基于 Camenisch-Lysyanskaya 签名的同步聚合签名方案的改进安全性证明
Improved Security Proof for the Camenisch-Lysyanskaya Signature-Based Synchronized Aggregate Signature Scheme
AI总结：
本文重新审视了 FC 2013 中基于 Camenisch-Lysyanskaya 签名的同步聚合签名方案，在随机预言机模型下以极小效率损失给出了基于 1-MSDH-2 静态假设的新安全性证明，避免了原有交互式和动态 q-type 假设的缺陷。
摘要：
CRYPTO 2004 提出的 Camenisch-Lysyanskaya 签名方案是构建隐私保护方案（如匿名凭证、群签名或环签名）的有用构建块。然而，该签名方案的安全性依赖于称为 LRSW 假设的交互式假设。即使交互式假设在通用群模型或双线性群模型中得到证明，密码学界对这些假设的担忧依然存在。这一事实给使用安全性依赖于这些假设的密码方案造成了障碍。最近，Pointcheval 和 Sanders 在 CT-RSA 2018 中提出了修改的 Camenisch-Lysyanskaya 签名方案。该方案在称为 Modified-q-Strong Diffie-Hellman-2 (q-MSDH-2) 假设的新 q-type 假设下满足 EUF-CMA 安全性。然而，q-type 假设的规模动态增长，这一事实导致了方案的低效。在本工作中，我们重新审视了 FC 2013 中基于 Camenisch-Lysyanskaya 签名的同步聚合签名方案。该方案是使用双线性群的最有效的同步聚合签名方案之一。然而，该同步聚合方案的安全性是在随机预言机模型下的 one-time LRSW 假设下证明的。我们在随机预言机模型中，以极小的效率损失，在 1-MSDH-2（静态）假设下给出了该同步聚合方案的新的安全性证明。
英文摘要：
The Camenisch-Lysyanskaya signature scheme in CRYPTO 2004 is a useful building block to construct privacy-preserving schemes such as anonymous credentials, group signatures or ring signatures. However, the security of this signature scheme relies on the interactive assumption called the LRSW assumption. Even if the interactive assumptions are proven in the generic group model or bilinear group model, the concerns about these assumptions arise in a cryptographic community. This fact caused a barrier to the use of cryptographic schemes whose security relies on these assumptions. Recently, Pointcheval and Sanders proposed the modified Camenisch-Lysyanskaya signature scheme in CT-RSA 2018. This scheme satisfies the EUF-CMA security under the new q-type assumption called the Modified-q-Strong Diffie-Hellman-2 (q-MSDH-2) assumption. However, the size of a q- type assumptions grows dynamically and this fact leads to inefficiency of schemes. In this work, we revisit the Camenisch-Lysyanskaya signature-based synchronized aggregate signature scheme in FC 2013. This scheme is one of the most efficient synchronized aggregate signature schemes with bilinear groups. However, the security of this synchronized aggregate scheme was proven under the one-time LRSW assumption in the random oracle model. We give the new security proof for this synchronized aggregate scheme under the 1-MSDH-2 (static) assumption in the random oracle model with little loss of efficiency.
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