How to Avoid Obfuscation using Witness PRFs

Abstract: Recently, program obfuscation has proven to be an extremely powerful tool and has been used to construct a variety of cryptographic primitives with amazing properties.  However, current candidate obfuscators are somewhat inefficient and rely on unnatural hardness assumptions about multilinear maps.

 

In this work, we seek to avoid the complexity associated with obfuscation.  We show that, for several applications, a weaker primitive called witness pseudorandom functions (witness PRFs) suffices.  Applications include multiparty key exchange without trusted setup, polynomially-many hardcore bits for any one-way function, and more.  We then show how to instantiate witness PRFs from multilinear maps.  Our witness PRFs are simpler and more efficient than current obfuscation candidates, and involve very natural hardness assumptions about the underlying maps.