More Efficient (Almost) Tightly Secure Structure-Preserving Signatures.

We provide a structure-preserving signature (SPS) scheme with an (almost) tight security reduction to a standard assumption. Compared to the state-of-the-art tightly secure SPS scheme of Abe et al. (CRYPTO 2017), our scheme has smaller signatures and public keys (of about 56%, resp. 40% of the size of signatures and public keys in Abe et al.'s scheme), and a lower security loss (of O(logQ) instead of O(lambda), where lambda is the security parameter, and Q = poly(lambda) is the number of adversarial signature queries). While our scheme is still less compact than structure-preserving signature schemes without tight security reduction, it significantly lowers the price to pay for a tight security reduction. In fact, when accounting for a non-tight security reduction with larger key (i.e., group) sizes, the computational efficiency of our scheme becomes at least comparable to that of non-tightly secure SPS schemes. Technically, we combine and refine recent existing works on tightly secure encryption and SPS schemes. Our technical novelties include a modular treatment (that develops an SPS scheme out of a basic message authentication code), and a refined hybrid argument that enables a lower security loss of O(logQ) (instead of O(lambda)).