On signatures with tight security in the multi-user setting

In this paper, we construct efficient and practical signature schemes which allows a tight reduction from security in the multi-user setting to standard hardness assumptions. Firstly, we show that, for a general class of signature schemes, which we denote key convertible schemes, it is possible to construct a tight reduction from multi-user security to single-user security. Combined with the well-known BLS signature scheme modified to achieve a tight security reduction in the single-user setting, we obtain a very efficient scheme tightly secure in the multi-user setting based on the computational Diffie-Hellman problem. Secondly, we take a different approach based on signature schemes which rely on rerandomizable hard problems as well as satisfying certain other properties. While we do not provide a formal framework capturing this approach, we show that, based on this, a concrete signature scheme by Katz and Wang can be shown tightly secure in the multi-user setting based on the decisional Diffe-Hellman problem. The security of both schemes is shown in the random oracle model. Compared to the recent scheme tightly secure in the multi-user setting by Bader, our schemes provides substantially shorter signatures, but are secure in the plain multi-user setting, whereas Barder considers an extended model allowing adaptive corruption.