The Computational Mathematics Program of the National Sciences Foundation has awarded Robert Gilman, Professor in the Department of Mathematical Sciences, a three-year grant. Co-PIs on the grant are Professors Aleksey D. Myasnikov, Alexei G. Miasnikov, and Alexander Ushakov, also of the Department of Mathematical Sciences, and Professor Mark Sapir of Vanderbilt University’s Mathematics Department.
The grant will enable researchers to advance knowledge of the feasibility of various hard computational problems in combinatorial group theory by 1) finding improvements in algorithms for some well-known hard problems, 2) developing and testing algorithms for a variety of new hard combinatorial group theoretic problems, originating in cryptography and other areas, and 3) by investigating the distribution of difficult instances of hard problems.
“We’re interested in math problems that come from modern cryptography and are related to the security of cryptosystems,” says Gilman.
The security of modern private key cryptosystems depends on the difficulty of underlying computational problems. For example, the well-known RSA system, which is widely used to protect e-commerce and ATM transactions, depends for its security on the difficulty of factoring certain large numbers that are hundreds of digits long. The investigators wish to gain insight into the underlying key computational problems of private key cryptosystems by studying similar phenomena occurring in the world of combinatorial group theory.
The Stevens researchers working on this grant are members of Stevens’ Algebraic Cryptography Center, which promotes activities aimed at facilitating the use of heuristic and theoretical techniques to gain insight into mathematical problems from cryptography and cybersecurity.