Linear Lossy Identification Scheme derives Tightly-Secure Multisignature

For the multisignature schemes, the tight security in the plain public key model is considered as one of the desirable features. In this paper, we first give a generic construction of multisignature schemes which is tightly secure in the plain public key model. Our construction is based on the ID schemes which have two properties called the lossiness and the linearity. Moreover, we then find that the lossiness of most of the schemes is proven from the linearity. In this sense, we propose a new property of ID schemes and show that the combination of the linearity of ID schemes and the new property implies the lossiness. This result implies the relationship between these properties to shrink the conditions required for our generic construction.