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.

翻译：我们提出了一种新颖的统一框架，该框架能够产生一系列具有认证删除功能的密码学原语。这些原语使得持有量子密文的各方能够生成经典证书，证明加密的明文已被信息论意义上删除，且即使拥有无限计算资源也无法恢复。 - 对于X ∈ {公钥、基于属性、全同态、见证、定时释放}，我们的编译器可将任何（后量子）X加密方案转换为带认证删除的X加密方案。此外，我们将统计绑定承诺编译为具有统计绑定的带认证的永恒隐藏承诺。作为推论，我们还在假设统计绑定承诺存在的前提下，获得了针对QMA的统计可靠零知识证明，且具有认证的永恒零知识特性。 - 对于不诚实多数设置下的两方与多方计算，我们同时获得了强形式的永恒安全性。尽管已知在此设置下无法同时针对所有参与方实现永恒安全性，但我们引入了永恒安全转移（EST）概念。该技术允许任意一方（或部分参与方）在协议执行后动态且可认证地以信息论方式删除其他参与方的数据。我们基于统计绑定承诺（可基于单向函数或伪随机量子态实现）构造了具有EST功能的通用安全计算。我们的成果通过开发一种新型证明技术得以实现：该技术可论证当敌手输出有效的删除证书后，尽管此前信息论上密文已完全决定其视图中的比特b，但该比特已从敌手视角中被信息论删除。该技术可能具有独立的研究价值。