Improvement of a fuzzy identity-based lattice signature scheme

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.