Leakage-Resilient Lattice-Based Partially Blind Signatures

Abstract

Blind signature schemes (BSS) play a pivotal role in privacy-oriented cryptography. However, with blind signature schemes, the signed message remains unintelligible to the signer, giving them no guarantee that the blinded message he signed actually contained valid information. Partially-blind signature schemes (PBSS) were introduced to address precisely this problem. In this paper we present the first leakage-resilient, lattice-based partially-blind signature scheme in the literature. Our construction is provably secure in the random oracle model (ROM) and offers quasilinear 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 $˜ O(n^4)$ in dimension $n$. Our 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