{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,16]],"date-time":"2025-09-16T21:10:00Z","timestamp":1758057000870,"version":"3.44.0"},"reference-count":32,"publisher":"Springer Science and Business Media LLC","issue":"9","license":[{"start":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T00:00:00Z","timestamp":1749081600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T00:00:00Z","timestamp":1749081600000},"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":["Des. Codes Cryptogr."],"published-print":{"date-parts":[[2025,9]]},"DOI":"10.1007\/s10623-025-01646-4","type":"journal-article","created":{"date-parts":[[2025,6,5]],"date-time":"2025-06-05T12:43:03Z","timestamp":1749127383000},"page":"3641-3669","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Optimizing and securing GLV multiplication over BLS pairings-friendly curves"],"prefix":"10.1007","volume":"93","author":[{"given":"Kamel Mohamed","family":"Faraoun","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nadia","family":"El Mrabet","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2025,6,5]]},"reference":[{"key":"1646_CR1","unstructured":"Aranha D.F., Gouv\u00eaa C.P.L., Markmann T., Wahby R.S., Liao K.: RELIC is an efficient library for cryptography. https:\/\/github.com\/relic-toolkit\/relic"},{"key":"1646_CR2","unstructured":"Arkworks Contributors. Arkworks zksnark ecosystem. https:\/\/arkworks.rs (2022)"},{"key":"1646_CR3","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1109\/TEC.1961.5219227","volume":"3","author":"A Avizienis","year":"1961","unstructured":"Avizienis A.: Signed-digit number representations for fast parallel arithmetic. IRE Trans. Electron. Comput. 3, 389\u2013400 (1961).","journal-title":"IRE Trans. Electron. Comput."},{"key":"1646_CR4","doi-asserted-by":"crossref","unstructured":"Barreto P.S., Lynn B., Scott M.: Constructing elliptic curves with prescribed embedding degrees. In Security in Communication Networks: Third International Conference, SCN 2002 Amalfi, Italy, September 11\u201313, 2002 Revised Papers 3, pp.\u00a0257\u2013267, Springer (2003)","DOI":"10.1007\/3-540-36413-7_19"},{"key":"1646_CR5","first-page":"56","volume-title":"International Conference on the Theory and Applications of Cryptographic Techniques","author":"D Boneh","year":"2004","unstructured":"Boneh D., Boyen X.: Short signatures without random oracles. In: International Conference on the Theory and Applications of Cryptographic Techniques, pp. 56\u201373. Springer, Cham (2004)."},{"key":"1646_CR6","first-page":"213","volume-title":"Annual International Cryptology Conference","author":"D Boneh","year":"2001","unstructured":"Boneh D., Franklin M.: Identity-based encryption from the weil pairing. In: Annual International Cryptology Conference, pp. 213\u2013229. Springer, Cham (2001)."},{"issue":"2","key":"1646_CR7","doi-asserted-by":"crossref","first-page":"236","DOI":"10.1093\/qjmam\/4.2.236","volume":"4","author":"AD Booth","year":"1951","unstructured":"Booth A.D.: A signed binary multiplication technique. Quart. J. Mech. Appl. Math. 4(2), 236\u2013240 (1951).","journal-title":"Quart. J. Mech. Appl. Math."},{"key":"1646_CR8","doi-asserted-by":"crossref","unstructured":"Bos J.W., Costello C., Naehrig M.: Exponentiating in pairing groups. In Selected Areas in Cryptography\u2013SAC 2013: 20th International Conference, Burnaby, BC, Canada, August 14-16, 2013, Revised Selected Papers 20, pp.\u00a0438\u2013455, Springer (2014)","DOI":"10.1007\/978-3-662-43414-7_22"},{"key":"1646_CR9","doi-asserted-by":"publisher","unstructured":"Botrel G., Piellard T., Housni Y.E., Tabaie A., Kubjas I.: Go library for finite fields, elliptic curves and pairings for zero-knowledge proof systems. https:\/\/doi.org\/10.5281\/zenodo.6092968 (2022)","DOI":"10.5281\/zenodo.6092968"},{"key":"1646_CR10","unstructured":"Developers T.R.P.: The rust programming language. https:\/\/www.rust-lang.org (2024) Version 1.x"},{"key":"1646_CR11","doi-asserted-by":"crossref","unstructured":"Dutta A., Hutchinson A., Karabina K.: Extending the signed non-zero bit and sign-aligned columns methods to general bases for use in cryptography. In International Conference on Cryptology in India, pp.\u00a0248\u2013270, Springer (2020)","DOI":"10.1007\/978-3-030-65277-7_11"},{"key":"1646_CR12","doi-asserted-by":"crossref","DOI":"10.1201\/9781315370170","volume-title":"Guide to Pairing-Based Cryptography","author":"N El Mrabet","year":"2017","unstructured":"El Mrabet N., Joye M.: Guide to Pairing-Based Cryptography. CRC Press, Baco Raton (2017)."},{"key":"1646_CR13","doi-asserted-by":"crossref","unstructured":"Faz-Hern\u00e1ndez A., Longa P., S\u00e1nchez A.H.: Efficient and secure algorithms for glv-based scalar multiplication and their implementation on glv-gls curves. In Topics in Cryptology \u2013 CT-RSA 2014, J.\u00a0Benaloh (ed.), vol.\u00a08366 of Lecture Notes in Computer Science, pp.\u00a01\u201327, Springer, Cham (2014)","DOI":"10.1007\/978-3-319-04852-9_1"},{"key":"1646_CR14","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1007\/s13389-014-0085-7","volume":"5","author":"A Faz-Hern\u00e1ndez","year":"2015","unstructured":"Faz-Hern\u00e1ndez A., Longa P., S\u00e1nchez A.H.: Efficient and secure algorithms for GLV-based scalar multiplication and their implementation on GLV-GLS curves (extended version). J. Cryptogr. Eng. 5, 31\u201352 (2015).","journal-title":"J. Cryptogr. Eng."},{"key":"1646_CR15","doi-asserted-by":"crossref","first-page":"224","DOI":"10.1007\/s00145-009-9048-z","volume":"23","author":"D Freeman","year":"2010","unstructured":"Freeman D., Scott M., Teske E.: A taxonomy of pairing-friendly elliptic curves. J. Cryptol. 23, 224\u2013280 (2010).","journal-title":"J. Cryptol."},{"key":"1646_CR16","doi-asserted-by":"crossref","unstructured":"Gallant R.P., Lambert R.J., Vanstone S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In Annual International Cryptology Conference, pp.\u00a0190\u2013200, Springer (2001)","DOI":"10.1007\/3-540-44647-8_11"},{"key":"1646_CR17","first-page":"1","volume-title":"Encyclopedia of Cryptography, Security and Privacy","author":"D Hankerson","year":"2021","unstructured":"Hankerson D., Menezes A.: Elliptic curve cryptography. In: Encyclopedia of Cryptography, Security and Privacy, pp. 1\u20132. Springer, Cham (2021)."},{"key":"1646_CR18","doi-asserted-by":"crossref","unstructured":"Joye M., Tunstall M.: Exponent recoding and regular exponentiation algorithms. In Progress in Cryptology\u2013AFRICACRYPT 2009: Second International Conference on Cryptology in Africa, Gammarth, Tunisia, June 21-25, 2009. Proceedings 2, pp.\u00a0334\u2013349, Springer (2009)","DOI":"10.1007\/978-3-642-02384-2_21"},{"key":"1646_CR19","doi-asserted-by":"crossref","unstructured":"Karabina K.: In: A survey of scalar multiplication algorithms, Chung, F., Graham, R., Hoffman, F., Mullin, RC, Hogben, L., West, DB (eds.), vol.\u00a050, pp.\u00a0359\u2013386 (2019)","DOI":"10.1201\/9780429280092-20"},{"key":"1646_CR20","unstructured":"Kilic O.: High-speed implementation of curves in go. https:\/\/github.com\/kilic\/bls12-381"},{"key":"1646_CR21","first-page":"345","volume-title":"Annual International Cryptology Conference","author":"K Koyama","year":"1992","unstructured":"Koyama K., Tsuruoka Y.: Speeding up elliptic cryptosystems by using a signed binary window method. In: Annual International Cryptology Conference, pp. 345\u2013357. Springer, Cham (1992)."},{"key":"1646_CR22","unstructured":"Faraoun K.M.: Efficient and constant-time rust implementation of pairings on BLS12, BLS24 and BLS48 curves. https:\/\/github.com\/kamel78\/efficient-rust-pairings"},{"key":"1646_CR23","unstructured":"Faraoun K.M.: Optimization of BLS elliptic curve scalar multiplication on $$\\mathbb{G}_1$$. https:\/\/github.com\/kamel78\/GLV-Endomorphism"},{"key":"1646_CR24","doi-asserted-by":"crossref","first-page":"324","DOI":"10.1007\/3-540-45439-X_22","volume-title":"International Conference on Information Security","author":"B M\u00f6ller","year":"2001","unstructured":"M\u00f6ller B.: Securing elliptic curve point multiplication against side-channel attacks. In: International Conference on Information Security, pp. 324\u2013334. Springer, Cham (2001)."},{"key":"1646_CR25","doi-asserted-by":"crossref","unstructured":"Okeya K., Takagi T.: The width-w naf method provides small memory and fast elliptic scalar multiplications secure against side channel attacks. In: Topics in Cryptology\u2013CT-RSA 2003: The Cryptographers\u2019 Track at the RSA Conference 2003 San Francisco, CA, USA, April 13\u201317, 2003 Proceedings, pp.\u00a0328\u2013343, Springer (2003)","DOI":"10.1007\/3-540-36563-X_23"},{"key":"1646_CR26","doi-asserted-by":"crossref","unstructured":"Pinto A.M.: An introduction to the use of zk-snarks in blockchains. In Mathematical Research for Blockchain Economy: 1st International Conference MARBLE 2019, Santorini, Greece, pp.\u00a0233\u2013249, Springer (2020)","DOI":"10.1007\/978-3-030-37110-4_16"},{"key":"1646_CR27","unstructured":"Qiao Z., Liang S., Davis S., Jiang H.: Survey of attribute based encryption. In 15th IEEE\/ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel\/Distributed Computing (SNPD)"},{"key":"1646_CR28","first-page":"231","volume-title":"Advances in Computers","author":"GW Reitwiesner","year":"1960","unstructured":"Reitwiesner G.W.: Binary arithmetic. In: Advances in Computers, vol. 1, pp. 231\u2013308. Elsevier, Amsterdam (1960)."},{"key":"1646_CR29","doi-asserted-by":"crossref","unstructured":"Rondepierre F.: Revisiting atomic patterns for scalar multiplications on elliptic curves. In International Conference on Smart Card Research and Advanced Applications, pp.\u00a0171\u2013186, Springer (2013)","DOI":"10.1007\/978-3-319-08302-5_12"},{"key":"1646_CR30","unstructured":"Sakemi Y., Kobayashi T., Saito T., Wahby R.S.: Pairing-friendly curves. Internet-Draft draft-irtf-cfrg-pairing-friendly-curves-08, May (2023)"},{"key":"1646_CR31","unstructured":"Zcash. Zero-knowledge cryptography in rust. https:\/\/github.com\/zkcrypto\/bls12_381"},{"key":"1646_CR32","doi-asserted-by":"crossref","unstructured":"Zhang F., Safavi-Naini R., Susilo W.: An efficient signature scheme from bilinear pairings and its applications. In Public Key Cryptography\u2013PKC 2004: 7th International Workshop on Theory and Practice in Public Key Cryptography, Singapore, March 1-4, 2004. Proceedings 7, pp.\u00a0277\u2013290, Springer (2004)","DOI":"10.1007\/978-3-540-24632-9_20"}],"container-title":["Designs, Codes and Cryptography"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01646-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10623-025-01646-4\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10623-025-01646-4.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,9,15]],"date-time":"2025-09-15T17:30:54Z","timestamp":1757957454000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10623-025-01646-4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,6,5]]},"references-count":32,"journal-issue":{"issue":"9","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["1646"],"URL":"https:\/\/doi.org\/10.1007\/s10623-025-01646-4","relation":{},"ISSN":["0925-1022","1573-7586"],"issn-type":[{"type":"print","value":"0925-1022"},{"type":"electronic","value":"1573-7586"}],"subject":[],"published":{"date-parts":[[2025,6,5]]},"assertion":[{"value":"14 October 2024","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 April 2025","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"2 May 2025","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 June 2025","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"The authors declare no competing interests.","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}}]}}