NIZK Proofs from Group-Action-Based Assumptions

Determine whether non-interactive zero-knowledge proofs exist under group-action-based cryptographic assumptions, rather than relying on the learning-with-errors assumption.

Background

The paper compares its black-box constructions of robust public-key encryption with secure key leasing and robust single-decryptor encryption to an alternative approach based on appending non-interactive zero-knowledge proofs that certify ciphertext well-formedness. Although NIZK proofs are known under the learning-with-errors assumption, the paper explicitly notes that their existence under group-action-based assumptions is unresolved. This is relevant because the paper’s constructions use public-key encryption and hinting pseudorandom generators, both of which can be instantiated under group-action-based assumptions, whereas the NIZK-based alternative currently cannot be justified under the same assumption class.