Colloquium: On the Nature of Mathematical Proofs: A Cryptographic Perspective

Speaker: Jonathan Katz (UMD)

Title: On the Nature of Mathematical Proofs: A Cryptographic Perspective

Beginning in the mid-'80s, complexity theorists began radically
revising the notion of what (mathematical) proof might entail,
introducing and extending the ideas of using both randomness and
interaction as part of the proof-verification process. Cryptographers
took this one step further with the idea of *zero-knowledge proofs*,
which are supposed to reveal "no information" beyond the validity of
the theorem being proven.

We give an introductory survey of these fundamental and now-classical
concepts, and conclude with a brief discussion of current research
exploring their applications and extensions to the settings of secure
distributed computation and verifiable outsourcing.

Jonathan Katz is a professor of computer science at the University of
Maryland, and director of the Maryland Cybersecurity Center. He
received an undergraduate degree in mathematics from MIT, and a PhD in
computer science from Columbia University. His research interests lie
broadly in the fields of cryptography, privacy, and science of
cybersecurity, and he is a co-author of the widely used textbook
"Introduction to Modern Cryptography." Katz was a member of the DARPA
Computer Science Study Group from 2009-2010, and received a Humboldt
Research Award in 2015. He currently serves on the steering committee
for the IEEE cybersecurity initiative, as well as the State of
Maryland Cybersecurity Council.