Practical Signatures from Standard Assumptions

We put forward new techniques for designing signature schemes. As a result, we present practical signature schemes based on the CDH, the RSA, and the SIS assumptions. Our schemes compare favorably with existing schemes based on these assumptions. Our core idea is the use of tag-based signatures. Concretely, each signatures contains a tag which is uniformly chosen from a suitable tag set. Intuitively, the tag provides a way to embed instances of computational problems. Indeed, carefully choosing these tag spaces provides new ways to partition the set of possible message-tag pairs into "signable" and "unsignable" pairs. In our security proof, we will thus be able to sign all adversarially requested messages, and at the same time use an adversarially generated forgery with suitably large probability.