In this paper, we propose a multi-signature scheme, in which each signer can express her intention associating with the message to be signed. Signers' intentions mean a kind of information which can be newly attached to a signature in signers' generating it. However, we have been introduced no multi-signature scheme dealing with intentions without loss of its efficiency. First, we consider a multi-signature scheme realizing the concept of signers' intentions by utilizing existing schemes, and name it primitive method. After that, we introduce the proposed multi-signature scheme which is more efficient than the primitive method in view of the computational cost for verification and in view of the signature size. The proposed multi-signature scheme is shown to be secure even against adaptive chosen message insider attacks.
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