具有安全密钥租赁和复制保护功能的陷门函数
Trapdoor Functions with Secure Key Leasing and Copy Protection
- NTT Social Informatics Laboratories（NTT社会信息学实验室）
- NTT Research Center for Theoretical Quantum Information（NTT理论量子信息中心）
- Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究首次将陷门函数引入安全密钥租赁与复制保护领域，基于LWE等假设构造了相关方案，并解决了现有加密方案中量子密钥易被破坏的问题。
AI中文摘要：
受量子理论中不可克隆定理的启发，各种具有不可克隆功能的量子密码学原语，如安全密钥租赁和复制保护，已被提出并引起了广泛关注。然而，陷门函数（TDFs）作为公钥密码学中的基本原语，在这些领域尚未得到广泛研究。在这项工作中，我们开创了在安全密钥租赁和复制保护两种设置下对TDFs的研究。我们首先引入了具有安全密钥租赁的TDFs（TDF-SKL）的定义，该定义支持量子陷门的租赁和删除。我们在有无域采样器两种情况下形式化了TDF-SKL，并基于LWE假设给出了无域采样器的TDF-SKL构造，以及基于任何标准PKE方案结合提示性伪随机生成器[Koppula和Waters，CRYPTO 2019]的带域采样器的TDF-SKL构造。接下来，我们定义了具有复制保护的TDFs（TDF-CP），其中反演功能通过量子陷门进行复制保护。我们遵循Ananth和Behera [CRYPTO 2024]提出的模块化复制保护框架，在假设不可区分混淆和LWE假设的前提下，建立了TDF-CP的构造。我们还展示了TDF-SKL和TDF-CP的应用。现有的具有安全密钥租赁的公钥加密（PKE-SKL）和单解密器加密（SDE）构造存在一个关键漏洞：量子解密密钥在解密恶意选择的密文后可能被破坏。我们分别从TDF-SKL和TDF-CP构造了具有鲁棒量子解密密钥的PKE-SKL方案和SDE方案，这些密钥在解密任意密文后仍可重复使用。
英文摘要：
Inspired by the no-cloning theorem in quantum theory, a variety of quantum cryptographic primitives with unclonable functionalities, such as secure key leasing and copy protection, have been proposed and attracted significant attention. However, trapdoor functions (TDFs), fundamental primitives in public-key cryptography, have not been extensively studied in these areas. In this work, we initiate a study of TDFs in both secure key leasing and copy protection settings. We first introduce the definition of TDFs with secure key leasing (TDF-SKL), which enables leasing and deleting of quantum trapdoors. We formalize TDF-SKL both with and without domain sampler, and give a construction of TDF-SKL without domain sampler based on the LWE assumption and a construction of TDF-SKL with domain sampler based on any standard PKE schemes combined with hinting pseudorandom generators [Koppula and Waters, CRYPTO 2019]. Next, we define TDFs with copy protection (TDF-CP), where the inversion functionality is copy protected by a quantum trapdoor. We establish a construction of TDF-CP assuming indistinguishability obfuscation and the LWE assumption, following a modular framework of copy protection proposed by Ananth and Behera [CRYPTO 2024]. We also present applications of TDF-SKL and TDF-CP. Existing constructions of public-key encryption with secure key leasing (PKE-SKL) and single-decryptor encryption (SDE) suffer from a critical vulnerability: quantum decryption keys may be destroyed after decrypting maliciously chosen ciphertexts. We construct PKE-SKL schemes and SDE schemes with robust quantum decryption keys that remain reusable after decrypting arbitrary ciphertexts from TDF-SKL and TDF-CP, respectively.
