  We propose a new, unifying framework that yields an array of cryptographic
primitives with 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 X \in {public-key, attribute-based, fully-homomorphic, witness,
timed-release}, our compiler converts any (post-quantum) X encryption to X
encryption with certified deletion. In addition, we compile
statistically-binding commitments to statistically-binding commitments with
certified everlasting hiding. As a corollary, we also obtain
statistically-sound zero-knowledge proofs for QMA with certified everlasting
zero-knowledge assuming statistically-binding commitments.
  - We also obtain a strong form of everlasting security for two-party and
multi-party computation in the dishonest majority setting. While simultaneously
achieving everlasting security against all parties in this setting is known to
be impossible, we introduce everlasting security transfer (EST). This enables
any one party (or a subset of parties) to dynamically and certifiably
information-theoretically delete other participants' data after protocol
execution. We construct general-purpose secure computation with EST assuming
statistically-binding commitments, which can be based on one-way functions or
pseudorandom quantum states.
  We obtain our results by developing a novel proof technique to argue that a
bit b has been information-theoretically deleted from an adversary's view once
they output a valid deletion certificate, despite having been previously
information-theoretically determined by the ciphertext they held in their view.
This technique may be of independent interest.
