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 MissouriColumbia, 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 ... 
On the theory of integer sequences
(University of MissouriColumbia, 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 MissouriColumbia, 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 = ...