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Full-Text Articles in Number Theory
The Vulnerabilities To The Rsa Algorithm And Future Alternative Algorithms To Improve Security, James Johnson
The Vulnerabilities To The Rsa Algorithm And Future Alternative Algorithms To Improve Security, James Johnson
Cybersecurity Undergraduate Research Showcase
The RSA encryption algorithm has secured many large systems, including bank systems, data encryption in emails, several online transactions, etc. Benefiting from the use of asymmetric cryptography and properties of number theory, RSA was widely regarded as one of most difficult algorithms to decrypt without a key, especially since by brute force, breaking the algorithm would take thousands of years. However, in recent times, research has shown that RSA is getting closer to being efficiently decrypted classically, using algebraic methods, (fully cracked through limited bits) in which elliptic-curve cryptography has been thought of as the alternative that is stronger than …
Explicit Constructions Of Canonical And Absolute Minimal Degree Lifts Of Twisted Edwards Curves, William Coleman Bitting Iv
Explicit Constructions Of Canonical And Absolute Minimal Degree Lifts Of Twisted Edwards Curves, William Coleman Bitting Iv
Doctoral Dissertations
Twisted Edwards Curves are a representation of Elliptic Curves given by the solutions of bx^2 + y^2 = 1 + ax^2y^2. Due to their simple and unified formulas for adding distinct points and doubling, Twisted Edwards Curves have found extensive applications in fields such as cryptography. In this thesis, we study the Canonical Liftings of Twisted Edwards Curves and the associated lift of points Elliptic Teichmu ̈ller Lift. The coordinate functions of the latter are proved to be polynomials, and their degrees and derivatives are computed. Moreover, an algorithm is described for explicit computations, and some properties of the general …
A Visual Tour Of Dynamical Systems On Color Space, Jonathan Maltsman
A Visual Tour Of Dynamical Systems On Color Space, Jonathan Maltsman
HMC Senior Theses
We can think of a pixel as a particle in three dimensional space, where its x, y and z coordinates correspond to its level of red, green, and blue, respectively. Just as a particle’s motion is guided by physical rules like gravity, we can construct rules to guide a pixel’s motion through color space. We can develop striking visuals by applying these rules, called dynamical systems, onto images using animation engines. This project explores a number of these systems while exposing the underlying algebraic structure of color space. We also build and demonstrate a Visual DJ circuit board for …