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Unveiling The Power Of Shor's Algorithm: Cryptography In A Post Quantum World, Dylan Phares
Unveiling The Power Of Shor's Algorithm: Cryptography In A Post Quantum World, Dylan Phares
CMC Senior Theses
Shor's Algorithm is an extremely powerful tool, in utilizing this tool it is important to understand how it works and why it works. As well as the vast implications it could have for cryptography
Efficiency Of Homomorphic Encryption Schemes, Kyle Yates
Efficiency Of Homomorphic Encryption Schemes, Kyle Yates
All Theses
In 2009, Craig Gentry introduced the first fully homomorphic encryption scheme using bootstrapping. In the 13 years since, a large amount of research has gone into improving efficiency of homomorphic encryption schemes. This includes implementing leveled homomorphic encryption schemes for practical use, which are schemes that allow for some predetermined amount of additions and multiplications that can be performed on ciphertexts. These leveled schemes have been found to be very efficient in practice. In this thesis, we will discuss the efficiency of various homomorphic encryption schemes. In particular, we will see how to improve sizes of parameter choices in homomorphic …
Analyzing And Creating Playing Card Cryptosystems, Isaac A. Reiter
Analyzing And Creating Playing Card Cryptosystems, Isaac A. Reiter
Honors Student Research
Before computers, military tacticians and government agents had to rely on pencil-and-paper methods to encrypt information. For agents that want to use low-tech options in order to minimize their digital footprint, non-computerized ciphers are an essential component of their toolbox. Still, the presence of computers limits the pool of effective hand ciphers. If a cipher is not unpredictable enough, then a computer will easily be able to break it. There are 52! ≈ 2^225.58 ways to mix a deck of cards. If each deck order is a key, this means that there are 52! ≈ 2^225.58 different ways to encrypt …
Universal Quantum Computation, Junya Kasahara
Universal Quantum Computation, Junya Kasahara
Theses, Dissertations and Capstones
We study quantum computers and their impact on computability. First, we summarize the history of computer science. Only a few articles have determined the direction of computer science and industry despite the fact that many works have been dedicated to the present success. We choose articles by A. M. Turing and D. Deutsch, because A. M. Turing proposed the basic architecture of modern computers while D. Deutsch proposed an architecture for the next generation of computers called quantum computers. Second, we study the architecture of modern computers using Turing machines. The Turing machine has the basic design of modern computers …
Elliptic Curve Cryptography: Extensions Of Subfield Curves In Characteristic 2, Joel Dearmond
Elliptic Curve Cryptography: Extensions Of Subfield Curves In Characteristic 2, Joel Dearmond
Pence-Boyce STEM Student Scholarship
This paper examines subfield curve extensions on a number of elliptic curves over finite fields in characteristic 2. The data generated is aimed to assist further understanding into the nature of elliptic curves, and any possible characteristics or patterns that they share. The total rational points on base fields were found using C++, and points on their field extensions were calculated using Scientific Workplace. Different extensions were then categorized based on the factorization of their respective points. We found that the total number of points on a base field will divide the total number of points of any extension of …
Cyclic Codes And Cyclic Lattices, Scott Maislin
Cyclic Codes And Cyclic Lattices, Scott Maislin
CMC Senior Theses
In this thesis, we review basic properties of linear codes and lattices with a certain focus on their interplay. In particular, we focus on the analogous con- structions of cyclic codes and cyclic lattices. We start out with a brief overview of the basic theory and properties of linear codes. We then demonstrate the construction of cyclic codes and emphasize their importance in error-correcting coding theory. Next we survey properties of lattices, focusing on algorithmic lattice problems, exhibit the construction of cyclic lattices and discuss their applications in cryptography. We emphasize the similarity and common prop- erties of the two …
Cayley Graphs Of Semigroups And Applications To Hashing, Bianca Sosnovski
Cayley Graphs Of Semigroups And Applications To Hashing, Bianca Sosnovski
Dissertations, Theses, and Capstone Projects
In 1994, Tillich and Zemor proposed a scheme for a family of hash functions that uses products of matrices in groups of the form $SL_2(F_{2^n})$. In 2009, Grassl et al. developed an attack to obtain collisions for palindromic bit strings by exploring a connection between the Tillich-Zemor functions and maximal length chains in the Euclidean algorithm for polynomials over $F_2$.
In this work, we present a new proposal for hash functions based on Cayley graphs of semigroups. In our proposed hash function, the noncommutative semigroup of linear functions under composition is considered as platform for the scheme. We will also …
The Evolution Of Cryptology, Gwendolyn Rae Souza
The Evolution Of Cryptology, Gwendolyn Rae Souza
Electronic Theses, Projects, and Dissertations
We live in an age when our most private information is becoming exceedingly difficult to keep private. Cryptology allows for the creation of encryptive barriers that protect this information. Though the information is protected, it is not entirely inaccessible. A recipient may be able to access the information by decoding the message. This possible threat has encouraged cryptologists to evolve and complicate their encrypting methods so that future information can remain safe and become more difficult to decode. There are various methods of encryption that demonstrate how cryptology continues to evolve through time. These methods revolve around different areas of …
An Elliptic Exploration, David Curtis Swart
An Elliptic Exploration, David Curtis Swart
Online Theses and Dissertations
In this paper I will be giving an introduction to an interesting kind of equation called elliptic curves, and how they can be used to protect our national security through Cryptology. We will explore the unique operation for adding points on elliptic curves and the group structure that it creates, as well as the ECC method, which stands among the RSA and AES methods as one of the modern day's most secure systems of cryptography. In addition, I will also introduce several algorithms and methods that are useful for working with ECC such as Schoof's Algorithm, and I will also …
A Limit Theorem In Cryptography., Kevin Lynch
A Limit Theorem In Cryptography., Kevin Lynch
Electronic Theses and Dissertations
Cryptography is the study of encryptying and decrypting messages and deciphering encrypted messages when the code is unknown. We consider Λπ(Δx, Δy) which is a count of how many ways a permutation satisfies a certain property. According to Hawkes and O'Connor, the distribution of Λπ(Δx, Δy) tends to a Poisson distribution with parameter ½ as m → ∞ for all Δx,Δy ∈ (Z/qZ)m - 0. We give a proof of this theorem using the Stein-Chen method: As qm …