ABSTRACT
In this paper, we propose memory- and round-efficient protocols for securely evaluating arithmetic primitives. We focus on secure two-party computation over the ring ℤ2k that achieves security against semi-honest adversaries and works in the pre-processing model. Our protocols rely on the unit vectorization technique introduced by Boyle et al. (TCC 2019). The unit vectorization technique provides online-optimal protocols for several fundamental operations in the pre-processing model. However, a relatively large memory cost for correlated randomness is required, which might become an obstacle in a large-scale application. In order to achieve both memory and communication efficiency, we propose a size reduction method that uses unit vectorization only for short-length inputs, and based on this, construct two-round protocols for equality test, detecting the most significant non-zero bit, detecting wrap-around, and less-than comparison. In addition, as applications of these results, we provide practically efficient protocols for integer division, integer square root, integer logarithm, and modular exponentiation.
- Mehrdad Aliasgari, Marina Blanton, Yihua Zhang, and Aaron Steele. 2013. Secure Computation on Floating Point Numbers. In NDSS 2013. The Internet Society.Google Scholar
- Abdelrahaman Aly, Aysajan Abidin, and Svetla Nikova. 2018. Practically Efficient Secure Distributed Exponentiation Without Bit-Decomposition. In FC 2018 (LNCS, Vol. 10957),, Sarah Meiklejohn and Kazue Sako (Eds.). Springer, Heidelberg, 291--309. https://doi.org/10.1007/978-3-662-58387-6_16Google ScholarDigital Library
- Abdelrahaman Aly and Nigel P. Smart. 2019. Benchmarking Privacy Preserving Scientific Operations. In ACNS 19 (LNCS, Vol. 11464),, Robert H. Deng, Valérie Gauthier-Uma na, Martín Ochoa, and Moti Yung (Eds.). Springer, Heidelberg, 509--529. https://doi.org/10.1007/978-3-030-21568-2_25Google ScholarDigital Library
- Toshinori Araki, Jun Furukawa, Yehuda Lindell, Ariel Nof, and Kazuma Ohara. 2016. High-Throughput Semi-Honest Secure Three-Party Computation with an Honest Majority. In ACM CCS 2016, Edgar R. Weippl, Stefan Katzenbeisser, Christopher Kruegel, Andrew C. Myers, and Shai Halevi (Eds.). ACM Press, 805--817. https://doi.org/10.1145/2976749.2978331Google ScholarDigital Library
- David W. Archer, Dan Bogdanov, Yehuda Lindell, Liina Kamm, Kurt Nielsen, Jakob Illeborg Pagter, Nigel P. Smart, and Rebecca N. Wright. 2018. From Keys to Databases - Real-World Applications of Secure Multi-Party Computation. Comput. J., Vol. 61 (2018), 1749--1771.Google Scholar
- Nuttapong Attrapadung, Goichiro Hanaoaka, Takahiro Matsuda, Hiraku Morita, Kazuma Ohara, Jacob C. N. Schuldt, Tadanori Teruya, and Kazunari Tozawa. 2021. Oblivious Linear Group Actions and Applications. In ACM CCS 2021,, Yongdae Kim, Jong Kim, Giovanni Vigna, and Elaine Shi (Eds.). ACM Press, 630--650. https://doi.org/10.1145/3460120.3484584Google ScholarDigital Library
- Donald Beaver. 1992. Efficient Multiparty Protocols Using Circuit Randomization. In CRYPTO'91 (LNCS, Vol. 576),, Joan Feigenbaum (Ed.). Springer, Heidelberg, 420--432. https://doi.org/10.1007/3-540-46766-1_34Google Scholar
- Dan Bogdanov, Liina Kamm, Baldur Kubo, Reimo Rebane, Ville Sokk, and Riivo Talviste. 2016. Students and Taxes: a Privacy-Preserving Study Using Secure Computation. Proc. Priv. Enhancing Technol., Vol. 2016, 3 (2016), 117--135. https://doi.org/10.1515/popets-2016-0019Google ScholarCross Ref
- Dan Bogdanov, Margus Niitsoo, Tomas Toft, and Jan Willemson. 2012. High-Performance Secure Multi-Party Computation for Data Mining Applications. Int. J. Inf. Secur., Vol. 11 (2012), 403--418. https://doi.org/10.1007/s10207-012-0177--2Google ScholarCross Ref
- Elette Boyle, Nishanth Chandran, Niv Gilboa, Divya Gupta, Yuval Ishai, Nishant Kumar, and Mayank Rathee. 2021. Function Secret Sharing for Mixed-Mode and Fixed-Point Secure Computation. In EUROCRYPT 2021, Part II (LNCS, Vol. 12697),, Anne Canteaut and Franccois-Xavier Standaert (Eds.). Springer, Heidelberg, 871--900. https://doi.org/10.1007/978-3-030-77886-6_30Google ScholarDigital Library
- Elette Boyle, Niv Gilboa, and Yuval Ishai. 2016. Function Secret Sharing: Improvements and Extensions. In ACM CCS 2016,, Edgar R. Weippl, Stefan Katzenbeisser, Christopher Kruegel, Andrew C. Myers, and Shai Halevi (Eds.). ACM Press, 1292--1303. https://doi.org/10.1145/2976749.2978429Google ScholarDigital Library
- Elette Boyle, Niv Gilboa, and Yuval Ishai. 2019. Secure Computation with Preprocessing via Function Secret Sharing. In TCC 2019, Part I (LNCS, Vol. 11891),, Dennis Hofheinz and Alon Rosen (Eds.). Springer, Heidelberg, 341--371. https://doi.org/10.1007/978-3-030-36030-6_14Google ScholarDigital Library
- Ran Canetti. 2000. Universally Composable Security: A New Paradigm for Cryptographic Protocols. Cryptology ePrint Archive, Report 2000/067. https://eprint.iacr.org/2000/067.Google Scholar
- Geoffroy Couteau. 2018. New Protocols for Secure Equality Test and Comparison. In ACNS 18 (LNCS, Vol. 10892),, Bart Preneel and Frederik Vercauteren (Eds.). Springer, Heidelberg, 303--320. https://doi.org/10.1007/978-3-319-93387-0_16Google ScholarDigital Library
- Ronald Cramer, Ivan Damgr ard, Daniel Escudero, Peter Scholl, and Chaoping Xing. 2018. SPD ℤ2k: Efficient MPC mod 2kfor Dishonest Majority. In CRYPTO 2018, Part II (LNCS, Vol. 10992),, Hovav Shacham and Alexandra Boldyreva (Eds.). Springer, Heidelberg, 769--798. https://doi.org/10.1007/978-3-319-96881-0_26Google ScholarDigital Library
- Ivan Damgr ard, Daniel Escudero, Tore Kasper Frederiksen, Marcel Keller, Peter Scholl, and Nikolaj Volgushev. 2019. New Primitives for Actively-Secure MPC over Rings with Applications to Private Machine Learning. In 2019 IEEE Symposium on Security and Privacy. IEEE Computer Society Press, 1102--1120. https://doi.org/10.1109/SP.2019.00078Google Scholar
- Ivan Damgård, Matthias Fitzi, Eike Kiltz, Jesper Buus Nielsen, and Tomas Toft. 2006. Unconditionally Secure Constant-Rounds Multi-party Computation for Equality, Comparison, Bits and Exponentiation. In TCC 2006 (LNCS, Vol. 3876), Shai Halevi and Tal Rabin (Eds.). Springer, Heidelberg, 285--304. https://doi.org/10.1007/11681878_15Google ScholarDigital Library
- Daniel Escudero, Satrajit Ghosh, Marcel Keller, Rahul Rachuri, and Peter Scholl. 2020. Improved Primitives for MPC over Mixed Arithmetic-Binary Circuits. In CRYPTO 2020, Part II (LNCS, Vol. 12171),, Daniele Micciancio and Thomas Ristenpart (Eds.). Springer, Heidelberg, 823--852. https://doi.org/10.1007/978-3-030-56880-1_29Google ScholarDigital Library
- Keitaro Hiwatashi, Satsuya Ohata, and Koji Nuida. 2020. An Efficient Secure Division Protocol Using Approximate Multi-bit Product and New Constant-Round Building Blocks. In ACNS 20, Part I (LNCS, Vol. 12146), Mauro Conti, Jianying Zhou, Emiliano Casalicchio, and Angelo Spognardi (Eds.). Springer, Heidelberg, 357--376. https://doi.org/10.1007/978-3-030-57808-4_18Google ScholarDigital Library
- Yuval Ishai, Eyal Kushilevitz, Sigurd Meldgaard, Claudio Orlandi, and Anat Paskin-Cherniavsky. 2013. On the Power of Correlated Randomness in Secure Computation. In TCC 2013 (LNCS, Vol. 7785),, Amit Sahai (Ed.). Springer, Heidelberg, 600--620. https://doi.org/10.1007/978-3-642-36594-2_34Google ScholarDigital Library
- Ryo Kikuchi, Dai Ikarashi, Takahiro Matsuda, Koki Hamada, and Koji Chida. 2018. Efficient Bit-Decomposition and Modulus-Conversion Protocols with an Honest Majority. In ACISP 18 (LNCS, Vol. 10946),, Willy Susilo and Guomin Yang (Eds.). Springer, Heidelberg, 64--82. https://doi.org/10.1007/978-3-319-93638-3_5Google Scholar
- Eyal Kushilevitz, Yehuda Lindell, and Tal Rabin. 2006. Information-theoretically secure protocols and security under composition. In 38th ACM STOC,, Jon M. Kleinberg (Ed.). ACM Press, 109--118. https://doi.org/10.1145/1132516.1132532Google ScholarDigital Library
- Serge Lang. 2005. Algebra. Springer New York. 01054916Google Scholar
- Manuel Liedel. 2012. Secure Distributed Computation of the Square Root and Applications. In Information Security Practice and Experience (LNCS, Vol. 7232), Mark D. Ryan, Ben Smyth, and Guilin Wang (Eds.). Springer, Heidelberg, 277--288. https://doi.org/10.1007/978-3-642-29101-2_19Google ScholarDigital Library
- Helger Lipmaa and Tomas Toft. 2013. Secure Equality and Greater-Than Tests with Sublinear Online Complexity. In ICALP 2013, Part II (LNCS, Vol. 7966),, Fedor V. Fomin, Rusins Freivalds, Marta Z. Kwiatkowska, and David Peleg (Eds.). Springer, Heidelberg, 645--656. https://doi.org/10.1007/978-3-642-39212-2_56Google ScholarDigital Library
- Eleftheria Makri, Dragos Rotaru, Frederik Vercauteren, and Sameer Wagh. 2021. Rabbit: Efficient Comparison for Secure Multi-Party Computation. In FC 2021 (LNCS, Vol. 12674),, Nikita Borisov and Claudia Díaz (Eds.). Springer, Heidelberg, 249--270. https://doi.org/10.1007/978-3-662-64322-8_12Google ScholarDigital Library
- Payman Mohassel and Yupeng Zhang. 2017. SecureML: A System for Scalable Privacy-Preserving Machine Learning. In 2017 IEEE Symposium on Security and Privacy. IEEE Computer Society Press, 19--38. https://doi.org/10.1109/SP.2017.12Google Scholar
- Hiraku Morita, Nuttapong Attrapadung, Satsuya Ohata, Koji Nuida, Shota Yamada, Kana Shimizu, Goichiro Hanaoka, and Kiyoshi Asai. 2018. Secure Division Protocol and Applications to Privacy-preserving Chi-squared Tests. In 2018 International Symposium on Information Theory and Its Applications (ISITA). 530--534. https://doi.org/10.23919/ISITA.2018.8664337Google ScholarDigital Library
- Chao Ning and Qiuliang Xu. 2011. Constant-Rounds, Linear Multi-party Computation for Exponentiation and Modulo Reduction with Perfect Security. In ASIACRYPT 2011 (LNCS, Vol. 7073), Dong Hoon Lee and Xiaoyun Wang (Eds.). Springer, Heidelberg, 572--589. https://doi.org/10.1007/978-3-642-25385-0_31Google ScholarDigital Library
- Satsuya Ohata and Koji Nuida. 2020. Communication-Efficient (Client-Aided) Secure Two-Party Protocols and Its Application. In FC 2020 (LNCS, Vol. 12059),, Joseph Bonneau and Nadia Heninger (Eds.). Springer, Heidelberg, 369--385. https://doi.org/10.1007/978-3-030-51280-4_20Google ScholarDigital Library
- Dragos Rotaru and Tim Wood. 2019. MArBled Circuits: Mixing Arithmetic and Boolean Circuits with Active Security. In INDOCRYPT 2019 (LNCS, Vol. 11898),, Feng Hao, Sushmita Ruj, and Sourav Sen Gupta (Eds.). Springer, Heidelberg, 227--249. https://doi.org/10.1007/978-3-030-35423-7_12Google ScholarDigital Library
- Tomas Toft. 2011. Sub-linear, Secure Comparison with Two Non-colluding Parties. In PKC 2011 (LNCS, Vol. 6571),, Dario Catalano, Nelly Fazio, Rosario Gennaro, and Antonio Nicolosi (Eds.). Springer, Heidelberg, 174--191. https://doi.org/10.1007/978-3-642-19379-8_11Google Scholar
- Thijs Veugen. 2010. Encrypted integer division. In 2010 IEEE International Workshop on Information Forensics and Security. 1--6. https://doi.org/10.1109/WIFS.2010.5711448Google ScholarCross Ref
- Thijs Veugen. 2014 Encrypted Integer Division and Secure Comparison. Int. J. Appl. Cryptol., Vol. 3, 2 (2014), 166--180. https://doi.org/10.5555/2635720.2635725Google ScholarDigital Library
- Andrew Chi-Chih Yao. 1982. Protocols for Secure Computations (Extended Abstract). In 23rd FOCS. IEEE Computer Society Press, 160--164. https://doi.org/10.1109/SFCS.1982.38Google Scholar
- Ching-Hua Yu, Sherman S. M. Chow, Kai-Min Chung, and Feng-Hao Liu. 2011. Efficient Secure Two-Party Exponentiation. In CT-RSA 2011 (LNCS, Vol. 6558), Aggelos Kiayias (Ed.). Springer, Heidelberg, 17--32. https://doi.org/10.1007/978-3-642-19074-2_2Google ScholarCross Ref
Index Terms
- Memory and Round-Efficient MPC Primitives in the Pre-Processing Model from Unit Vectorization
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