EUF-CMA-Secure Structure-Preserving Signatures on Equivalence Classes

At ASIACRYPT’14 Hanser and Slamanig proposed a new primitive called structure-preserving signa-tures on equivalence classes (SPS-EQ) and used it to construct very efficient attribute-based anonymous credentials. They also presented a candidate construction of an SPS-EQ scheme and claimed that the scheme was existentially unforgeable under adaptive chosen message attacks (EUF-CMA). Fuchsbauer has however recently shown that the construction is insecure under adaptive queries and consequently the security claim is invalid. We fix this issue by providing an EUF-CMA-secure construction of an SPS-EQ, which is also more efficient than the original construction in every respect. We prove our scheme secure in the generic group model for Type-3 bilinear groups.