Browsing Department of Mathematics (MU) by Thesis Advisor "Banks, William David, 1964-"
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Elliptic curves and their applications in cryptography
(University of Missouri--Columbia, 2009)In 1985, Koblitz and Miller proposed elliptic curves to be used for public key cryptosystems. This present thesis examines the role of elliptic curves on cryptography and basic problems involving implementation and security ... -
Exponential sums, character sums, sieve methods and distribution of prime numbers /
(University of Missouri--Columbia, 2017)[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This thesis is focus on the methods of exponential sums and sieve methods applying to distribution of primes numbers in several forms, such as ... -
On the theory of integer sequences
(University of Missouri--Columbia, 2010)We explore certain sequences of integers which appear in the number theory. We start by exploring properties of Beatty sequences. We concentrate on looking at the sum of primes from a Beatty sequence and properties of ... -
Results in analytic and algebraic number theory
(University of Missouri--Columbia, 2012)The thesis begins with proving some theorems about Gauss sums and Jacobi sums. Using theorems the first chapter ends with a proof that if p is a prime such that p ≡ 1 (mod 4), then there are integers a and b such that p = ...