DualRing-PRF: Post-quantum (Linkable) Ring Signatures from Legendre and Power Residue PRFs

Ring signatures allow a signer to anonymously sign a message on behalf of a spontaneously formed group. It not only ensures the authenticity of the message but also conceals the true signer within the group. An important extension of ring signatures is linkable ring signatures, which prevent a signer from signing twice without being detected (under some constraints). Linkable ring signatures offer advantages in applications where full anonymity might jeopardize the intended purpose, such as privacy-oriented cryptocurrencies like Monero. In this work, we introduce post-quantum ring signature (DualRing-PRF) and linkable ring signature ( \(DualRing_{L}\) -PRF) schemes whose security solely rely on symmetric-key primitives (namely, Legendre PRF and power residue PRF). Our construction of the ring signature departs from previous approaches with similar security assumptions, offering the most competitive signature sizes for small and medium-sized rings.