Revisiting CK17 Linearly Homomorphic Ring Signature based on SIS

In SCIS 2017, Choi and Kim introduced the new linearly homomorphic ring signature scheme (CK17 scheme) based on the hardness of SIS problem, which overcomes the limitation of Boneh and Freeman’s scheme to implement homomorphic signatures to the real world scenario under multiple signers setting for a message. They replace the original sampling algorithm SamplePre() by Gentry et al. with Wang and Sun’s sampling algorithm GenSamplePre() to achieve the multiple-signer functionality but their work is lack of the rigorous security proof. Thus, this paper revisits the CK17 scheme and makes an advanced definition which is subring-identical linearly homomorphic signature, and suggests a security requirements on it. Then, we show the correctness and subring-identical linear homomorphism of the proposed scheme.