How to Avoid Obfuscation Using Witness PRFs
By Mark Zhandry
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 far from practical and rely on unnatural hardness assumptions about multilinear maps. In this work, we bring several applications of obfuscation closer to practice by showing that 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.
Low Overhead Broadcast Encryption from Multilinear Maps
By Dan Boneh, Brent Waters, and Mark Zhandry
In CRYPTO 2014
We use multilinear maps to provide a solution to the long-standing problem of public-key broadcast encryption where all parameters in the system are small. In our constructions, ciphertext overhead, private key size, and public key size are all poly-logarithmic in the total number of users. The systems are fully collusion-resistant against any number of colluders. All our systems are based on an O(log N)-way multilinear map to support a broadcast system for N users. We present three constructions based on different types of multilinear maps and providing different security guarantees. Our systems naturally give identity-based broadcast systems with short parameters.