{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T15:20:49Z","timestamp":1774365649666,"version":"3.50.1"},"reference-count":42,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2021,2,19]],"date-time":"2021-02-19T00:00:00Z","timestamp":1613692800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100014188","name":"Ministry of Science and ICT, South Korea","doi-asserted-by":"publisher","award":["IITP-2020-0-01797"],"award-info":[{"award-number":["IITP-2020-0-01797"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100014188","name":"Ministry of Science and ICT, South Korea","doi-asserted-by":"publisher","award":["2019-0-01343"],"award-info":[{"award-number":["2019-0-01343"]}],"id":[{"id":"10.13039\/501100014188","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we present a high-speed, unified elliptic curve cryptography (ECC) processor for arbitrary Weierstrass curves over GF(p), which to the best of our knowledge, outperforms other similar works in terms of execution time. Our approach employs the combination of the schoolbook long and Karatsuba multiplication algorithm for the elliptic curve point multiplication (ECPM) to achieve better parallelization while retaining low complexity. In the hardware implementation, the substantial gain in speed is also contributed by our n-bit pipelined Montgomery Modular Multiplier (pMMM), which is constructed from our n-bit pipelined multiplier-accumulators that utilizes digital signal processor (DSP) primitives as digit multipliers. Additionally, we also introduce our unified, pipelined modular adder\/subtractor (pMAS) for the underlying field arithmetic, and leverage a more efficient yet compact scheduling of the Montgomery ladder algorithm. The implementation for 256-bit modulus size on the 7-series FPGA: Virtex-7, Kintex-7, and XC7Z020 yields 0.139, 0.138, and 0.206 ms of execution time, respectively. Furthermore, since our pMMM module is generic for any curve in Weierstrass form, we support multi-curve parameters, resulting in a unified ECC architecture. Lastly, our method also works in constant time, making it suitable for applications requiring high speed and SCA-resistant characteristics.<\/jats:p>","DOI":"10.3390\/s21041451","type":"journal-article","created":{"date-parts":[[2021,2,19]],"date-time":"2021-02-19T09:06:10Z","timestamp":1613725570000},"page":"1451","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["High-Speed and Unified ECC Processor for Generic Weierstrass Curves over GF(p) on FPGA"],"prefix":"10.3390","volume":"21","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5994-2823","authenticated-orcid":false,"given":"Asep Muhamad","family":"Awaludin","sequence":"first","affiliation":[{"name":"School of Computer Science and Engineering, Pusan National University, Busan 609735, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6143-4134","authenticated-orcid":false,"given":"Harashta Tatimma","family":"Larasati","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Pusan National University, Busan 609735, Korea"},{"name":"School of Electrical Engineering and Informatics, Institut Teknologi Bandung, Bandung 40116, Indonesia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8475-7294","authenticated-orcid":false,"given":"Howon","family":"Kim","sequence":"additional","affiliation":[{"name":"School of Computer Science and Engineering, Pusan National University, Busan 609735, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,2,19]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"37251","DOI":"10.1109\/ACCESS.2019.2905347","article-title":"5G communication: An overview of vehicle-to-everything, drones, and healthcare use-cases","volume":"7","author":"Ullah","year":"2019","journal-title":"IEEE Access"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Park, J.H., and Park, J.H. 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