Improved lattice-based ring signature schemes from basis delegation

Ring signature enables the members to sign anonymously without a manager, it has many online applications, such as e-voting, e-money, whistle blowing etc. As a promising post-quantum candidate, lattice-based cryptography attracts much attention recently. Several efficient lattice-based ring signatures have been naturally constructed from lattice basis delegation, but all of them have large verification key sizes. Our observation finds that a new concept called the split- small integer solution （SIS） problem introduced by Nguyen et al. at PKC＇I 5 is excellent in reducing the public key sizes of lattice-based ring signature schemes from basis delegation. In this research, we first define an extended concept called the extended split-SIS problem, and then prove that the hardness of the extended problem is as hard as the approximating shortest independent vectors problem （SIVP） problem within certain polynomial factor. Moreover, we present an improved ring signature and prove that it is anonymous and unforgeable against the insider corruption. Finally, we give two other improved existing ring signature schemes from lattices. In the end, we show the comparison with the original scheme in terms of the verification key sizes. Our research data illustrate that the public key sizes of the proposed schemes are reduced significantly.