An Optimized Inner Product Argument with More Application Scenarios

The inner product argument is an effective tool to reduce communication complexity in many cryptographic protocols. Bootle et al. (EUROCRYPT’16) presented an inner product argument with a statement including two vector commitments to two vectors and the inner product of the two vectors equals to a public scalar. Bunz et al. (S&P’18) then presented an inner product argument with a statement including only one vector commitment to two vectors. In this paper, we first summarize the scenarios to use inner product arguments based on Bootle et al. and Bunz et al. Then we propose and implement an improved inner product argument for the same statement as Bootle et al. Our argument has a lower communication complexity of \(4\log _2n\) which improves by about 30% when \(n=8192\). Moreover, as most existing inner product argument protocols have a recursive structure, we find the most appropriate recursive round that decides a better communication complexity.