On Higher-Order Cryptography (Long Version)
This work addresses a foundational question in cryptography, potentially impacting the design of secure systems, but it appears incremental as it builds on existing type-two constructions.
The paper tackles the problem of extending cryptographic schemes to higher-order algorithms, generalizing probabilistic polynomial time to orders beyond two, and proves both positive and negative results for authentication schemes and pseudorandom functions.
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.