Leakage-resilient lattice-based partially blind signatures

Abstract

Blind signature schemes (BSS) play a pivotal role in privacy-oriented cryptography. However, with BSS, the signed message remains unintelligible to the signer, giving them no guarantee that the blinded message he signed actually contained valid information. Partially BSS (PBSS) were introduced to address precisely this problem. In this study, the authors present the first leakage-resilient, lattice-based PBSS in the literature. The proposed construction is provably secure in the random oracle model and offers quasi-linear complexity w.r.t. key/signature sizes and signing speed. In addition, it offers statistical partial blindness and its unforgeability is based on the computational hardness of worst-case ideal lattice problems for approximation factors in O˜(n4) in dimension n. The proposed scheme benefits from the subexponential hardness of ideal lattice problems and remains secure even if a (1−o(1)) fraction of the signer's secret key leaks to an adversary via arbitrary side-channels. Several extensions of the security model, such as honest-user unforgeability and selective failure blindness, are also considered and concrete parameters for instantiation are proposed.