Cryptography with Certified Deletion

We propose a new, unifying framework that yields an array of cryptographic primitives with {\em certified deletion}. These primitives enable a party in possession of a quantum ciphertext to generate a classical certificate that the encrypted plaintext has been information-theoretically deleted, and cannot be recovered even given unbounded computational resources. For any $X \in \{\mathsf{public}\text{-}\mathsf{key},\mathsf{attribute\text{-}based},\mathsf{fully\text{-}homomorphic},\mathsf{witness},\mathsf{timed}\text{-}\mathsf{release}\}$, our compiler yields post-quantum $X$ encryption with certified deletion, assuming post-quantum $X$ encryption. In addition, assuming the existence of statistically binding commitments, our compiler yields statistically binding commitments with certified everlasting hiding as well as statistically sound zero-knowledge proofs for QMA with certified everlasting zero-knowledge. We also introduce and construct information-theoretic secret sharing with certified deletion. While encryption with certified deletion was first introduced by [BI20] in the context of an information-theoretic one-time pad, existing proposals [Unr14,HMNY21,HMNY22,Por22] for {\em public-key} primitives with certified deletion (1) have complex tailored constructions and non-generic proofs, (2) are not known to satisfy everlasting security after deletion in the plain model, and in many cases (3) resort to idealized models or stronger cryptographic assumptions like obfuscation. We remedy this situation by developing a novel proof technique to argue that a bit $b$ has been {\em information-theoretically deleted} from an adversary's view once they produce a valid deletion certificate, despite having been previously {\em information-theoretically determined} by the ciphertext they held in their view. This may be of independent interest.