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We propose a strongly secure certificateless signature schemesupporting batch verification, which makes it possible for a verifierto verify a set of signatures more efficiently than verifying themone by one. In an identity-based digital signature scheme, private key generator (PKG) knows each user's signing key, so it cangenerate a signature which is indistinguishable from the signaturegenerated by the user. This is a serious problem because theproperty of signature nonrepudiation will not be achieved. In ourproposed scheme, it is impossible for PKG to produce a signaturewhich is indistinguishable from any signature produced by a user. Compared with existing signature schemes with batch verification,although our proposed scheme is not the most efficient one, itachieves Girault's level-3 security, while the others have Girault'slevel-1 or level-2 security only. We also formally prove that the proposedscheme is unforgeable and satisfies Girault's level-3 security basedon hard problems

Strongly Secure Certificateless Signature Scheme Supporting Batch Verification