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Embed. Comput. Syst."],"published-print":{"date-parts":[[2024,11,30]]},"abstract":"<jats:p>Dilithium is a signature scheme that is currently being standardized to the Module-Lattice-Based Digital Signature Standard by NIST. It is believed to be secure even against attacks from large-scale quantum computers based on lattice problems. The implementation efficiency is important for promoting the migration of current cryptography algorithms to post-quantum cryptography algorithms. In this article, we optimize the implementation of Dilithium with several new approaches proposed. Firstly, we improve the efficiency of parallel NTT implementations. The overhead of shuffling operations is reduced in our implementations, and fewer loading instructions are invoked for the precomputations. Then, we optimize the sampling and bit-packing of polynomial coefficients in Dilithium. We can handle double the number of coefficients within one register using a new approach for the sampling of secret key polynomials. The approaches proposed in this article are applicable to implementations under AVX2 and AVX-512 instruction sets. Take Dilithium2 as an illustration, our AVX2 implementation demonstrates improvements of 22.7%, 16.9%, and 13.5% for KeyGen, Sign, and Verify compared with the previous implementation.<\/jats:p>","DOI":"10.1145\/3687309","type":"journal-article","created":{"date-parts":[[2024,8,10]],"date-time":"2024-08-10T11:44:08Z","timestamp":1723290248000},"page":"1-30","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Optimizing Dilithium Implementation with AVX2\/-512"],"prefix":"10.1145","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4816-3805","authenticated-orcid":false,"given":"Runqing","family":"Xu","sequence":"first","affiliation":[{"name":"Wuhan University, Wuhan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2446-7436","authenticated-orcid":false,"given":"Debiao","family":"He","sequence":"additional","affiliation":[{"name":"Wuhan University, Wuhan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1819-9332","authenticated-orcid":false,"given":"Min","family":"Luo","sequence":"additional","affiliation":[{"name":"Wuhan University, Wuhan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9958-3255","authenticated-orcid":false,"given":"Cong","family":"Peng","sequence":"additional","affiliation":[{"name":"Wuhan University, Wuhan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8351-8766","authenticated-orcid":false,"given":"Xiangyong","family":"Zeng","sequence":"additional","affiliation":[{"name":"Wuhan University, Wuhan, China"}]}],"member":"320","published-online":{"date-parts":[[2024,9,11]]},"reference":[{"doi-asserted-by":"publisher","key":"e_1_3_2_2_2","DOI":"10.46586\/TCHES.V2024.I1.87-132"},{"doi-asserted-by":"publisher","key":"e_1_3_2_3_2","DOI":"10.1007\/978-3-031-09234-3_42"},{"key":"e_1_3_2_4_2","first-page":"327","volume-title":"25th USENIX Security Symposium, USENIX Security 16, Austin, TX, USA, August 10-12, 2016","author":"Alkim Erdem","year":"2016","unstructured":"Erdem Alkim, L\u00e9o Ducas, Thomas P\u00f6ppelmann, and Peter Schwabe. 2016. Post-quantum key exchange - a new hope. In 25th USENIX Security Symposium, USENIX Security 16, Austin, TX, USA, August 10-12, 2016, Thorsten Holz and Stefan Savage (Eds.). USENIX Association, 327\u2013343. Retrieved from https:\/\/www.usenix.org\/conference\/usenixsecurity16\/technical-sessions\/presentation\/alkim"},{"unstructured":"Dor Mariel Alter Peter Schwabe and Joan Daemen. 2021. Optimizing the NIST post quantum candidate SPHINCS+ using AVX-512.","key":"e_1_3_2_5_2"},{"doi-asserted-by":"publisher","key":"e_1_3_2_6_2","DOI":"10.46586\/TCHES.V2023.I4.58-79"},{"key":"e_1_3_2_7_2","article-title":"Crystals-dilithium algorithm specifications and supporting documentation (version 3.1)","volume":"3","author":"Bai Shi","year":"2021","unstructured":"Shi Bai, L\u00e9o Ducas, Eike Kiltz, Tancrede Lepoint, Vadim Lyubashevsky, Peter Schwabe, Gregor Seiler, and Damien Stehl\u00e9. 2021. Crystals-dilithium algorithm specifications and supporting documentation (version 3.1). NIST Post-Quantum Cryptography Standardization Round 3 (2021).","journal-title":"NIST Post-Quantum Cryptography Standardization Round"},{"doi-asserted-by":"publisher","key":"e_1_3_2_8_2","DOI":"10.46586\/tches.v2022.i1.221-244"},{"doi-asserted-by":"publisher","key":"e_1_3_2_9_2","DOI":"10.46586\/tches.v2022.i2.41-68"},{"doi-asserted-by":"publisher","key":"e_1_3_2_10_2","DOI":"10.46586\/TCHES.V2021.I4.618-649"},{"doi-asserted-by":"publisher","key":"e_1_3_2_11_2","DOI":"10.1090\/S0025-5718-1965-0178586-1"},{"doi-asserted-by":"publisher","key":"e_1_3_2_12_2","DOI":"10.46586\/TCHES.V2023.I4.110-145"},{"doi-asserted-by":"publisher","unstructured":"National Institute of Standards and Technology. 2023. Module-lattice-based digital signature standard. (Department of Commerce Washington D.C.). Federal Information Processing Standards Publication (FIPS) NIST FIPS204ipd. 10.6028\/NIST.FIPS.204.ipd","key":"e_1_3_2_13_2","DOI":"10.6028\/NIST.FIPS.204.ipd"},{"doi-asserted-by":"publisher","key":"e_1_3_2_14_2","DOI":"10.13154\/tches.v2018.i1.238-268"},{"doi-asserted-by":"publisher","key":"e_1_3_2_15_2","DOI":"10.1145\/1464291.1464352"},{"doi-asserted-by":"publisher","key":"e_1_3_2_16_2","DOI":"10.46586\/tches.v2021.i1.1-24"},{"doi-asserted-by":"publisher","key":"e_1_3_2_17_2","DOI":"10.46586\/TCHES.V2024.I2.1-24"},{"doi-asserted-by":"publisher","key":"e_1_3_2_18_2","DOI":"10.1109\/EuroSPW55150.2022.00010"},{"doi-asserted-by":"publisher","key":"e_1_3_2_19_2","DOI":"10.1007\/s10623-014-9938-4"},{"doi-asserted-by":"publisher","key":"e_1_3_2_20_2","DOI":"10.1007\/s10623-014-9938-4"},{"doi-asserted-by":"publisher","key":"e_1_3_2_21_2","DOI":"10.1145\/3609223"},{"unstructured":"Zhichuang Liang and Yunlei Zhao. 2022. Number theoretic transform and its applications in lattice-based cryptosystems: A survey. arXiv:2211.13546. Retrieved from https:\/\/arxiv.org\/abs\/2211.13546","key":"e_1_3_2_22_2"},{"doi-asserted-by":"publisher","key":"e_1_3_2_23_2","DOI":"10.1109\/TIFS.2020.3045904"},{"doi-asserted-by":"publisher","key":"e_1_3_2_24_2","DOI":"10.1109\/TC.2017.2750146"},{"doi-asserted-by":"publisher","key":"e_1_3_2_25_2","DOI":"10.1007\/978-3-319-48965-0_8"},{"doi-asserted-by":"publisher","key":"e_1_3_2_26_2","DOI":"10.1007\/978-3-642-10366-7_35"},{"doi-asserted-by":"publisher","key":"e_1_3_2_27_2","DOI":"10.1007\/978-3-642-29011-4_43"},{"doi-asserted-by":"publisher","key":"e_1_3_2_28_2","DOI":"10.13154\/tches.v2019.i3.180-201"},{"doi-asserted-by":"publisher","unstructured":"Vincent Quentin Ulitzsch Soundes Marzougui Mehdi Tibouchi and Jean-Pierre Seifert. 2024. Profiling side-channel attacks on dilithium: A small bit-fiddling leak breaks It all. 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