Major Qualifying Project in Mathematics
Available in: postscript pdf.
Error correcting codes, such as Reed-Solomon codes, can be used to
create authentication codes based on orthogonal arrays. These codes are
provably secure up to a certain number of uses; however, as the number
of desired uses goes up, so does the keylength. This project researches
the security of a code whose messages (which function as private keys)
have specific form that allows them to be represented in a more compact
fashion. Specifically, messages with low Hamming weight are considered.
Interactive Qualifying Project
Using sources from the humanities, social sciences, and game theory,
we explored the conceptual and real-world relationships among games,
play, and rationality. In contrast to traditional game theory
emphasizing only winning, we postulate a "play rationality" that allows
for additional goals (like having fun). To observe the implications of
"play rationality," we developed a "Student's Dilemma" game based on
classic game theory. Our analysis looks at observations of our game in
light of both experimental game theory and "play rationality."
Major Qualifying Project in Computer Science
As elliptic curves become more accepted and used in the field of
cryptography, more curves will be needed for the growing number of
ellptic curve cryptosystems. Traditional trial and error methods of
curve generation can take a long time, and do not always produce a curve
with desired characteristics. For an elliptic curve reference library, a
curve generator was designed and written in the Java programming
language, using the method of complex multiplication, desirable for its
efficiency and flexibility.
Sufficiency in Humanities and Arts
In the development and growth of language and religion, often times
each will have an influence on the other. Through looking at the
language and religion pairs of Hebrew and Judaism, and Latin and
Christianity, the effects of parallel development of language and
religion on the forms of these influences can be seen. In parallel
development, a religion has stronger influence on the language; when the
language and religion develop independently, the language has a stronger
influence.
Games, Play, and the Student's Dilemma
Coauthor: Lucas Ackerman
Available in: doc pdf.
Elliptic Curve Generation via Complex Multiplication in Java
Available in: postscript pdf.
Parallel Development of Language and Religion
Available in: postscript pdf.