Efficient Blind Signatures and Threshold Signatures from Pairing-Free Groups and Lattices

Abstract

Blind signatures and threshold signatures are two fundamental cryptographic primitives that have attracted significant real-world interest, largely due to the development of practically efficient schemes. This thesis focuses on designing efficient constructions in pairing-free groups and lattices, along with rigorous security analyses. Pairing-free constructions are attractive because of their compact key/signature sizes and well-established library support, while lattice-based constructions are of particular interest as they are conjectured to remain secure against quantum adversaries. The thesis makes progress in the following three directions: - Pairing-free blind signatures: The thesis proposes the most efficient pairing-free construction that is provably secure in the concurrent setting, under the discrete logarithm (DL) assumption in the algebraic group model (AGM) and the random oracle model (ROM). - Pairing-free threshold signatures: This thesis introduces a new syntax and security hierarchy for analyzing FROST, the state-of-the-art pairing-free threshold signature scheme. It provides the first security proof of FROST in the ROM under the one-more discrete logarithm (OMDL) assumption, and further proposes variants of FROST that is provably secure under the standard DL assumption. Those are the first partially non-interactive constructions based on the DL assumption. - Lattice-based threshold signatures: This thesis develops new techniques that establish the provable security of one of the state-of-the-art two-round lattice-based threshold signature schemes under standard lattice assumptions, in contrast to prior work which relied on a new non-standard assumption. These techniques also yield a new security analysis for another state-of-the-art two-round scheme with a simpler setup, significantly improving its efficiency.