Algebraic pseudorandom functions with improved efficiency from the augmented cascade

Authors:
Dan Boneh;Hart William Montgomery;Ananth Raghunathan
Affiliations:
Stanford University, Stanford, CA, USA;Stanford University, Stanford, CA, USA;Stanford University, Stanford, CA, USA
Venue:
Proceedings of the 17th ACM conference on Computer and communications security
Year:
2010

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Abstract

We construct an algebraic pseudorandom function (PRF) that is more efficient than the classic Naor-Reingold algebraic PRF. Our PRF is the result of adapting the cascade construction, which is the basis of HMAC, to the algebraic settings. To do so we define an augmented cascade and prove it secure when the underlying PRF satisfies a property called parallel security. We then use the augmented cascade to build new algebraic PRFs. The algebraic structure of our PRF leads to an efficient large-domain Verifiable Random Function (VRF) and a large-domain simulatable VRF.