In this work, we consider the problem of secure key leasing, also known as revocable cryptography (Agarwal et. al. Eurocrypt' 23, Ananth et. al. TCC' 23), as a strengthened security notion of its predecessor put forward in Ananth et. al. Eurocrypt' 21. This problem aims to leverage unclonable nature of quantum information to allow a lessor to lease a quantum key with reusability for evaluating a classical functionality. Later, the lessor can request the lessee to provably delete the key and then the lessee will be completely deprived of the capability to evaluate. In this work, we construct a secure key leasing scheme to lease a decryption key of a (classical) public-key, homomorphic encryption scheme from standard lattice assumptions. We achieve strong form of security where: * The entire protocol uses only classical communication between a classical lessor (client) and a quantum lessee (server). * Assuming standard assumptions, our security definition ensures that every computationally bounded quantum adversary could not simultaneously provide a valid classical deletion certificate and yet distinguish ciphertexts. Our security relies on the hardness of learning with errors assumption. Our scheme is the first scheme to be based on a standard assumption and satisfying the two properties above.

翻译：本文研究安全密钥租赁问题（亦称可撤销密码学，Agarwal等, Eurocrypt'23; Ananth等, TCC'23），作为Ananth等人在Eurocrypt'21中提出的原始概念的强化安全定义。该问题旨在利用量子信息不可克隆的特性，允许出租方租借可重复使用的量子密钥以评估经典功能。随后，出租方可要求承租方对密钥进行可验证删除，使承租方完全丧失评估能力。我们基于标准格假设，构建了面向(经典)公钥同态加密方案解密密钥的安全密钥租赁机制，实现了以下强安全性：* 整个协议仅涉及经典出租方（客户端）与量子承租方（服务器）之间的经典通信。* 在标准假设下，我们的安全定义确保任意计算有界的量子敌手无法同时提供有效的经典删除证书并能区分密文。本方案的安全性基于带误差学习假设的困难性，是首个满足上述两项性质且基于标准假设的方案。