{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,27]],"date-time":"2025-03-27T05:55:36Z","timestamp":1743054936135,"version":"3.40.3"},"publisher-location":"Cham","reference-count":25,"publisher":"Springer Nature Switzerland","isbn-type":[{"type":"print","value":"9783031818233"},{"type":"electronic","value":"9783031818240"}],"license":[{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2025]]},"DOI":"10.1007\/978-3-031-81824-0_17","type":"book-chapter","created":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T07:31:08Z","timestamp":1740727868000},"page":"274-292","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["SMALL: Scalable Matrix OriginAted Large Integer PoLynomial Multiplication Accelerator for\u00a0Lattice-Based Post-Quantum Cryptography"],"prefix":"10.1007","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4814-1318","authenticated-orcid":false,"given":"Jiafeng","family":"Xie","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3461-4548","authenticated-orcid":false,"given":"Pengzhou","family":"He","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3654-2536","authenticated-orcid":false,"given":"Samira Carolina Oliva","family":"Madrigal","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2572-9565","authenticated-orcid":false,"given":"\u00c7etin Kaya","family":"Ko\u00e7","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,2,28]]},"reference":[{"key":"17_CR1","unstructured":"Saber. https:\/\/www.esat.kuleuven.be\/cosic\/pqcrypto\/saber\/"},{"key":"17_CR2","doi-asserted-by":"publisher","unstructured":"Bao, T., He, P., Bai, S., Xie, J.: TINA: TMVP-initiated novel accelerator for lightweight ring-LWE-based PQC. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. (01), 1\u201313 (2023). https:\/\/doi.org\/10.1109\/TVLSI.2023.3341037","DOI":"10.1109\/TVLSI.2023.3341037"},{"key":"17_CR3","doi-asserted-by":"publisher","unstructured":"Basso, A., Roy, S.S.: Optimized polynomial multiplier architectures for post-quantum KEM saber. In: 2021 58th ACM\/IEEE Design Automation Conference (DAC), pp. 1285\u20131290. IEEE (2021). https:\/\/doi.org\/10.1109\/DAC18074.2021.9586219","DOI":"10.1109\/DAC18074.2021.9586219"},{"key":"17_CR4","doi-asserted-by":"publisher","unstructured":"Buchmann, J., G\u00f6pfert, F., G\u00fcneysu, T., Oder, T., P\u00f6ppelmann, T.: High-performance and lightweight lattice-based public-key encryption. In: Proceedings of the 2nd ACM international workshop on IoT privacy, trust, and security, pp.\u00a02\u20139 (2016). https:\/\/doi.org\/10.1145\/2899007.2899011","DOI":"10.1145\/2899007.2899011"},{"issue":"12","key":"17_CR5","doi-asserted-by":"publisher","first-page":"4574","DOI":"10.1109\/TCSII.2023.3290192","volume":"70","author":"P Choi","year":"2023","unstructured":"Choi, P., Kim, D.K.: Lightweight polynomial multiplication accelerator for NTRU using shared SRAM. IEEE Trans. Circuits Syst. II Express Briefs 70(12), 4574\u20134578 (2023). https:\/\/doi.org\/10.1109\/TCSII.2023.3290192","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"17_CR6","unstructured":"Fan, J., Vercauteren, F.: Somewhat practical fully homomorphic encryption. Cryptology ePrint Archive (2012)"},{"key":"17_CR7","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1038\/s41586-022-05172-4","volume":"610","author":"A Fawzi","year":"2022","unstructured":"Fawzi, A., et al.: Discovering faster matrix multiplication algorithms with reinforcement learning. Nature 610, 47\u201353 (2022). https:\/\/doi.org\/10.1038\/s41586-022-05172-4","journal-title":"Nature"},{"key":"17_CR8","unstructured":"Han, J., Fan, H.: Toeplitz matrix-vector product based $${GF}(2^n)$$ shifted polynomial basis multipliers for all irreducible pentanomials. Cryptology ePrint Archive, Paper 2013\/427 (2013). https:\/\/eprint.iacr.org\/2013\/427"},{"key":"17_CR9","doi-asserted-by":"publisher","unstructured":"He, P., Bao, T., Xie, J., Amin, M.: FPGA implementation of compact hardware accelerators for ring-binary-LWE-based post-quantum cryptography. ACM Trans. Reconfigurable Technol. Syst. 16(3) (2023). https:\/\/doi.org\/10.1145\/3569457","DOI":"10.1145\/3569457"},{"issue":"2","key":"17_CR10","doi-asserted-by":"publisher","first-page":"383","DOI":"10.1109\/JETCAS.2021.3075456","volume":"11","author":"P He","year":"2021","unstructured":"He, P., Guin, U., Xie, J.: Novel low-complexity polynomial multiplication over hybrid fields for efficient implementation of binary ring-LWE post-quantum cryptography. IEEE J. Emerg. Sel. Top. Circuits Syst. 11(2), 383\u2013394 (2021). https:\/\/doi.org\/10.1109\/JETCAS.2021.3075456","journal-title":"IEEE J. Emerg. Sel. Top. Circuits Syst."},{"key":"17_CR11","doi-asserted-by":"publisher","unstructured":"He, P., Tu, Y., Xie, J., Jacinto, H.: KINA: karatsuba initiated novel accelerator for ring-binary-LWE (RBLWE)-based post-quantum cryptography. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 31(10), 1551\u20131564 (2023). https:\/\/doi.org\/10.1109\/TVLSI.2023.3302289","DOI":"10.1109\/TVLSI.2023.3302289"},{"key":"17_CR12","doi-asserted-by":"publisher","unstructured":"Hu, J., Wang, W., Cheung, R.C., Wang, H.: Optimized polynomial multiplier over commutative rings on FPGAS: a case study on bike. In: 2019 International Conference on Field-Programmable Technology (ICFPT), pp. 231\u2013234 (2019). https:\/\/doi.org\/10.1109\/ICFPT47387.2019.00035","DOI":"10.1109\/ICFPT47387.2019.00035"},{"issue":"2","key":"17_CR13","doi-asserted-by":"publisher","first-page":"65","DOI":"10.1109\/CJECE.2014.2317983","volume":"37","author":"A Khayyat","year":"2014","unstructured":"Khayyat, A., Manjikian, N.: Analysis of blocking and scheduling for FPGA-based floating-point matrix multiplication analyse du blocage et de l\u2019ordonnancement d\u2019une multiplication matricielle \u00e0 virgule flottante sur un FPGA. Can. J. Electr. Comput. Eng. 37(2), 65\u201375 (2014). https:\/\/doi.org\/10.1109\/CJECE.2014.2317983","journal-title":"Can. J. Electr. Comput. Eng."},{"issue":"1","key":"17_CR14","doi-asserted-by":"publisher","first-page":"17","DOI":"10.1109\/LCA.2022.3160394","volume":"21","author":"BJ Lucas","year":"2022","unstructured":"Lucas, B.J., et al.: Lightweight hardware implementation of binary ring-LWE PQC accelerator. IEEE Comput. Archit. Lett. 21(1), 17\u201320 (2022). https:\/\/doi.org\/10.1109\/LCA.2022.3160394","journal-title":"IEEE Comput. Archit. Lett."},{"key":"17_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-13190-5_1","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"V Lyubashevsky","year":"2010","unstructured":"Lyubashevsky, V., Peikert, C., Regev, O.: On ideal lattices and learning with errors over rings. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol. 6110, pp. 1\u201323. Springer, Heidelberg (2010). https:\/\/doi.org\/10.1007\/978-3-642-13190-5_1"},{"key":"17_CR16","unstructured":"Mouilleron, C.: Efficient computation with structured matrices and arithmetic expressions (2011)"},{"issue":"114","key":"17_CR17","doi-asserted-by":"publisher","first-page":"365","DOI":"10.1090\/S0025-5718-1971-0301966-0","volume":"25","author":"JM Pollard","year":"1971","unstructured":"Pollard, J.M.: The fast fourier transform in a finite field. Math. Comput. 25(114), 365\u2013374 (1971)","journal-title":"Math. Comput."},{"issue":"6","key":"17_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/1568318.1568324","volume":"56","author":"O Regev","year":"2009","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. J. ACM (JACM) 56(6), 1\u201340 (2009). https:\/\/doi.org\/10.1145\/1568318.1568324","journal-title":"J. ACM (JACM)"},{"key":"17_CR19","doi-asserted-by":"publisher","unstructured":"Samsi, S., Helfer, B., Kepner, J., Reuther, A., Ricke, D.O.: A linear algebra approach to fast DNA mixture analysis using GPUS. In: 2017 IEEE High Performance Extreme Computing Conference (HPEC), pp.\u00a01\u20136 (2017). https:\/\/doi.org\/10.1109\/HPEC.2017.8091027","DOI":"10.1109\/HPEC.2017.8091027"},{"issue":"09","key":"17_CR20","doi-asserted-by":"publisher","first-page":"2454","DOI":"10.1109\/TC.2023.3251847","volume":"72","author":"W Tan","year":"2023","unstructured":"Tan, W., Wang, A., Zhang, X., Lao, Y., Parhi, K.K.: High-speed VLSI architectures for modular polynomial multiplication via fast filtering and applications to lattice-based cryptography. IEEE Trans. Comput. 72(09), 2454\u20132466 (2023). https:\/\/doi.org\/10.1109\/TC.2023.3251847","journal-title":"IEEE Trans. Comput."},{"issue":"07","key":"17_CR21","doi-asserted-by":"publisher","first-page":"1830","DOI":"10.1109\/TC.2023.3238129","volume":"72","author":"ZY Wong","year":"2023","unstructured":"Wong, Z.Y., Wong, D.C.K., Lee, W.K., Mok, K.M., Yap, W.S., Khalid, A.: KaratSaber: new speed records for saber polynomial multiplication using efficient karatsuba FPGA architecture. IEEE Trans. Comput. 72(07), 1830\u20131842 (2023). https:\/\/doi.org\/10.1109\/TC.2023.3238129","journal-title":"IEEE Trans. Comput."},{"key":"17_CR22","doi-asserted-by":"publisher","unstructured":"Xie, J., He, P., Lee, C.Y.: Crop: FPGA implementation of high-performance polynomial multiplication in saber KEM based on novel cyclic-row oriented processing strategy. In: 2021 IEEE 39th International Conference on Computer Design (ICCD), pp. 130\u2013137 (2021). https:\/\/doi.org\/10.1109\/ICCD53106.2021.00031","DOI":"10.1109\/ICCD53106.2021.00031"},{"issue":"3","key":"17_CR23","doi-asserted-by":"publisher","first-page":"1670","DOI":"10.1109\/TCSII.2024.3357836","volume":"71","author":"J Xie","year":"2024","unstructured":"Xie, J., Zhao, W., Lee, H., Roy, D.B., Zhang, X.: Hardware circuits and systems design for post-quantum cryptography-a tutorial brief. IEEE Trans. Circuits Syst. II Express Briefs 71(3), 1670\u20131676 (2024). https:\/\/doi.org\/10.1109\/TCSII.2024.3357836","journal-title":"IEEE Trans. Circuits Syst. II Express Briefs"},{"key":"17_CR24","doi-asserted-by":"publisher","unstructured":"Xu, T., Cui, Y., Liu, D., Wang, C., Liu, W.: Lightweight and efficient hardware implementation for saber using NTT multiplication. In: 2022 IEEE Asia Pacific Conference on Circuits and Systems (APCCAS), pp. 601\u2013605 (2022). https:\/\/doi.org\/10.1109\/APCCAS55924.2022.10090310","DOI":"10.1109\/APCCAS55924.2022.10090310"},{"key":"17_CR25","doi-asserted-by":"publisher","unstructured":"Zhang, Y., et\u00a0al.: A lightweight and efficient schoolbook polynomial multiplier for saber. In: 2022 IEEE International Symposium on Circuits and Systems (ISCAS), pp. 2251\u20132255. IEEE (2022). https:\/\/doi.org\/10.1109\/ISCAS48785.2022.9937496","DOI":"10.1109\/ISCAS48785.2022.9937496"}],"container-title":["Lecture Notes in Computer Science","Arithmetic of Finite Fields"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-031-81824-0_17","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,2,28]],"date-time":"2025-02-28T07:31:19Z","timestamp":1740727879000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-031-81824-0_17"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025]]},"ISBN":["9783031818233","9783031818240"],"references-count":25,"URL":"https:\/\/doi.org\/10.1007\/978-3-031-81824-0_17","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2025]]},"assertion":[{"value":"28 February 2025","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"WAIFI","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Workshop on the Arithmetic of Finite Fields","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Ottawa, ON","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Canada","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2024","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10 June 2024","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"12 June 2024","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"10","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"waifi2024","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"http:\/\/waifi.org\/2024\/","order":11,"name":"conference_url","label":"Conference URL","group":{"name":"ConferenceInfo","label":"Conference Information"}}]}}