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 on one-time pad (OTP) encryption, or use 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. The constructions combine an information-theoretic key encapsulation mechanism (iKEM) with a data encapsulation mechanism that provides certified deletion (DEM-CD) and, respectively, provide {\em information-theoretic certified deletion}, where both confidentiality and deletion properties are provided against a computationally unbounded adversary; and {\em everlasting certified deletion}, where confidentiality is computational before deletion, and upon successful verification of the deletion certificate, the message becomes information-theoretically hidden from an adversary that is computationally unbounded. Our pHE-CD schemes provide IND-$q_e$-CPA notion of security and support encryption of arbitrarily long messages. In the second construction, using a computationally secure DEM-CD that is quantum-safe (i.e. constructed using quantum coding and AES), we obtain quantum-safe security with keys that are significantly shorter than the message. Instantiating the proposed framework using quantum enabled kem (qKEM) as the iKEM, is a future work.

翻译：可验证删除允许Alice将数据外包给Bob，并在之后获得可验证的保证：该文件已根据她的请求被不可逆地删除。尽管仅使用经典信息无法实现此功能，但利用量子信息可达成该目标。现有方法依赖于一次性密码本加密，或使用可能受未来经典或量子计算进展威胁的计算硬度假设。本文在预处理模型中引入并形式化了具有可验证删除的混合加密方案，并提出两种具体构造。这些构造将信息论密钥封装机制与提供可验证删除的数据封装机制相结合，分别实现了以下特性：一是信息论可验证删除，即针对计算能力无界的敌手同时保障机密性与删除可验证性；二是永久可验证删除，即在删除前机密性为计算安全，而在成功验证删除凭证后，消息对计算无界敌手具有信息论隐藏性。我们的方案满足IND-$q_e$-CPA安全概念，并支持任意长度消息的加密。在第二种构造中，通过采用量子安全（即基于量子编码与AES构建）的计算安全DEM-CD，我们实现了密钥长度显著短于消息长度的量子安全方案。未来工作将探索用量子增强密钥封装机制作为信息论KEM来实例化本框架。