{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,31]],"date-time":"2026-03-31T13:38:16Z","timestamp":1774964296241,"version":"3.50.1"},"reference-count":45,"publisher":"Association for Computing Machinery (ACM)","issue":"2","license":[{"start":{"date-parts":[[2021,6,5]],"date-time":"2021-06-05T00:00:00Z","timestamp":1622851200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"funder":[{"DOI":"10.13039\/501100018532","name":"Major Scientific and Technological Innovation Project of Shandong Province","doi-asserted-by":"crossref","award":["2020CXGC010115"],"award-info":[{"award-number":["2020CXGC010115"]}],"id":[{"id":"10.13039\/501100018532","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["61972294, 61932016 and 61802180"],"award-info":[{"award-number":["61972294, 61932016 and 61802180"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Special Project on Science and Technology Program of Hubei Provience","award":["2020AEA013"],"award-info":[{"award-number":["2020AEA013"]}]},{"DOI":"10.13039\/501100003819","name":"Natural Science Foundation of Hubei Province","doi-asserted-by":"crossref","award":["2020CFA052"],"award-info":[{"award-number":["2020CFA052"]}],"id":[{"id":"10.13039\/501100003819","id-type":"DOI","asserted-by":"crossref"}]},{"name":"Wuhan Municipal Science and Technology Project","award":["2020010601012187"],"award-info":[{"award-number":["2020010601012187"]}]},{"name":"Cloud Technology Endowed Professorship"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Reconfigurable Technol. Syst."],"published-print":{"date-parts":[[2021,6,30]]},"abstract":"<jats:p>\n            As quantum computers become more affordable and commonplace, existing security systems that are based on classical cryptographic primitives, such as RSA and\n            <jats:bold>Elliptic Curve Cryptography<\/jats:bold>\n            (\n            <jats:bold>ECC<\/jats:bold>\n            ), will no longer be secure. Hence, there has been interest in designing\n            <jats:bold>post-quantum cryptographic<\/jats:bold>\n            (\n            <jats:bold>PQC<\/jats:bold>\n            ) schemes, such as those based on\n            <jats:bold>lattice-based cryptography<\/jats:bold>\n            (\n            <jats:bold>LBC<\/jats:bold>\n            ). The potential of LBC schemes is evidenced by the number of such schemes passing the selection of NIST PQC Standardization Process Round-3. One such scheme is the Crystals-Dilithium signature scheme, which is based on the hard module-lattice problem. However, there is no efficient implementation of the Crystals-Dilithium signature scheme. Hence, in this article, we present a compact hardware architecture containing elaborate modular multiplication units using the Karatsuba algorithm along with smart generators of address sequence and twiddle factors for NTT, which can complete polynomial addition\/multiplication with the parameter setting of Dilithium in a short clock period. Also, we propose a fast software\/hardware co-design implementation on\n            <jats:bold>Field Programmable Gate Array<\/jats:bold>\n            (\n            <jats:bold>FPGA<\/jats:bold>\n            ) for the Dilithium scheme with a tradeoff between speed and resource utilization. Our co-design implementation outperforms a pure C implementation on a Nios-II processor of the platform Altera DE2-115, in the sense that our implementation is 11.2 and 7.4 times faster for signature and verification, respectively. In addition, we also achieve approximately 51% and 31% speed improvement for signature and verification, in comparison to the pure C implementation on processor ARM Cortex-A9 of ZYNQ-7020 platform.\n          <\/jats:p>","DOI":"10.1145\/3447812","type":"journal-article","created":{"date-parts":[[2021,6,5]],"date-time":"2021-06-05T23:30:46Z","timestamp":1622935846000},"page":"1-21","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":35,"title":["A Software\/Hardware Co-Design of Crystals-Dilithium Signature Scheme"],"prefix":"10.1145","volume":"14","author":[{"given":"Zhen","family":"Zhou","sequence":"first","affiliation":[{"name":"School of Cyber Science and Engineering, Wuhan University, China and Cyberspace Security Research Center, Peng Cheng Laboratory, Shenzhen, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2446-7436","authenticated-orcid":false,"given":"Debiao","family":"He","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, Wuhan University, Wuhan, China"}]},{"given":"Zhe","family":"Liu","sequence":"additional","affiliation":[{"name":"College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, China"}]},{"given":"Min","family":"Luo","sequence":"additional","affiliation":[{"name":"School of Cyber Science and Engineering, Wuhan University, Wuhan, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9208-5336","authenticated-orcid":false,"given":"Kim-Kwang Raymond","family":"Choo","sequence":"additional","affiliation":[{"name":"Department of Information Systems and Cyber Security, Department of Electrical and Computer Engineering, and Department of Computer Science, University of Texas at San Antonio, San Antonio, USA"}]}],"member":"320","published-online":{"date-parts":[[2021,6,5]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-319-29485-8_20"},{"key":"e_1_2_1_2_1","doi-asserted-by":"publisher","DOI":"10.1145\/237814.237838"},{"key":"e_1_2_1_3_1","volume-title":"et\u00a0al","author":"Alagic Gorjan","year":"2020","unstructured":"Gorjan Alagic , Gorjan Alagic , Jacob Alperin-Sheriff , Daniel Apon , David Cooper , Quynh Dang , Yi-Kai Liu , Carl Miller , Dustin Moody , Rene Peralta , et\u00a0al . 2020 . Status report on the second round of the NIST PQC standardization process. U.S. Department of Commerce, National Institute of Standards and Technology . Gorjan Alagic, Gorjan Alagic, Jacob Alperin-Sheriff, Daniel Apon, David Cooper, Quynh Dang, Yi-Kai Liu, Carl Miller, Dustin Moody, Rene Peralta, et\u00a0al. 2020. Status report on the second round of the NIST PQC standardization process. U.S. Department of Commerce, National Institute of Standards and Technology."},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.46586\/tches.v2020.i3.219-242"},{"key":"e_1_2_1_5_1","unstructured":"Michael Baentsch. 2019. The Dilithium Implementation in pq-Crystals. Retrieved from https:\/\/github.com\/pq-crystals\/dilithium.  Michael Baentsch. 2019. The Dilithium Implementation in pq-Crystals. Retrieved from https:\/\/github.com\/pq-crystals\/dilithium."},{"key":"e_1_2_1_6_1","first-page":"1140","article-title":"Sapphire: A configurable crypto-processor for post-quantum lattice-based protocols (Extended Version)","volume":"2019","author":"Banerjee Utsav","year":"2019","unstructured":"Utsav Banerjee , Tenzin S. Ukyab , and Anantha P. Chandrakasan . 2019 . Sapphire: A configurable crypto-processor for post-quantum lattice-based protocols (Extended Version) . IACR Cryptol. ePrint Arch. 2019 (2019), 1140 . Utsav Banerjee, Tenzin S. Ukyab, and Anantha P. Chandrakasan. 2019. Sapphire: A configurable crypto-processor for post-quantum lattice-based protocols (Extended Version). IACR Cryptol. ePrint Arch. 2019 (2019), 1140.","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"e_1_2_1_7_1","first-page":"47","article-title":"NIST post-quantum cryptography-A hardware evaluation study","volume":"2019","author":"Basu Kanad","year":"2019","unstructured":"Kanad Basu , Deepraj Soni , Mohammed Nabeel , and Ramesh Karri . 2019 . NIST post-quantum cryptography-A hardware evaluation study . IACR Cryptology ePrint Archive 2019 (2019), 47 . Kanad Basu, Deepraj Soni, Mohammed Nabeel, and Ramesh Karri. 2019. NIST post-quantum cryptography-A hardware evaluation study. IACR Cryptology ePrint Archive 2019 (2019), 47.","journal-title":"IACR Cryptology ePrint Archive"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1016\/0024-3795(95)00696-6"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1145\/2633600"},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01178683"},{"key":"e_1_2_1_11_1","volume-title":"Report on Post-Quantum Cryptography","author":"Chen Lily","unstructured":"Lily Chen , Stephen Jordan , Yi-Kai Liu , Dustin Moody , Rene Peralta , Ray Perlner , and Daniel Smith-Tone . 2016. Report on Post-Quantum Cryptography . Vol. 12 . U.S. Department of Commerce , National Institute of Standards and Technology. Lily Chen, Stephen Jordan, Yi-Kai Liu, Dustin Moody, Rene Peralta, Ray Perlner, and Daniel Smith-Tone. 2016. Report on Post-Quantum Cryptography. Vol. 12. U.S. Department of Commerce, National Institute of Standards and Technology."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1965-0178586-1"},{"key":"e_1_2_1_13_1","doi-asserted-by":"publisher","DOI":"10.1109\/ICFPT47387.2019.00032"},{"key":"e_1_2_1_14_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISCAS.2016.7527456"},{"key":"e_1_2_1_15_1","unstructured":"L\u00e9o Ducas Eike Kiltz Tancr\u00e8de Lepoint Vadim Lyubashevsky Peter Schwabe Gregor Seiler and Damien Stehl\u00e9. 2017. Crystals-Dilithium.  L\u00e9o Ducas Eike Kiltz Tancr\u00e8de Lepoint Vadim Lyubashevsky Peter Schwabe Gregor Seiler and Damien Stehl\u00e9. 2017. Crystals-Dilithium."},{"key":"e_1_2_1_17_1","first-page":"556","article-title":"RLWE-oriented high-speed polynomial multiplier utilizing multi-lane Stockham NTT algorithm","volume":"67","author":"Feng Xiang","year":"2019","unstructured":"Xiang Feng , Shuguo Li , and Sufen Xu . 2019 . RLWE-oriented high-speed polynomial multiplier utilizing multi-lane Stockham NTT algorithm . IEEE Trans. Circ. Syst. II: Express Briefs 67 , 3 (2019), 556 -- 559 . Xiang Feng, Shuguo Li, and Sufen Xu. 2019. RLWE-oriented high-speed polynomial multiplier utilizing multi-lane Stockham NTT algorithm. IEEE Trans. Circ. Syst. II: Express Briefs 67, 3 (2019), 556--559.","journal-title":"IEEE Trans. Circ. Syst. II: Express Briefs"},{"key":"e_1_2_1_18_1","first-page":"446","article-title":"RISQ-V: Tightly coupled RISC-V accelerators for post-quantum cryptography","volume":"2020","author":"Fritzmann Tim","year":"2020","unstructured":"Tim Fritzmann , Georg Sigl , and Johanna Sep\u00falveda . 2020 . RISQ-V: Tightly coupled RISC-V accelerators for post-quantum cryptography . IACR Cryptol. ePrint Arch. 2020 (2020), 446 . Tim Fritzmann, Georg Sigl, and Johanna Sep\u00falveda. 2020. RISQ-V: Tightly coupled RISC-V accelerators for post-quantum cryptography. IACR Cryptol. ePrint Arch. 2020 (2020), 446.","journal-title":"IACR Cryptol. ePrint Arch."},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/1464291.1464352"},{"key":"e_1_2_1_20_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-33027-8_30"},{"key":"e_1_2_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/3005344"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1145\/2897937.2898037"},{"key":"e_1_2_1_23_1","volume-title":"Ofman","author":"Karatsuba Anatolii Alekseevich","year":"1962","unstructured":"Anatolii Alekseevich Karatsuba and Yu P . Ofman . 1962 . Multiplication of many-digital numbers by automatic computers. In Doklady Akademii Nauk, Vol. 145 . Russian Academy of Sciences , 293\u2013294. Anatolii Alekseevich Karatsuba and Yu P. Ofman. 1962. Multiplication of many-digital numbers by automatic computers. In Doklady Akademii Nauk, Vol. 145. Russian Academy of Sciences, 293\u2013294."},{"key":"e_1_2_1_24_1","unstructured":"Po-Chun Kuo Wen-Ding Li Yu-Wei Chen Yuan-Che Hsu Bo-Yuan Peng Chen-Mou Cheng and Bo-Yin Yang. 2017. High performance post-quantum key exchange on FPGAs. Cryptology ePrint Archive.  Po-Chun Kuo Wen-Ding Li Yu-Wei Chen Yuan-Che Hsu Bo-Yuan Peng Chen-Mou Cheng and Bo-Yin Yang. 2017. High performance post-quantum key exchange on FPGAs. Cryptology ePrint Archive."},{"key":"e_1_2_1_25_1","doi-asserted-by":"publisher","DOI":"10.1109\/TVLSI.2019.2922999"},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-29011-4_43"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1007\/11787006_13"},{"key":"e_1_2_1_28_1","doi-asserted-by":"publisher","DOI":"10.1145\/2535925"},{"key":"e_1_2_1_29_1","doi-asserted-by":"publisher","DOI":"10.1109\/DSD.2019.00045"},{"key":"e_1_2_1_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/800205.806332"},{"key":"e_1_2_1_31_1","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-1985-0777282-X"},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISLPED.2019.8824979"},{"key":"e_1_2_1_33_1","volume-title":"Software and hardware implementation of lattice-cased cryptography schemes","author":"Nejatollahi Hamid","year":"2017","unstructured":"Hamid Nejatollahi , Nikil Dutt , Sandip Ray , Francesco Regazzoni , Indranil Banerjee , and Rosario Cammarota . 2017. Software and hardware implementation of lattice-cased cryptography schemes . University of California Irvine , CECS TR 17, 4 ( 2017 ). Hamid Nejatollahi, Nikil Dutt, Sandip Ray, Francesco Regazzoni, Indranil Banerjee, and Rosario Cammarota. 2017. Software and hardware implementation of lattice-cased cryptography schemes. University of California Irvine, CECS TR 17, 4 (2017)."},{"key":"e_1_2_1_34_1","volume-title":"International Conference on Cryptology and Information Security in Latin America. Springer, 128\u2013142","author":"Oder Tobias","year":"2017","unstructured":"Tobias Oder and Tim G\u00fcneysu . 2017 . Implementing the NewHope-Simple key exchange on low-cost FPGAs . In International Conference on Cryptology and Information Security in Latin America. Springer, 128\u2013142 . Tobias Oder and Tim G\u00fcneysu. 2017. Implementing the NewHope-Simple key exchange on low-cost FPGAs. In International Conference on Cryptology and Information Security in Latin America. 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IACR Cryptology ePrint Archive 2018 (2018), 39 . Gregor Seiler. 2018. Faster AVX2 optimized NTT multiplication for Ring-LWE lattice cryptography. IACR Cryptology ePrint Archive 2018 (2018), 39.","journal-title":"IACR Cryptology ePrint Archive"},{"key":"e_1_2_1_43_1","doi-asserted-by":"publisher","DOI":"10.1137\/S0036144598347011"},{"key":"e_1_2_1_44_1","unstructured":"Thom Wiggers. [n. d.]. PQClean: Clean portable tested implementations of post-quantum cryptography. Retrieved from https:\/\/github.com\/PQClean\/PQClean.  Thom Wiggers. [n. d.]. PQClean: Clean portable tested implementations of post-quantum cryptography. Retrieved from https:\/\/github.com\/PQClean\/PQClean."},{"key":"e_1_2_1_45_1","doi-asserted-by":"publisher","DOI":"10.1109\/ISCAS.2018.8351649"},{"key":"e_1_2_1_46_1","doi-asserted-by":"publisher","DOI":"10.1109\/TCSI.2020.2983185"}],"container-title":["ACM Transactions on Reconfigurable Technology and Systems"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3447812","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3447812","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T20:48:05Z","timestamp":1750193285000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3447812"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,6,5]]},"references-count":45,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2021,6,30]]}},"alternative-id":["10.1145\/3447812"],"URL":"https:\/\/doi.org\/10.1145\/3447812","relation":{},"ISSN":["1936-7406","1936-7414"],"issn-type":[{"value":"1936-7406","type":"print"},{"value":"1936-7414","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,6,5]]},"assertion":[{"value":"2020-06-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-01-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2021-06-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}