In this paper, we propose multisignature schemes, in which each signer can express her intention associating with the message to be signed, moreover, proposed scheme is efficiency and provable security. Signers' intentions mean a kind of information which can be newly attached to a signature in signers' generating it. However, we have never been introduced any multisignature scheme dealing with signers, intentions without loss of efficiency. First, we consider a multisignature scheme realizing the concept of signers' intentions by utilizing existing models, and name it Primitive model. After that, we introduce our multisignature model with siners' intentions which is more efficient in view of the computational cost for verification and in view of the signature size than primitive model. A multisignature scheme with signers' intentions derived from our model is shown to be provably secure if the multi-round identification schemes with signers' intentions is based, provides soundness and zero-know1edge property.
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