In this work we present a new interactive Zero-Knowledge Argument of knowledge for general arithmetic circuits. Our protocol is based on the “MPC-in-the-head”-paradigm of Ishai et al. (STOC 2009) and follows the recent “MPC-in-the-head with Preprocessing” as proposed by Katz, Kolesnikov and Wang (ACM CCS 2018). However, in contrast to Katz et al. who used the “cut-and-choose” approach for pre-processing, we show how to incorporate the well-known “sacrificing” paradigm into “MPC-in-the-head”, which reduces the proof size when working over arithmetic circuits. Our argument system uses only lightweight symmetric-key primitives and utilizes a simplified version of the so-called SPDZ-protocol. Based on specific properties of our protocol we then show how it can be used to construct an efficient Zero-Knowledge Argument of Knowledge for instances of the Short Integer Solution (SIS) problem. We present different protocols that are tailored to specific uses of SIS, while utilizing the advantages of our scheme. In particular, we present a variant of our argument system that allows the parties to sample the circuit “on the fly”, which may be of independent interest. We furthermore implemented our Zero-Knowledge argument for SIS and show that using our protocols it is possible to run a complete interactive proof, even for general SIS instances which result in a circuit with gates, in less than 0.5 s.
|Title of host publication||Public-Key Cryptography – PKC 2020 - 23rd IACR International Conference on Practice and Theory of Public-Key Cryptography, Proceedings|
|Editors||Aggelos Kiayias, Markulf Kohlweiss, Petros Wallden, Vassilis Zikas|
|Number of pages||32|
|State||Published - 2020|
|Event||23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography, PKC 2020 - Edinburgh, United Kingdom|
Duration: 4 May 2020 → 7 May 2020
|Name||Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)|
|Conference||23rd IACR International Conference on the Practice and Theory of Public-Key Cryptography, PKC 2020|
|Period||4/05/20 → 7/05/20|
Bibliographical noteFunding Information:
Thanks and Acknowledgements. The authors want to thank Roey Sefi and Assi Barak for their help with the implementation as well as Carmit Hazay, Yehuda Lindell and Avishay Yanai as well as the anonymous reviewers for their helpful comments. The work of both authors was mainly done at Bar Ilan University. Both authors acknowledge support by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office. The work of Carsten was additionally funded by the European Research Council (ERC) under the European Unions’ Horizon 2020 research and innovation programme under grant agreement No 669255 (MPCPRO).
© 2020, International Association for Cryptologic Research.