### More Efficient Shuffle Argument from Unique Factorization

Toomas Krips and Helger Lipmaa

##### Abstract

Efficient shuffle arguments are essential in mixnet-based e-voting solutions. Terelius and Wikström (TW) proposed a 5-round shuffle argument based on unique factorization in polynomial rings. Their argument is available as the Verificatum software solution for real-world developers, and has been used in real-world elections. It is also the fastest non-patented shuffle argument. We will use the same basic idea as TW but significantly optimize their approach. We generalize the TW characterization of permutation matrices; this enables us to reduce the communication without adding too much to the computation. We make the TW shuffle argument computationally more efficient by using Groth's coefficient-product argument (JOC, 2010). Additionally, we use batching techniques. The resulting shuffle argument is the fastest known $\leq 5$-message shuffle argument, and, depending on the implementation, can be faster than Groth's argument (the fastest 7-message shuffle argument).

Available format(s)
Category
Cryptographic protocols
Publication info
Published elsewhere. CT-RSA 2021
Keywords
Mix-netshuffle argumentunique factorization
Contact author(s)
helger lipmaa @ gmail com
History
Short URL
https://ia.cr/2021/438

CC BY

BibTeX

@misc{cryptoeprint:2021/438,
author = {Toomas Krips and Helger Lipmaa},
title = {More Efficient Shuffle Argument from Unique Factorization},
howpublished = {Cryptology ePrint Archive, Paper 2021/438},
year = {2021},
note = {\url{https://eprint.iacr.org/2021/438}},
url = {https://eprint.iacr.org/2021/438}
}

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