An identity-based strongly unforgeable signature without random oracles from bilinear pairings

Abstract

This paper proposes an identity-based (ID-based) signature (IBS) scheme which is strongly unforgeable in the standard model whose security is reduced to the hardness of the computational Diffie-Hellman (CDH) problem in bilinear groups. Currently, the ID-based encryption scheme (IBE) due to Waters is known to be the most practically efficient IBE whose security is guaranteed in the standard model depending on the decisional bilinear Diffie-Hellman (BDH) assumption. While as a solution for an ID-based signature of a total ID-based public key cryptosystem cooperating with Waters IBE, we share Waters’s construction and system parameters to keep a key pair corresponding to each identity unchanged, our IBS needs only one group element for signing of messages and two elements for its randomness as supplementary parameters plus the original system parameters. Accordingly, thanks to requiring about half the system parameters against previous ID-based signatures proved secure without using random oracles under the standard complexity assumptions like CDH or BDH, our IBS is the more suitable for storage and communication requirements. In particular, this covers a stronger security property called strong unforgeability in the standard model in itself without applying any transformation technique.