{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T15:10:23Z","timestamp":1778944223248,"version":"3.51.4"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"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":["J Cryptogr Eng"],"published-print":{"date-parts":[[2026,4]]},"DOI":"10.1007\/s13389-026-00392-0","type":"journal-article","created":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T12:04:30Z","timestamp":1775563470000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Faster $$\\text {GF}(2)[x]$$ polynomial multiplication using SIMD instructions"],"prefix":"10.1007","volume":"16","author":[{"given":"Jihoon","family":"Jang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Myeonghoon","family":"Lee","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suhri","family":"Kim","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seog Chung","family":"Seo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Seokhie","family":"Hong","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,7]]},"reference":[{"issue":"2","key":"392_CR1","doi-asserted-by":"publisher","first-page":"303","DOI":"10.1137\/S0036144598347011","volume":"41","author":"PW Shor","year":"1999","unstructured":"Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Rev. 41(2), 303\u2013332 (1999). https:\/\/doi.org\/10.1137\/S0036144598347011","journal-title":"SIAM Rev."},{"key":"392_CR2","unstructured":"Aguilar-Melchor, C., Aragon, N., Bettaieb, S., Bidoux, L., Blazy, O., Deneuville, J.-C., Gaborit, P., Persichetti, E., Z\u00e9mor, G., Bos, J., Dion, A., Lacan, J., Robert, J.-M., Veron, P.: HQC. Technical report, National Institute of Standards and Technology (2022). available at https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/round-4-submissions"},{"key":"392_CR3","unstructured":"Aragon, N., Barreto, P., Bettaieb, S., Bidoux, L., Blazy, O., Deneuville, J.-C., Gaborit, P., Gueron, S., Guneysu, T., Aguilar-Melchor, C., Misoczki, R., Persichetti, E., Sendrier, N., Tillich, J.-P., Z\u00e9mor, G., Vasseur, V., Ghosh, S., Richter-Brokmann, J.: BIKE. Technical report, National Institute of Standards and Technology (2022). available at https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/round-4-submissions"},{"key":"392_CR4","doi-asserted-by":"publisher","unstructured":"Alagic, G., Bros, M., Ciadoux, P., Cooper, D., Dang, Q., Dang, T., Kelsey, J., Lichtinger, J., Liu, Y.-K., Miller, C., Moody, D., Peralta, R., Perlner, R., Robinson, A., Silberg, H., Smith-Tone, D., Waller, N.: Status report on the fourth round of the NIST post-quantum cryptography standardization process. NIST Internal Report (IR) NIST IR 8545, National Institute of Standards and Technology (NIST), Gaithersburg, MD (2025). https:\/\/doi.org\/10.6028\/NIST.IR.8545","DOI":"10.6028\/NIST.IR.8545"},{"key":"392_CR5","unstructured":"Karatsuba, A.A., Ofman, Y.P.: Multiplication of many-digital numbers by automatic computers. In: Dokl. Akad. Nauk SSSR 145, 293\u2013294 (1962) Russian Academy of Sciences"},{"key":"392_CR6","doi-asserted-by":"publisher","first-page":"291","DOI":"10.2307\/1995359","volume":"142","author":"SA Cook","year":"1969","unstructured":"Cook, S.A., Aanderaa, S.O.: On the minimum computation time of functions. Trans. Am. Math. Soc. 142, 291\u2013314 (1969). https:\/\/doi.org\/10.2307\/1995359","journal-title":"Trans. Am. Math. Soc."},{"key":"392_CR7","doi-asserted-by":"publisher","unstructured":"Bodrato, M.: Towards optimal toom-cook multiplication for univariate and multivariate polynomials in characteristic 2 and 0. In: Arithmetic of Finite Fields, 116\u2013133. Springer, Berlin, Heidelberg (2007). https:\/\/doi.org\/10.1007\/978-3-540-73074-3_10","DOI":"10.1007\/978-3-540-73074-3_10"},{"key":"392_CR8","unstructured":"Lyubashevsky, V., Ducas, L., Kiltz, E., Lepoint, T., Schwabe, P., Seiler, G., Stehl\u00e9, D., Bai, S.: CRYSTALS-DILITHIUM. Technical report, National Institute of Standards and Technology (2022). available at https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/selected-algorithms-2022"},{"key":"392_CR9","unstructured":"Schwabe, P., Avanzi, R., Bos, J., Ducas, L., Kiltz, E., Lepoint, T., Lyubashevsky, V., Schanck, J.M., Seiler, G., Stehl\u00e9, D., Ding, J.: CRYSTALS-KYBER. Technical report, National Institute of Standards and Technology (2022). available at https:\/\/csrc.nist.gov\/Projects\/post-quantum-cryptography\/selected-algorithms-2022"},{"issue":"2","key":"392_CR10","doi-asserted-by":"publisher","first-page":"285","DOI":"10.1016\/0097-3165(89)90020-4","volume":"50","author":"DG Cantor","year":"1989","unstructured":"Cantor, D.G.: On arithmetical algorithms over finite fields. Journal of Combinatorial Theory, Series A 50(2), 285\u2013300 (1989). https:\/\/doi.org\/10.1016\/0097-3165(89)90020-4","journal-title":"Journal of Combinatorial Theory, Series A"},{"issue":"12","key":"392_CR11","doi-asserted-by":"publisher","first-page":"6265","DOI":"10.1109\/TIT.2010.2079016","volume":"56","author":"S Gao","year":"2010","unstructured":"Gao, S., Mateer, T.: Additive fast fourier transforms over finite fields. IEEE Trans. Inf. Theor. 56(12), 6265\u20136272 (2010). https:\/\/doi.org\/10.1109\/TIT.2010.2079016","journal-title":"IEEE Trans. Inf. Theor."},{"issue":"3","key":"392_CR12","doi-asserted-by":"publisher","first-page":"97","DOI":"10.46586\/tches.v2021.i3.97-124","volume":"2021","author":"M-S Chen","year":"2021","unstructured":"Chen, M.-S., Chou, T., Krausz, M.: Optimizing BIKE for the intel haswell and ARM Cortex-M4. IACR TCHES 2021(3), 97\u2013124 (2021). https:\/\/doi.org\/10.46586\/tches.v2021.i3.97-124","journal-title":"IACR TCHES"},{"issue":"17","key":"392_CR13","doi-asserted-by":"publisher","first-page":"36318","DOI":"10.1109\/JIOT.2025.3583021","volume":"12","author":"M Lee","year":"2025","unstructured":"Lee, M., Jang, J., Kim, S., Hong, S.: Improved frobenius fft for code-based cryptography on cortex-m4. IEEE Internet Things J. 12(17), 36318\u201336327 (2025). https:\/\/doi.org\/10.1109\/JIOT.2025.3583021","journal-title":"IEEE Internet Things J."},{"key":"392_CR14","unstructured":"Jang, J., Lee, M., Kwon, D., Hong, S., Kim, S., Lee, S.: Efficient Polynomial Multiplication for HQC on ARM Cortex-M4. Cryptology ePrint Archive, Paper 2025\/1939 (2025). https:\/\/eprint.iacr.org\/2025\/1939"},{"issue":"1","key":"392_CR15","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1007\/s13389-021-00278-3","volume":"13","author":"J-M Robert","year":"2023","unstructured":"Robert, J.-M., V\u00e9ron, P.: Faster multiplication over $${\\mathbb{F} }_2[{X}]$$ using AVX512 instruction set and VPCLMULQDQ instruction. J. Cryptogr. Eng. 13(1), 37\u201355 (2023). https:\/\/doi.org\/10.1007\/s13389-021-00278-3","journal-title":"J. Cryptogr. Eng."},{"key":"392_CR16","unstructured":"Brent, R.P., Gaudry, P., Thom\u00e9, E., Zimmermann, P.: gf2x library. https:\/\/gitlab.inria.fr\/gf2x\/gf2x. Accessed: Feb. 11, 2023. [Online] (2023)"},{"key":"392_CR17","doi-asserted-by":"publisher","unstructured":"C\u00e2mara, D., Gouv\u00eaa, C.P.L., L\u00f3pez, J., Dahab, R.: Fast software polynomial multiplication on arm processors using the neon engine. In: Security Engineering and Intelligence Informatics, pp. 137\u2013154. Springer, Berlin, Heidelberg (2013). https:\/\/doi.org\/10.1007\/978-3-642-40588-4_10","DOI":"10.1007\/978-3-642-40588-4_10"},{"key":"392_CR18","doi-asserted-by":"publisher","unstructured":"Gouv\u00eaa, C.P., L\u00f3pez, J.: Implementing gcm on armv8. CT-RSA\u00a02015. LNCS 9048, 167\u2013180 (2015). https:\/\/doi.org\/10.1007\/978-3-319-16715-2_9","DOI":"10.1007\/978-3-319-16715-2_9"},{"issue":"13","key":"392_CR19","doi-asserted-by":"publisher","first-page":"2051","DOI":"10.1002\/sec.1462","volume":"9","author":"H Seo","year":"2016","unstructured":"Seo, H., Liu, Z., Nogami, Y., Choi, J., Kim, H.: Binary field multiplication on armv8. Security and Communication Networks 9(13), 2051\u20132058 (2016). https:\/\/doi.org\/10.1002\/sec.1462","journal-title":"Security and Communication Networks"},{"key":"392_CR20","doi-asserted-by":"crossref","unstructured":"Chen, M.-S., Chiu, C.-M., Peng, C.-T., Yang, B.-Y.: Accelerating HQC with Additive FFT. Cryptology ePrint Archive, Paper 2026\/014 (2026). https:\/\/eprint.iacr.org\/2026\/014","DOI":"10.46586\/tches.v2026.i2.520-544"},{"key":"392_CR21","doi-asserted-by":"publisher","unstructured":"Drucker, N., Gueron, S., Kostic, D.: Fast Polynomial Inversion for Post Quantum QC-MDPC Cryptography. In: Cyber Security Cryptography and Machine Learning, 110\u2013127. Springer, Cham (2020). https:\/\/doi.org\/10.1007\/978-3-030-49785-9_8","DOI":"10.1007\/978-3-030-49785-9_8"},{"key":"392_CR22","doi-asserted-by":"publisher","unstructured":"Chen, M.-S., G\u00fcneysu, T., Krausz, M., Thoma, J.P.: Carry-less to BIKE faster. ACNS 22. LNCS 13269, 833\u2013852 (2022). https:\/\/doi.org\/10.1007\/978-3-031-09234-3_41","DOI":"10.1007\/978-3-031-09234-3_41"},{"key":"392_CR23","doi-asserted-by":"publisher","unstructured":"Brent, R.P., Gaudry, P., Thom\u00e9, E., Zimmermann, P.: Faster multiplication in gf(2)[x]. In: Algorithmic Number Theory, 153\u2013166. Springer, Berlin, Heidelberg (2008).https:\/\/doi.org\/10.1007\/978-3-540-79456-1_10","DOI":"10.1007\/978-3-540-79456-1_10"}],"container-title":["Journal of Cryptographic Engineering"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13389-026-00392-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s13389-026-00392-0","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s13389-026-00392-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,16]],"date-time":"2026-05-16T14:13:52Z","timestamp":1778940832000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s13389-026-00392-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":23,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["392"],"URL":"https:\/\/doi.org\/10.1007\/s13389-026-00392-0","relation":{},"ISSN":["2190-8508","2190-8516"],"issn-type":[{"value":"2190-8508","type":"print"},{"value":"2190-8516","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"4 July 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare no competing interests.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}],"article-number":"3"}}