Abstract: Certificateless aggregate signature scheme with universal designated verifier (CTL-ASWUDV) can effectively solve the problem of protecting the privacy of the signer.An improved CTL-ASWUDV scheme (CTL-ASWUDV-1) was proposed according to the problems existing in Zhang et al.’s CTL-ASWUDV scheme on the invalid construction and two types of adversary attacks.The improved scheme not only keeps the advantages of constant aggregate signature length and constant bilinear pairing operation number,but also overcomes the attacks from two types of adversaries.This paper further proposed a highly efficient CTL-ASWUDV scheme (CTL-ASWUDV-2).In the random oracle mo-del,the security of the second improved scheme can be reduced to computational Diffie-Hellman problem.At the same time,compared with the existing similar schemes,the proposed second scheme has the following advantages.It has no bilinear pairing operation in both single signature and aggregate signature,and the number of bilinear pairing operation needed by the aggregate signature verification is independent on the number of signers and it is equivalent to the number of a single signature verification,i.e.one pairing operation.The length of an aggregate signature and the length of a desi-gnated verifier signature are both independent on the number of signers and they are equivalent to the length of a single signature verification,i.e.one element,which largely saves the network bandwidth.

Key words: Network security,Certificateless signature,Aggregate signature,Designated verifier signature,Bilinear pairing