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：2004年CRYPTO CARYPTO的Camenisch-Lysyanskaya 签名计划是构建匿名证书、团体签名或环形签名等隐私保护计划的一个有用基石,然而,这一签名计划的安全性依赖于称为LRSW假设的互动式假设。即使互动假设在通用群体模型或双线群体模型中得到了证明,对于这些假设的关切也出现在加密社区中。这一事实阻碍了使用基于这些假设的安全性加密计划。最近,Pointcheval和Sanders在CT-RSA 2018中提出了修改过的Camenisch-Lysyanskaya签名同步签名计划。这个计划满足了新的q类假设下的EUF-CMA安全性,称为LSW假设。即使这些互动假设在通用群体模型或双线组模型中得到了证明,对于q类型假设的规模越来越大,这一事实导致计划的效率。在FC 2013年,C-RS-RS-LS签名基于同步的签名计划中,这个计划与SHSW最高效的总体总体安全性计划一起被证明。</s>