Related papers: Pythagorean Triples and Cryptographic Coding

Cryptography protects users by providing functionality for the encryption of data and authentication of other users. This technology lets the receiver of an electronic message verify the sender, ensures that a message can be read only by…

A secret can be an encrypted message or a private key to decrypt the ciphertext. One of the main issues in cryptography is keeping this secret safe. Entrusting secret to one person or saving it in a computer can conclude betrayal of the…

In this dissertation, we explore the structure of inversion graphs of permutations--a class of graphs that naturally arises by representing each permutation as a graph, where vertices correspond to entries and edges encode inversions.…

In this book, we have introduced several new classes of codes to aid cryptologists and computer scientists. We have explained these codes very non-technically so that a strong mathematical foundation is not needed to understand them. This…

Cryptanalysis increases the level of confidence in cryptographic algorithms. We analyze the security of a symmetric cryptographic algorithm - quantum permutation pad (QPP) [8]. We found the instances of ciphertext the same as plaintext even…

The paper explains that post-quantum cryptography is necessary due to the introduction of quantum computing causing certain algorithms to be broken. We analyze the different types of post-quantum cryptography, quantum cryptography and…

This article highlights interactions of diverse areas: the Heron formula for the area of a triangle, the Descartes circle equation, and right triangles with integer or rational sides. New and old results are synthesized. We show that every…

We study the computational model of polygraphs. For that, we consider polygraphic programs, a subclass of these objects, as a formal description of first-order functional programs. We explain their semantics and prove that they form a…

Typography is a ubiquitous art form that affects our understanding, perception, and trust in what we read. Thousands of different font-faces have been created with enormous variations in the characters. In this paper, we learn the style of…

Cryptographic primitives have been used for various non-cryptographic objectives, such as eliminating or reducing randomness and interaction. We show how to use cryptography to improve the time complexity of solving computational problems.…

In this paper we address the problem of constructing a class of representations of Clifford algebras that can be named "alphabetic (re)presentations". The Clifford algebras generators are expressed as m-letter words written with a…

Developments in the distributed ledger technology have led to new types of assets with a broad range of purposes. Although some classification frameworks for common instruments from traditional finance and some for these new, so called…

Besides achieving secure communication between two spatially-separated parties, another important issue in modern cryptography is related to secure communication in time, i.e., the possibility to confidentially store information on a memory…

We give a new algorithm for constructing Picard curves over a finite field with a given endomorphism ring. This has important applications in cryptography since curves of genus 3 allow for smaller key sizes than elliptic curves. For a…

Consider the smooth quadric Q_6 in P^7. The middle homology group H_6(Q_6,Z) is two-dimensional with a basis given by two classes of linear subspaces. We classify all threefolds of bidegree (1,p) inside Q_6.

We introduce Poisson triple systems, which are vector spaces with 3 trilinear operations satisfying 9 polynomial identities of degree 5. We show that every Poisson triple system has a universal enveloping Poisson algebra. Finally, we…

A detailed analysis of the PPT square conjecture is given.

Cryptography is the science of encrypting the information so that it is rendered unreadable for an intruder. Cryptographic techniques are of utmost importance in today's world as the information to be sent might be of invaluable importance…

The right triangles represented in the Plimpton 322 data have integer sides $(a, b, d)$ with $a < b < d$, by inspecting the data we propose $b=M\,Q_{M}$ with $M,Q_{M}$ positive integers. In this way we present a new data-driven family of…

We show how to design families of operational criteria that distinguish entangled from separable quantum states. The simplest of these tests corresponds to the well-known Peres-Horodecki positive partial transpose (PPT) criterion, and the…