Some applications of noncommutative groups and semigroups to information security

Author

Lisa Bromberg, Graduate Center, City University of New York

Date of Degree

5-2015

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Vladimir Shpilrain

Subject Categories

Mathematics

Keywords

cryptography; hash functions; information security

Abstract

We present evidence why the Burnside groups of exponent 3 could be a good candidate for a platform group for the HKKS semidirect product key exchange protocol. We also explore hashing with matrices over SL₂(F_p), and compute bounds on the girth of the Cayley graph of the subgroup of SL₂(F_p) for specific generators A, B. We demonstrate that even without optimization, these hashes have comparable performance to hashes in the SHA family.

Recommended Citation

Bromberg, Lisa, "Some applications of noncommutative groups and semigroups to information security" (2015). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/871