We introduce the notion of public key encryption with secure key leasing (PKE-SKL). Our notion supports the leasing of decryption keys so that a leased key achieves the decryption functionality but comes with the guarantee that if the quantum decryption key returned by a user passes a validity test, then the user has lost the ability to decrypt. Our notion is similar in spirit to the notion of secure software leasing (SSL) introduced by Ananth and La Placa (Eurocrypt 2021) but captures significantly more general adversarial strategies. In more detail, our adversary is not restricted to use an honest evaluation algorithm to run pirated software. Our results can be summarized as follows: 1. Definitions: We introduce the definition of PKE with secure key leasing and formalize security notions. 2. Constructing PKE with Secure Key Leasing: We provide a construction of PKE-SKL by leveraging a PKE scheme that satisfies a new security notion that we call consistent or inconsistent security against key leasing attacks (CoIC-KLA security). We then construct a CoIC-KLA secure PKE scheme using 1-key Ciphertext-Policy Functional Encryption (CPFE) that in turn can be based on any IND-CPA secure PKE scheme. 3. Identity Based Encryption, Attribute Based Encryption and Functional Encryption with Secure Key Leasing: We provide definitions of secure key leasing in the context of advanced encryption schemes such as identity based encryption (IBE), attribute-based encryption (ABE) and functional encryption (FE). Then we provide constructions by combining the above PKE-SKL with standard IBE, ABE and FE schemes.

翻译：我们引入了具有安全密钥租赁的公钥加密（PKE-SKL）的概念。该概念支持解密密钥的租赁，使得租赁的密钥既具备解密功能，又保证如果用户返回的量子解密密钥通过有效性测试，则该用户将失去解密能力。这一概念与Ananth和La Placa（Eurocrypt 2021）提出的安全软件租赁（SSL）理念相似，但涵盖了更广泛的对抗策略。具体而言，我们的对手不受限于使用诚实的评估算法来运行盗版软件。我们的研究结果总结如下：1. **定义**：我们提出了具有安全密钥租赁的公钥加密定义，并形式化了安全概念。2. **构建具有安全密钥租赁的公钥加密**：我们利用一种满足新型安全概念（称为针对密钥租赁攻击的一致或不一致安全性，即CoIC-KLA安全性）的公钥加密方案，构建了PKE-SKL。随后，我们使用基于任何IND-CPA安全公钥加密方案的1密钥密文策略功能加密（CPFE）构建了CoIC-KLA安全的公钥加密方案。3. **具有安全密钥租赁的身份基加密、属性基加密和功能加密**：我们为高级加密方案（如身份基加密（IBE）、属性基加密（ABE）和功能加密（FE））定义了安全密钥租赁的概念，并通过将上述PKE-SKL与标准IBE、ABE和FE方案结合，提供了具体构造。