules, and we give a conceptual construction of toroidal vertex algebras and their modules. As an application, we associate toroidal vertex algebras and their modules to toroidal…
We describe a cryptographic protocol in which Wheeler's delayed choice experiment is used to generate the key distribution. The protocol, which uses photons polarized only along one axis, is secure against general attacks.
Analogously as in classical algebraic geometry, linear pencils of tropical plane curves are parameterized by tropical lines in a coefficient space. A special example of such a linear pencil is the set of tropical plane curves with an…
We give an interpretation of full classical linear logic, and linear proofs in terms of operations on the blockchain.
The security of the Internet rests on a small number of open-source cryptographic libraries: a vulnerability in any one of them threatens to compromise a significant percentage of web traffic. Despite this potential for security impact, the…
Tropical curves in $\mathbb{R}^2$ correspond to metric planar graphs but not all planar graphs arise in this way. We describe several new classes of graphs which cannot occur. For instance, this yields a full combinatorial characterization…
Scalar multiplication kP is a critical operation in Elliptic Curve Cryptosystems (ECC), often targeted by Side-Channel Analysis (SCA). Despite strategies based on atomic patterns to enhance security, the binary kP algorithms remain…
We introduce a natural generalization of the golden cryptography, which uses general unimodular matrices in place of the traditional Q-matrices, and prove that it preserves the original error correction properties of the encryption.…
We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide two algorithms for finding them in affine spaces of complementary dimension to the zero set. We use these…
Tropical recurrent sequences are introduced satisfying a given vector (being a tropical counterpart of classical linear recurrent sequences). We consider the case when Newton polygon of the vector has a single (bounded) edge. In this case…
We consider the enciphering of a data stream while being compressed by a LZ algorithm. This has to be compared to the classical encryption after compression methods used in security protocols. Actually, most cryptanalysis techniques exploit…
The tropicalization of a linear space over a non-archimedean field is a tropical linear space. In this paper, we present a method for computing the tropicalization of any lattice over a valuation ring. The resulting tropical semimodule is…
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…
The advent of quantum computing poses a significant threat to the foundational cryptographic algorithms that secure modern digital communications. Protocols such as HTTPS, digital certificates, and public key infrastructures (PKIs) heavily…
Dense and sparse tensors allow the representation of most bulk data structures in computational science applications. We show that sparse tensor algebra can also be used to express many of the transformations on these datasets, especially…
Blockchain is one of the most discussed and highly accepted technologies, primarily due to its application in almost every field where third parties are needed for trust. Blockchain technology relies on distributed consensus for trust,…
In this work we review the security vulnerability of Quantum Cryptography with respect to "man-in-the-middle attacks" and the standard authentication methods applied to counteract these attacks. We further propose a modified authentication…
Tropical Geometry and Mathematical Morphology share the same max-plus and min-plus semiring arithmetic and matrix algebra. In this chapter we summarize some of their main ideas and common (geometric and algebraic) structure, generalize and…
In this article, we propose a method to construct self orthogonal matrix, orthogonal matrix and anti orthogonal matrix over the finite field. Orthogonal matrices has numerous applications in cryptography, so here we demonstrate the…
Threats from the internet, particularly malicious software (i.e., malware) often use cryptographic algorithms to disguise their actions and even to take control of a victim's system (as in the case of ransomware). Malware and other threats…