In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy

Luis Moraes

will defend his dissertation proposal

Analysis of Cryptographic Hash Functions

Abstract

Cryptographic hash functions have a unique position among cryptographic primitives. What makes them so interesting is the paradoxical notion that an infinite number of messages map to the same output yet finding two of these messages should be difficult. Furthermore, the unkeyed nature of hash functions require an a nalysis of the fundamental complexity of a function as a consequence of its structure. I propose a more thorough examination of the structure of hash functions. Although the literature can point us toward what properties a hash function should have as a whole, there is less work in analyzing how the internals of a hash function contribute to its security concretely. How a hash function is represented should affect which properties are readily discernible. Therefore, a comparison needs to be made to determine the strengths and weaknesses of different representations. In particular, SAT encodings have been underrepresented. Their introduction did not provide a performance breakthrough, but their analytic potential remains to be fully explored. On the other hand, the algebraic form of boolean functions is a well established representation for analyzing their security/complexity properties. If we consider the cryptographic hash function as a black box it more closely resembles boolean ma ppings. The theory of boolean functions and mappings provides many useful tools for analyzing hash functions, thus extending them to other representations would be beneficial. Studying the relationships between these different representations should yield interesting results.

Date: Thursday, December 17, 2015
Time: 11:00 AM
Place: PGH 550
Advisor: Dr. Rakesh Verma

Faculty, students, and the general public are invited.