A signature scheme constructed from zero knowledge argument of knowledge for the subgraph isomorphism problem

In this paper, we propose an honest-verifier zero knowledge argument of knowledge for subgraph isomorphism and convert it into a signature scheme by using the well-known Fiat-Shamir transformation. Our protocol generalizes the famous Blum's zero knowledge proof for graph Hamiltonicity, but with a major difference: we additionally commit to the permuted subgraph isomorphism during commitment phase. This modification is made to satisfy a property called quantum computationally unique response, which ensures that an efficient quantum adversary cannot distinguish whether the superposition of the response is measured. This property is utilized to prove that the resulting signature scheme achieves EUF-CMA security in the quantum random oracle model.