Logarithmic identity-based ring signature over lattices and linkable variant

The ring signature is extensively utilized in many fields, including e-voting, cryptocurrency, blockchain settings, etc. This paper proposes an effective identity-based ring signature (IBRS) from the lattice assumption by using logarithmic size OR proofs of group action to make the ring signature able to cope with the challenges of quantum attacks. Our construction has been proven anonymous and unforgeable in the random oracle model (ROM) under the hardness of Module Small Integer Solution (MSIS) assumption from lattices, a hot quantum-resistant cryptographic primitive. The anonymity makes it possible for a signer to sign the same message twice or more without being detected by the verifier. This would bring repeated e-voting or double spending of the same money in blockchain. Therefore, as an additional work, we give a linkable variant. Compared with existing IBRS schemes with linear sizes, the size of our scheme is relatively short and achieves logarithmic communication cost with its ring scale $N$. Our research data show that the signature size of our proposal has significant advantages over several existing schemes with an increase of $N$. When the ring scale $N$ is set to be 32 (512, resp.), our scheme has a signature size of 177.13KiB (179.75KiB, resp.), while the previous scheme has a size of at least 154.06KiB (2695.74KiB, resp.).