My main research interests are in cryptology, algebraic combinatorics, coding theory, and algorithms and their complexity, particularly those related to computational group theory. For over 40 years I have been interested in group theoretic cryptography. I am also interested in data compression, specifically in applications of coding theory to lossless image compression. I am interested in combinatorial designs and related finite geometries, including t-designs, Large Sets of t-designs, Room Rectangles, mutually orthogonal Latin squares, projective planes, orthogonal and perpendicular arrays. I am also interested in algorithmic methods in design theory, especially those methods which lead to proofs of existence/non-existence of designs for large t, and small lambda. These methods include the use of groups, large knap-sack solvers, and isomorphism testing.
Some of the highlights include: The invention of group theoretic Cryptosystem PGM, and cryptosystems MSTi, i=1,2,3. The discovery of the world's first simple 6-design, and the construction of infinite families of 5-designs. New ideas in the non-abelian discrete logarithm problem, leading to a collaboration and cryptanalysis of the foundational Tillich-Zemor hash function, the discovery of new large sets of t-designs and collaborations in the discovery of large sets of geometric t-designs, and some constructions and decompositions of well known strongly regular graphs. Research in lattice basis reduction using permutation codes and optimization techniques.
