Offline Witness Encryption from Witness PRF and Randomized Encoding in CRS Model

Abstract

Witness pseudorandom functions, in short witness PRFs, (Zhandry, TCC 2016) and witness encryption (Garg et al., ACM 2013) are two powerful cryptographic primitives where the former produce a pseudorandom value corresponding to an instance of an NP language and the latter possesses the ability to encrypt a message with an NP problem. Mostly, these primitives are constructed using computationally expensive tools like obfuscation or multilinear maps. In this work, we build (single relation) witness PRFs using a puncturable pseudorandom function and a randomized encoding in common reference string (CRS) model. Next, we propose construction of an offline witness encryption having short ciphertexts from a public-key encryption scheme, an extractable witness PRF and a randomized encoding in CRS model. Furthermore, we show how to convert our single relation witness PRF into a multi-relation witness PRF and the offline witness encryption into an offline functional witness encryption scheme.