Abstract
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. Bünz 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 Bünz 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.
Z. Zhang, Z. Zhou and W. Li contributed equally.
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Notes
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We refer to the bulletproof library at https://github.com/ZenGo-X/bulletproofs.
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Acknowledgment
This work is partly supported by the National Natural Science Foundation of China (61972017), the National Cryptography Development Fund (MMJJ20180215), and the Fundamental Research Funds for the Central Universities (YWF-21-BJ-J-1040).
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Zhang, Z., Zhou, Z., Li, W., Tao, H. (2021). An Optimized Inner Product Argument with More Application Scenarios. In: Gao, D., Li, Q., Guan, X., Liao, X. (eds) Information and Communications Security. ICICS 2021. Lecture Notes in Computer Science(), vol 12919. Springer, Cham. https://doi.org/10.1007/978-3-030-88052-1_20
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