对一个模糊身份格基签名方案的改进

Improvement of a Fuzzy Identity-Based Lattice Signature Scheme

对第一个基于格理论构造的模糊身份签名方案进行了深入分析,指出了它的安全性证明中存在的两个问题:1)对私钥提取查询的应答会导致Hash函数碰撞的产生;2)对于和挑战目标相同比特位数大于门限值的身份的签名查询无法应答.针对这些问题,给出了相应的改进方法,并且利用格上固定维数的格基代理方法,避免了原方案中维数的扩张,给出了一个私钥维数和签名维数更短的模糊身份格基签名方案.最后,给出了新方案的安全性证明.

A fuzzy identity-based signature scheme based on short integer solution problem was designed. in 2013. Two weaknesses about its security proof are illustrated as follows： 1 ） the response to private key extraction queries leads to hash function collision; 2） for identities who have same bits with the target identity, and the number of same bits is larger than the threshold value, the challenger couldn＇ t response to signature queries. The modifications were given to improve the above mentioned items. In addition, the lattice basis delegation with fixed dimension was used. A new fuzzy identity-based lattice signature scheme was obtained with smaller lattice dimension. The security proof of new signature scheme was proposed as well.