{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,15]],"date-time":"2025-11-15T10:16:22Z","timestamp":1763201782938,"version":"build-2065373602"},"reference-count":11,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2013,7,23]],"date-time":"2013-07-23T00:00:00Z","timestamp":1374537600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Elliptic curve cryptography (ECC) is one of the most promising public-key techniques in terms of short key size and various crypto protocols. For this reason, many studies on the implementation of ECC on resource-constrained devices within a practical execution time have been conducted. To this end, we must focus on scalar multiplication, which is the most expensive operation in ECC. A number of studies have proposed pre-computation and advanced scalar multiplication using a non-adjacent form (NAF) representation, and more sophisticated approaches have employed a width-w NAF representation and a modified pre-computation table. In this paper, we propose a new pre-computation method in which zero occurrences are much more frequent than in previous methods. This method can be applied to ordinary group scalar multiplication, but it requires large pre-computation table, so we combined the previous method with ours for practical purposes. This novel structure establishes a new feature that adjusts speed performance and table size finely, so we can customize the pre-computation table for our own purposes. Finally, we can establish a customized look-up table for embedded microprocessors.<\/jats:p>","DOI":"10.3390\/s130709483","type":"journal-article","created":{"date-parts":[[2013,7,23]],"date-time":"2013-07-23T13:28:05Z","timestamp":1374586085000},"page":"9483-9512","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Fixed-Base Comb with Window-Non-Adjacent Form (NAF) Method for Scalar Multiplication"],"prefix":"10.3390","volume":"13","author":[{"given":"Hwajeong","family":"Seo","sequence":"first","affiliation":[{"name":"Computer engineering, Pusan National University, Pusan 609-735, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hyunjin","family":"Kim","sequence":"additional","affiliation":[{"name":"Computer engineering, Pusan National University, Pusan 609-735, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Taehwan","family":"Park","sequence":"additional","affiliation":[{"name":"Computer engineering, Pusan National University, Pusan 609-735, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yeoncheol","family":"Lee","sequence":"additional","affiliation":[{"name":"Computer engineering, Pusan National University, Pusan 609-735, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Liu","sequence":"additional","affiliation":[{"name":"Laboratory of Algorithmics, Cryptology and Security, University of Luxembourg, 6, Rue Richard Coudenhove-Kalergi, Luxembourg L\u20131359, Luxembourg"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Howon","family":"Kim","sequence":"additional","affiliation":[{"name":"Computer engineering, Pusan National University, Pusan 609-735, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2013,7,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Cohen, H., Frey, G., Avanzi, R., Doche, C., Lange, T., Nguyen, K., and Vercauteren, F. (2006). Handbook of Elliptic and Hyperelliptic Curve Cryptography, Taylor and Francis Group LLC.","DOI":"10.1201\/9781420034981"},{"key":"ref_2","unstructured":"Hankerson, D., Menezes, A., and Vanstone, S. (2004). Guide to Elliptic Curve Cryptography, Springer."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Silverman, J.H. (1986). The Arithmetic of Elliptic Curves, Springer.","DOI":"10.1007\/978-1-4757-1920-8"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1090\/S0025-5718-1987-0866109-5","article-title":"Elliptic curve cryptosystems","volume":"48","author":"Koblitz","year":"1987","journal-title":"Math. Comput."},{"key":"ref_5","unstructured":"Williams, H.C. (1985, January 18\u201322). Use of Elliptic Curves in Cryptography. Santa Barbara, CA, USA."},{"key":"ref_6","unstructured":"Rueppel, R.A. (1992, January 24\u201328). Fast Exponentiation with Precomputation. Balatonfred, Hungary. Extended Abstract."},{"key":"ref_7","unstructured":"Desmedt, Y.G. (August, January 21\u2013). More Flexible Exponentiation with Precomputation. Santa Barbara, CA, USA. LNCS."},{"key":"ref_8","first-page":"1045","article-title":"Efficient algorithm for speeding up the computations of elliptic curve cryptosystem","volume":"168","author":"Tsaur","year":"2005","journal-title":"Appl. Math. Comput"},{"key":"ref_9","first-page":"1075","article-title":"Speeding up elliptic scalar multiplication using multidoubling","volume":"E-84-A","author":"Sakai","year":"2002","journal-title":"IEICE Trans. Inf. Syst."},{"key":"ref_10","unstructured":"Mitrokotsa, A., and Vaudenay, S. (July, January 10\u2013). Improved Fixed-Base Comb Method for Fast Scalar Multiplication. Morocco. LNCS."},{"key":"ref_11","unstructured":"A Statistical Test Suite for the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications Version sts-2.1. Available online: http:\/\/csrc.nist.gov\/groups\/ST\/toolkit\/rng\/index.html."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/7\/9483\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T21:48:09Z","timestamp":1760219289000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/13\/7\/9483"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,7,23]]},"references-count":11,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2013,7]]}},"alternative-id":["s130709483"],"URL":"https:\/\/doi.org\/10.3390\/s130709483","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2013,7,23]]}}}