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.

翻译：Camenisch-Lysyanskaya签名方案（CRYPTO 2004）是构建匿名凭证、群签名或环签名等隐私保护方案的重要基础模块。然而，该签名方案的安全性依赖于被称为LRSW假设的交互式假设。尽管交互式假设已在通用群模型或双线性群模型中得到证明，但密码学界对此类假设仍存有疑虑。这一事实阻碍了依赖此类假设的密码方案的实际应用。近期，Pointcheval与Sanders在CT-RSA 2018中提出了改进的Camenisch-Lysyanskaya签名方案。该方案在新的q型假设——改进q强Diffie-Hellman-2（q-MSDH-2）假设——下满足EUF-CMA安全性。然而，q型假设的规模会动态增长，这导致方案效率降低。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——该方案是双线性群中最高效的同步聚合签名方案之一。但该同步聚合方案的安全性先前仅在随机预言机模型下基于一次LRSW假设得到证明。我们给出了该同步聚合方案在随机预言机模型下基于1-MSDH-2（静态）假设的新安全性证明，且效率损失极小。