Certificateless and certificate‐based signatures from lattices

Certificateless signature and certificate‐based signature are two attractive replacements of regular signature and identity‐based signature because they can alleviate the vexing certificate management problem in regular signatures and can also eliminate the inherent key escrow problem in identity‐based signatures. Although a number of certificateless signatures and certificate‐based signatures from bilinear pairings have been proposed, their lattice‐based counterparts still remain unrealized. In this paper, we present the first constructions of certificateless signature and certificate‐based signature from lattices. Both constructions are proven to be secure in the random oracle model under conventional small integer solution assumption that is as hard as approximating several standard lattice problems.