Efficient and short certificateless signatures secure against realistic adversaries

The notion of certificateless cryptography is aimed to eliminate the use of certificates in traditional public key cryptography and also to solve the key-escrow problem in identity-based cryptography. Many kinds of security models have been designed for certificateless cryptography and many new schemes have been introduced based on the correspondence of the security models. In generally speaking, a stronger security model can ensure a certificateless cryptosystem with a higher security level, but a realistic model can lead to a more efficient scheme. In this paper, we focus on the efficiency of a certificateless signature (CLS) scheme and introduce an efficient CLS scheme with short signature size. On one hand, the security of the scheme is based on a realistic model. In this model, an adversary is not allowed to get any valid signature under false public keys. On the other hand, our scheme is as efficient as BLS short signature scheme in both communication and computation and, therefore, turns out to be more efficient than other CLS schemes proposed so far. We provide a rigorous security proof of our scheme in the random oracle model. The security of our scheme is based on the k-CAA hard problem and a new discovered hard problem, namely the modified k-CAA problem. Our scheme can be applied to systems where signatures are typed in by human or systems with low-bandwidth channels and/or low-computation power.