Certified deletion allows Alice to outsource data to Bob and, at a later time, obtain a verifiable guarantee that the file has been irreversibly deleted at her request. The functionality, while impossible using classical information alone, can be achieved using quantum information. Existing approaches rely either on one-time pad (OTP) encryption, or on computational hardness assumptions that may be vulnerable to future advances in classical or quantum computing. In this work, we introduce and formalize hybrid encryption with certified deletion in the preprocessing model (pHE-CD) and propose two constructions. Each construction composes an information-theoretic key encapsulation mechanism (iKEM) with a data encapsulation mechanism that provides certified deletion (DEM-CD) security, offering different types of security depending on the security properties of DEM-CD. When DEM-CD is one-time information theoretically secure, the composition provides {\em information-theoretic security} for both encryption and certified deletion. When DEM-CD is computationally secure, the composed construction offers computationally secure (post-quantum) encryption and {\em everlasting certified deletion} where confidentiality is computational up to the point that the deletion certificate is verified, and after successful verification of the certificate, becomes unconditional. That is, successful verification of deletion certificate guarantees that the data has been removed information-theoretically from the adversary's view. Both pHE-CD schemes are for encryption of arbitrarily long messages. Construction 2 is key efficient and uses a DEM-CD that is constructed using quantum coding and AES, providing quantum-safe security for encryption. We discuss our results and directions for future work.

翻译：可验证删除功能允许Alice将数据外包给Bob，并在后续时间点获得可验证的保证：文件已根据其请求被不可逆地删除。该功能虽然仅依赖经典信息无法实现，但可通过量子信息达成。现有方案要么依赖一次性密码本加密，要么基于可能受未来经典或量子计算进展威胁的计算复杂度假设。本文在预处理模型中引入并形式化了具备可验证删除功能的混合加密方案，并提出两种构造。每种构造均将信息论密钥封装机制与提供可验证删除安全性的数据封装机制相结合，根据数据封装机制的安全特性提供不同类型的安全性。当数据封装机制具备一次性信息论安全性时，该组合方案可为加密与可验证删除同时提供信息论安全性。当数据封装机制具备计算安全性时，组合构造可提供计算安全的（后量子）加密与永久性可验证删除——在删除证书验证前保密性为计算安全，而证书验证成功后则转为无条件安全。换言之，删除证书的成功验证可保证数据已从敌手视角被信息论地移除。两种预处理模型下的可验证删除混合加密方案均支持任意长度消息的加密。构造2具有密钥高效性，其采用基于量子编码与AES构建的数据封装机制，为加密提供量子安全保证。本文最后讨论了研究成果及未来研究方向。