Rewriting Methods in Groups with Applications to Cryptography

Author

Gabriel Zapata, The Graduate Center, City University of New YorkFollow

Date of Degree

6-2017

Document Type

Dissertation

Degree Name

Ph.D.

Program

Mathematics

Advisor

Vladimir Shpilrain

Committee Members

Melvyn Nathanson

Alexey Ovchinnikov

Subject Categories

Mathematics

Abstract

In this thesis we describe how various rewriting methods in combinatorial group theory can be used to diffuse information about group elements, which makes it possible to use these techniques as an important constituent in cryptographic primitives. We also show that, while most group-based cryptographic primitives employ the complexity of search versions of algorithmic problems in group theory, it is also possible to use the complexity of decision problems, in particular the word problem, to claim security of relevant protocols.

Recommended Citation

Zapata, Gabriel, "Rewriting Methods in Groups with Applications to Cryptography" (2017). CUNY Academic Works.
https://academicworks.cuny.edu/gc_etds/2030