Leopard: Sublinear Verifier Inner Product Argument Under Discrete Logarithm Assumption

Sungwook Kim, Gwangwoon Lee, Hyeonbum Lee, Jae Hong Seo

Abstract: An inner product (IP) argument is a proof system that convinces the verifier of an IP relation between committed integer vectors. IP arguments are crucial building blocks for range proof and zero knowledge arguments, which can be applied to verifiable computation, confidential transactions, decentralized identification, and so on. This paper proposes a novel efficient IP argument with a trustless setup. For integer vectors of size $N$ , the proposed IP argument provides a proof size of $O(\log _{2}{N})$ , a verification cost of $O(\sqrt {N})$ , and a size of public parameter size of $O(\sqrt {N})$ . The construction relies solely on the discrete logarithm (DL) assumption, a well-established standard cryptographic assumption. Consequently, we obtain the first DL-based IP argument with a trustless setup that achieves a sublinear verifier and logarithmic proof size, which we call Leopard. Furthermore, We empirically evaluate the performance of Leopard. The experimental results demonstrate that Leopard is highly efficient and scalable compared to previous works.