A pairing-based blind signature scheme with message recovery

Blind signatures enable users to obtain valid signatures for a message without revealing its content to the signer. This paper presents a new blind signature scheme, i.e. identity-based blind sig- nature scheme with message recovery. Due to the message recovery property, the new scheme requires less bandwidth than the identity- based blind signatures with similar constructions. The scheme is based on modified Weil/Tate pairings over elliptic curves, and thus requires smaller key sizes for the same level of security compared to previous approaches not utilizing bilinear pairings. Security and efficiency analysis for the scheme is provided in this paper. but cannot be used as the RSA signature scheme for encryption by inter-changing the roles of the private and public transfor- mations. The advantages are obvious: applications without a hash function are possible, smaller bandwidth for signatures of small messages, and direct use in other schemes such as identity-based public key systems or key agreement protocols. Thanks to their motivations, it is interesting to construct an identity-based blind signature scheme with message recovery. The bilinear pairings (6), especially modified Weil/Tate pairings have been a useful tool for cryptographic protocols since Joux's work (18). Due to the desirable use of the bilinear pairings in public key cryptography, identity based cryptography has been re-investigated since Shamir proposed the first identity-based cryptosystem (25). Recently, some identity-based schemes based on pairings have been proposed. Interesting examples include Boneh and Franklin's id-based encryption from the Weil pairing (6), Hess's id-based signa- tures based on pairings (16), Han et al's committal deniable signatures (14) and undeniable signatures (15), Libert and Quisquater's undeniable signatures based on pairings (21), and Verhel's self-blindable credential certificates from pairings

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