Signatures from trapdoor commitments with strong openings

In this paper, we propose a new generic construction of signatures from trapdoor commitments with strong openings in the random oracle model. Our construction is very efficient; signatures consist of just a single decommitment of the underlying commitment scheme. Furthermore, assuming the commitment scheme provides sufficiently strong statistical hiding and trapdoor opening properties, the reduction of the security of the signature scheme to the binding property of the commitment scheme is tight. To instantiate our construction, we propose two new commitment schemes with strong openings. Both of these are statistically hiding, and have binding properties based on a Diffie-Hellman inversion problem and factoring, respectively. The signature schemes obtained from these are very efficient; the first matches the performance of BLS signatures, which currently pro­vides the shortest signatures, and the second provides signatures which is one bit shorter than the shortest version of Rabin-Williams signatures while still being tightly related to factoring.