Last modified: August 16, 2018
I am a mathematician. I am currently working on problems in two somewhat
related research areas. On the theoretical side, my area of research is
On the applied side, I am also working on combinatorial aspects of
cryptography. This latter work is funded by the National Science
As of August 2018, my research in combinatorics is supported through a grant from the
United States National Science Foundation. This generous support is
Combinatorial Aspects of Cryptography
My interests in cryptography deal mainly with combinatorial and
other mathematical structures lying beneath various cryptographic
protocols. On the algorithmic side, I work on these issues with
Dr. Berk Sunar in the
Department of Electrical and Computer Engineering at WPI.
I currently supervise two graduate students
working on these problems.
Some topics of interest:
- almost universal hash families;
- almost orthogonal vectors in Euclidean spaces;
- algorithms for very low-power authentication with proofs of security;
- hardness amplification;
- pseudorandom generators and true random number generators;
- efficient combinatorial structures for pseudorandomness;
- homomorphic encryption.
In the optimal years, I help organize a
Cryptography Seminar which brings
world leaders in these research areas to WPI each term.
I work mostly with
These can be viewed as a generalization of groups or as a generalization
I am also interested in error-correcting
combinatorial designs. The
theory of association schemes (and
distance-regular graphs) provides an algebraic approach to
codes and designs and this approach has been very successful
over the past thirty years.
My most recent work aims to build a theory of
cometric association schemes
and to investigate applications related to these.
Applications that compel me, aside from cybersecurity, include quantum information theory, error-correcting codes,
quasi-Monte Carlo methods, and other strange designs.
The thesis of Philippe Delsarte played an important
role in establishing a connection between association schemes and the subjects
of error-correcting codes and combinatorial designs. It was published in
1973 as an entire volume of Philips Research Reports
Here are my papers on these subjects.
My other research interests include: theoretical computer science;
telecommunications; graph theory; pure mathematics.
A recent curriculum vita can be found here
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