基于格的可证明安全无用户私钥加密方案

Provably secure private-keyless encryption on ideal lattices

  • 摘要: 针对公钥加密方案涉及繁琐私钥管理问题,无用户私钥加密通过将传统用户私钥替代为一次性解密凭证,从而简化了私钥更新、撤销等相关复杂管理操作,避免了用户安全存储私钥的代价,成为该问题的有效解决方案之一. 据此,本文提出了一种理想格下的无用户私钥加密概念、方案及其安全性要求. 首先,给出了无用户私钥加密的形式化定义和可验证的凭证构造方法,通过由第三方可信机构验证用户身份后颁发一次性解密凭证,从而降低了私钥存储代价并简化了私钥管理流程,并可支持对用户访问数据权限的实时判决. 其次,引入密文刷新机制,由初始密文参数可直接生成当前时刻的刷新密文,建立了同一时刻下凭证与刷新密文的对应关系,仅需刷新部分密文,降低密文刷新计算开销. 此外,本文给出了无用户私钥加密安全性要求,包括选择时间攻击下的凭证和刷新密文的不可伪造性、时效性安全以及语义安全,并描述了这些安全性要求的对应关系. 最后,本文利用环上短整数解和带学习误差困难问题给出了标准模型下并借助R-SIS谕言机实现了该无用户私钥加密方案在理想格下的实例分析. 由安全性分析可知,所提实例满足凭证和刷新密文的不可伪造性、时效性安全以及语义安全. 时空复杂度分析和性能对比表明,所提PKLE方案可避免用户存储私钥代价以及私钥的定期更新与撤销等管理操作,更适配于隐私数据动态访问判决的场景,同时支持部分密文刷新机制且仅需一次环上乘法操作,减少了密文刷新的计算开销.

     

    Abstract: Private-keyless encryption (PKLE) addresses the cumbersome challenge of private key management by replacing traditional user private keys with one-time decryption credentials. This approach streamlines complex management processes, such as private key updates and revocations while eliminating the cost and burden of secure key storage for users. Building on this paradigm, this paper introduces the concept, scheme, and security requirements for a PKLE system constructed over ideal lattice. First, we define PKLE and propose a construction method for verifiable credentials. These credentials function as “one-time decryption keys” issued by a trusted third party (the “credential issuance center”) only after the user’s identity is verified. This model simplifies private key management, reduces storage costs, and enables real-time, dynamic decisions on user data access requirements. Second, we introduce a ciphertext-refreshing mechanism that establishes a temporal correspondence between a credential and ciphertext. This mechanism can generate a refreshed ciphertext for any arbitrary time point directly from the initial ciphertext parameters, requiring only partial refreshment of the ciphertext data. This partial-refresh approach significantly reduces the computational overhead of ciphertext refreshing. We also formulate the necessary security requirements for this PKLE scheme—including unforgeability of credentials and refreshed ciphertexts under chosen-time attacks, timeliness security, and semantic security—and elaborate on their interrelationships. A concrete instantiation of this scheme is then constructed over ideal lattices, leveraging the hardness of the ring-small integer solution (R-SIS) and ring-learning with errors (R-LWE) problems. In this construction, the credential is a short preimage vector sampled from a specified dual lattice using the center’s private key and a time-varying parameter. By embedding this parameter into the sampling coset, the credential’s validity is strictly confined to its designated time slot. Concurrently, the ciphertext-refreshing mechanism re-encapsulates the initial ciphertext based on the R-LWE problem. This binds the refreshed ciphertext to the same time-varying parameter, ensuring it can only be decrypted by the corresponding time-bound credential. Finally, we provide security proofs in the standard model, using an R-SIS oracle, demonstrating that our instantiation satisfies all required security properties: unforgeability of credentials and refreshed ciphertexts, timeliness, and semantic security. A complexity and performance analysis confirms that the proposed PKLE scheme eliminates user-side key-storage overhead and simplifies key management by eliminating the need for periodic updates or revocations. Therefore, the proposed scheme is highly suitable for scenarios requiring dynamic access control for sensitive data. Moreover, its support for a partial ciphertext refresh, requiring only a single ring multiplication, significantly reduces the computational cost of ciphertext updates.

     

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