An Efficient Certificateless Signature Scheme

Abstract

Abstract. Certificateless public key cryptography (CLPKC) is a paradigm to solve the inherent key escrow problem suffered by identity-based cryptography (IBC). While certificateless signature is one of the most important security primitives in CLPKC, there are relatively few proposed schemes in the literature. In this paper, we manage to construct an efficient certificateless signature scheme based on the intractability of the computational Diffie-Hellman problem. By using a shorter public key, two pairing computations can be saved in the verification algorithm. Besides, no pairing computation is needed in the signing algorithm. The proposed scheme is existential unforgeable in the random oracle model. We also present an extended construction whose trust level is the same as that of a traditional signature scheme.

New Efficient Certificateless Signature Scheme

“…And hence, C has successfully obtains the solution of DL problem. Table 1 gives a comparison of computational efforts required for our scheme with that of the signature schemes in [7,9,10,17,21] in the Sign and Verify algorithms. Here we only consider the costly operations which defined below, and we omit the computational effort of the hash operation H(ID) in the Sign algorithm, since it can be computed only once.…”

“…Here we only consider the costly operations which defined below, and we omit the computational effort of the hash operation H(ID) in the Sign algorithm, since it can be computed only once. Schemes Sign Verify Scheme in [7] 2S 3P + 1S + 1H Scheme in [9] 2P + 3S 4P + 1H + 1E Scheme in [10] 2S + 1H 4P + 1S + 2H Scheme in [17] 2S 2P + 1S + 1H Scheme in [21] 3S + 2H 4P + 3H Our Scheme 1S + 2E 1P + 1S + 2E P : Pairing Operation S: Scalar Multiplication in G1 H: MapToPoint Hash E: Exponentiation in G2 Our Sign algorithm requires no pairing operation and two exponentiation operations in G 2 . Our Verify algorithm requires only one pairing operation, much less than it is required in the Verify algorithms of the other schemes [7,9,10,17,21].…”

“…In [18], Yum and Lee presented a generic way to construct certificateless signature schemes, however, Hu et al [8] pointed out that this construction is insecure and presented a new one. Gorantla and Saxena [7], Yap, Heng, and Goi1 [17] also presented some efficient certificateless signature schemes. Unfortunately, their schemes [7,17] are subject to universal forgery, a type I adversary can forger signatures on any message [6,13,19].…”

“…Gorantla and Saxena [7], Yap, Heng, and Goi1 [17] also presented some efficient certificateless signature schemes. Unfortunately, their schemes [7,17] are subject to universal forgery, a type I adversary can forger signatures on any message [6,13,19]. With respect to the efficiency, the previous certificateless signature schemes all involve a relatively large amount of paring computation in the process of verification.…”

“…In this paper, we present a new efficient certificateless pairingbased signature scheme, yielding some advantages over previous constructions [7,9,10,17,21] in computational cost. Our signature scheme requires only one pairing operation in the signing and verification phases, so it is much more efficient than the schemes in [7,9,10,17,21]. The security of our scheme is based on the hardness of q-Strong Diffie-Hellman (q-SDH) Problem and the Discrete Logarithm (DL) Problem.…”