On Higher-Order Cryptography

by Ugo Dal Lago

• When: Friday, 23/04/2021, between 1pm and 2pm EDT (6pm - 7pm UTC)
• Where: Zoom; Outside guests please RSVP by emailing Harley Eades
• YouTube Stream/Recording: https://youtu.be/FyFT3ZariSA

Abstract

Type-two constructions abound in cryptography: adversaries for encryption and authentication schemes, if active, are modeled as algorithms having access to oracles, i.e. as second-order algorithms. But how about making cryptographic schemes themselves higher-order? This paper gives an answer to this question, by first describing why higher-order cryptography is interesting as an object of study, then showing how the concept of probabilistic polynomial time algorithm can be generalized so as to encompass algorithms of order strictly higher than two, and finally proving some positive and negative results about the existence of higher-order cryptographic primitives, namely authentication schemes and pseudorandom functions. This is a joint work with Boaz Barak and Raphaëlle Crubillé.