@inproceedings{43a1fdfb03104433a4110d8bf0c13ebc,
title = "Hadamard Product Argument from Lagrange-Based Univariate Polynomials",
abstract = "Hadamard product is a point-wise product for two vectors. This paper presents a new scheme to prove Hadamard-product relation as a sub-protocol for SNARKs based on univariate polynomials. Prover uses linear cryptographic operations to generate the proof containing logarithmic field elements. The verification takes logarithmic cryptographic operations with constant numbers of pairings in bilinear group. The construction of the scheme is based on the Lagrange-based KZG commitments (Kate, Zaverucha, and Goldberg at Asiacrypt 2010) and the folding technique. We construct an inner-product protocol from folding technique on univariate polynomials in Lagrange form, and by carefully choosing the random polynomials suitable for folding technique, we construct a Hadamard-product protocol from the inner-product protocol, giving an alternative to prove linear algebra relations in linear time, and the protocol has a better concrete proof size than previous works.",
keywords = "Hadamard product, SNARKs, interactive oracle proofs",
author = "Jie Xie and Yuncong Hu and Yu Yu",
note = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2024.; 29th Australasian Conference on Information Security and Privacy, ACISP 2024 ; Conference date: 15-07-2024 Through 17-07-2024",
year = "2024",
doi = "10.1007/978-981-97-5025-2\_24",
language = "英语",
isbn = "9789819750245",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Science and Business Media Deutschland GmbH",
pages = "472--492",
editor = "Tianqing Zhu and Yannan Li",
booktitle = "Information Security and Privacy - 29th Australasian Conference, ACISP 2024, Proceedings",
address = "德国",
}