Dr. Gilman uses the application of mathematics to advance cryptographic research. He is the leader of the Algebraic Cryptography Center at Stevens, which focuses research efforts on cryptanalysis of public key cryptosystems based on algebraic problems, theoretical development of generic complexity, and the application of generic complexity to the problem of testing the security of cryptosystems.

As part of the recent Geometric Asymptotic Group Theory Conference, Dr. Gilman discussed how using braids, or rather the geometric abstraction of braids, to protect data from hacking at quantum speeds. Quantum computing accounts for major technology hurdles in providing security, and the research by Dr. Gilman is leading the way towards innovative solutions.

Dr. Gilman has been a part of many journal articles, worked as an invited speaker in many conference proceedings, contributed to several books and is a member of the Editorial board of the Journal Groups, Complexity and Cryptology, published by Heldermann-Verlag, the Eastern Section Program Committee of the American Mathematical Society, the editorial board of the Journal of Mathematical Cryptology, published by De Gruyter, a founding member of the editorial board of the series Algorithms and Computation in Mathematics, published by Springer Verlag, organizer of the Workshop on Generic Complexity held at the American Institute of Mathematics, and the organizer of American Mathematical Society sectional meetings at Stevens.