  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.
