Offline witness encryption from witness PRF and randomized encoding in CRS model (Q2183915)

Witness encryption and witness pseudorandom functions and novel cryptographic primitives using instances of NP problems and witnesses are interesting. Witness encryption has the property that a message is encrypted wrt. an instance of an NP problem and only a witness holder can decrypt it. Similarly, witness pseudorandom functions have the property that a pseudorandom value computed from an NP instance and a secret can also be obtained from an evaluation key (corresponding to the secret), the NP instance and a witness. Whereas most of the primitives are constructed using obfuscation or multilinear maps, the authors present two new approaches. First, they present a construction on witness pseudorandom functions using punctured pseudorandom functions and randomized encoding in common reference string model. Afterwards, they present a construction for offline witness encryption. They remark that the presented single relation witness pseudorandom functions can be transformed into multi-relation witness pseudorandom functions and the offline witness encryption can be transformed into an offline functional witness encryption. The results are not surprising. Unfortunately, the paper is hard to follow and poorly written. Overall the paper lacks non-technical explanations, examples, instances and also a conclusion. Moreover, some variables and notions are used before their definition or not defined at all. For the entire collection see [Zbl 1428.68026].