{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:59:31Z","timestamp":1772283571323,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":31,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662531396","type":"print"},{"value":"9783662531402","type":"electronic"}],"license":[{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2016,1,1]],"date-time":"2016-01-01T00:00:00Z","timestamp":1451606400000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2016]]},"DOI":"10.1007\/978-3-662-53140-2_25","type":"book-chapter","created":{"date-parts":[[2016,8,3]],"date-time":"2016-08-03T15:33:43Z","timestamp":1470238423000},"page":"517-537","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Four$$\\mathbb {Q}$$ on FPGA: New Hardware Speed Records for Elliptic Curve Cryptography over Large Prime Characteristic Fields"],"prefix":"10.1007","author":[{"given":"Kimmo","family":"J\u00e4rvinen","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrea","family":"Miele","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Reza","family":"Azarderakhsh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Patrick","family":"Longa","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2016,8,4]]},"reference":[{"issue":"8","key":"25_CR1","doi-asserted-by":"publisher","first-page":"1453","DOI":"10.1109\/TVLSI.2011.2158595","volume":"20","author":"R Azarderakhsh","year":"2012","unstructured":"Azarderakhsh, R., Reyhani-Masoleh, A.: Efficient FPGA implementations of point multiplication on binary Edwards and generalized Hessian curves using Gaussian normal basis. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 20(8), 1453\u20131466 (2012)","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"issue":"6","key":"25_CR2","doi-asserted-by":"publisher","first-page":"1668","DOI":"10.1109\/TPDS.2014.2323062","volume":"26","author":"R Azarderakhsh","year":"2015","unstructured":"Azarderakhsh, R., Reyhani-Masoleh, A.: Parallel and high-speed computations of elliptic curve cryptography using hybrid-double multipliers. IEEE Trans. Parallel Distrib. Syst. 26(6), 1668\u20131677 (2015)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"issue":"1","key":"25_CR3","doi-asserted-by":"publisher","first-page":"91","DOI":"10.1007\/s12095-014-0111-8","volume":"7","author":"A Bauer","year":"2015","unstructured":"Bauer, A., Jaulmes, E., Prouff, E., Reinhard, J.R., Wild, J.: Horizontal collision correlation attack on elliptic curves. Crypt. Commun. 7(1), 91\u2013119 (2015)","journal-title":"Crypt. Commun."},{"key":"25_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"389","DOI":"10.1007\/978-3-540-68164-9_26","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2008","author":"DJ Bernstein","year":"2008","unstructured":"Bernstein, D.J., Birkner, P., Joye, M., Lange, T., Peters, C.: Twisted Edwards curves. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 389\u2013405. Springer, Heidelberg (2008)"},{"key":"25_CR5","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"207","DOI":"10.1007\/11745853_14","volume-title":"Public Key Cryptography - PKC 2006","author":"DJ Bernstein","year":"2006","unstructured":"Bernstein, D.J.: Curve25519: new Diffie-Hellman speed records. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958, pp. 207\u2013228. Springer, Heidelberg (2006)"},{"key":"25_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"214","DOI":"10.1007\/978-3-662-48797-6_10","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2015","author":"C Costello","year":"2015","unstructured":"Costello, C., Longa, P.: Four$$\\mathbb{Q}$$: four-dimensional decompositions on a Q-curve over the Mersenne prime. In: Iwata, T., et al. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 214\u2013235. Springer, Heidelberg (2015). \n                      https:\/\/eprint.iacr.org\/2015\/565"},{"issue":"1","key":"25_CR7","doi-asserted-by":"publisher","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. Cryptographic Eng. 5(1), 31\u201352 (2015)","journal-title":"J. Cryptographic Eng."},{"key":"25_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"190","DOI":"10.1007\/3-540-44647-8_11","volume-title":"Advances in Cryptology - CRYPTO 2001","author":"RP Gallant","year":"2001","unstructured":"Gallant, R.P., Lambert, R.J., Vanstone, S.A.: Faster point multiplication on elliptic curves with efficient endomorphisms. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 190\u2013200. Springer, Heidelberg (2001)"},{"key":"25_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"48","DOI":"10.1007\/978-3-642-15031-9_4","volume-title":"Cryptographic Hardware and Embedded Systems, CHES 2010","author":"N Guillermin","year":"2010","unstructured":"Guillermin, N.: A high speed coprocessor for elliptic curve scalar multiplications over $$\\mathbb{F}_p$$. In: Mangard, S., Standaert, F.-X. (eds.) CHES 2010. LNCS, vol. 6225, pp. 48\u201364. Springer, Heidelberg (2010)"},{"key":"25_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"79","DOI":"10.1007\/978-3-642-42033-7_5","volume-title":"Advances in Cryptology - ASIACRYPT 2013","author":"A Guillevic","year":"2013","unstructured":"Guillevic, A., Ionica, S.: Four-dimensional GLV via the Weil restriction. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 79\u201396. Springer, Heidelberg (2013)"},{"key":"25_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1007\/978-3-540-85053-3_5","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2008","author":"T G\u00fcneysu","year":"2008","unstructured":"G\u00fcneysu, T., Paar, C.: Ultra high performance ECC over NIST primes on commercial FPGAs. In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 62\u201378. Springer, Heidelberg (2008)"},{"key":"25_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"326","DOI":"10.1007\/978-3-540-89255-7_20","volume-title":"Advances in Cryptology - ASIACRYPT 2008","author":"H Hisil","year":"2008","unstructured":"Hisil, H., Wong, K.K.-H., Carter, G., Dawson, E.: Twisted Edwards curves revisited. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 326\u2013343. Springer, Heidelberg (2008)"},{"issue":"9","key":"25_CR13","doi-asserted-by":"publisher","first-page":"1162","DOI":"10.1109\/TVLSI.2008.2000728","volume":"16","author":"K J\u00e4rvinen","year":"2008","unstructured":"J\u00e4rvinen, K., Skytt\u00e4, J.: On parallelization of high-speed processors for elliptic curve cryptography. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 16(9), 1162\u20131175 (2008)","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"issue":"4","key":"25_CR14","doi-asserted-by":"publisher","first-page":"270","DOI":"10.1016\/j.vlsi.2010.08.001","volume":"44","author":"K J\u00e4rvinen","year":"2011","unstructured":"J\u00e4rvinen, K., Skytt\u00e4, J.: Optimized FPGA-based elliptic curve cryptography processor for high-speed applications. Integr. VLSI J. 44(4), 270\u2013279 (2011)","journal-title":"Integr. VLSI J."},{"key":"25_CR15","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1090\/S0025-5718-1987-0866109-5","volume":"48","author":"N Koblitz","year":"1987","unstructured":"Koblitz, N.: Elliptic curve cryptosystems. Math. Comput. 48, 203\u2013209 (1987)","journal-title":"Math. Comput."},{"key":"25_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"104","DOI":"10.1007\/3-540-68697-5_9","volume-title":"Advances in Cryptology - CRYPTO \u201996","author":"PC Kocher","year":"1996","unstructured":"Kocher, P.C.: Timing attacks on implementations of Diffie-Hellman, RSA, DSS, and other systems. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 104\u2013113. Springer, Heidelberg (1996)"},{"key":"25_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"388","DOI":"10.1007\/3-540-48405-1_25","volume-title":"Advances in Cryptology - CRYPTO \u201999","author":"PC Kocher","year":"1999","unstructured":"Kocher, P.C., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 388\u2013397. Springer, Heidelberg (1999)"},{"issue":"4\u20135","key":"25_CR18","doi-asserted-by":"publisher","first-page":"394","DOI":"10.1016\/j.micpro.2013.03.003","volume":"37","author":"KCC Loi","year":"2013","unstructured":"Loi, K.C.C., Ko, S.B.: High performance scalable elliptic curve cryptosystem processor for Koblitz curves. Microprocess. Microsyst. 37(4\u20135), 394\u2013406 (2013)","journal-title":"Microprocess. Microsyst."},{"issue":"11","key":"25_CR19","doi-asserted-by":"publisher","first-page":"2753","DOI":"10.1109\/TVLSI.2014.2375640","volume":"23","author":"KCC Loi","year":"2015","unstructured":"Loi, K.C.C., Ko, S.B.: Scalable elliptic curve cryptosystem FPGA processor for NIST prime curves. IEEE Trans. Very Large Scale Integr. (VLSI) Syst. 23(11), 2753\u20132756 (2015)","journal-title":"IEEE Trans. Very Large Scale Integr. (VLSI) Syst."},{"key":"25_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"421","DOI":"10.1007\/978-3-662-43414-7_21","volume-title":"Selected Areas in Cryptography \u2013 SAC 2013","author":"Y Ma","year":"2014","unstructured":"Ma, Y., Liu, Z., Pan, W., Jing, J.: A high-speed elliptic curve cryptographic processor for generic curves over GF(p). In: Lange, T., Lauter, K., Lison\u011bk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 421\u2013437. Springer, Heidelberg (2014)"},{"key":"25_CR21","first-page":"589","volume":"2004","author":"CJ McIvor","year":"2004","unstructured":"McIvor, C.J., McLoone, M., McCanny, J.V.: An FPGA elliptic curve cryptographic accelerator over $$GF(p)$$. Proc. Irish Signals Syst. Conf. 2004, 589\u2013594 (2004)","journal-title":"Proc. Irish Signals Syst. Conf."},{"issue":"9","key":"25_CR22","doi-asserted-by":"publisher","first-page":"1946","DOI":"10.1109\/TCSI.2006.880184","volume":"55","author":"CJ McIvor","year":"2006","unstructured":"McIvor, C.J., McLoone, M., McCanny, J.V.: Hardware elliptic curve cryptographic processor over $$GF(p)$$. IEEE Trans. Circuits Syst. I Regul. Pap. 55(9), 1946\u20131957 (2006)","journal-title":"IEEE Trans. Circuits Syst. I Regul. Pap."},{"key":"25_CR23","unstructured":"Mentens, N.: Secure and efficient coprocessor design for cryptographic applications on FPGAs. Ph.D. thesis, Katholieke Universiteit Leuven, July 2007"},{"key":"25_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1007\/3-540-39799-X_31","volume-title":"Advances in Cryptology","author":"VS Miller","year":"1986","unstructured":"Miller, V.S.: Use of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol. 218, pp. 417\u2013426. Springer, Heidelberg (1986)"},{"issue":"177","key":"25_CR25","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1090\/S0025-5718-1987-0866113-7","volume":"48","author":"PL Montgomery","year":"1987","unstructured":"Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Math. Comput. 48(177), 243\u2013264 (1987)","journal-title":"Math. Comput."},{"key":"25_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1007\/978-3-642-33027-8_29","volume-title":"Cryptographic Hardware and Embedded Systems \u2013 CHES 2012","author":"C Rebeiro","year":"2012","unstructured":"Rebeiro, C., Roy, S.S., Mukhopadhyay, D.: Pushing the limits of high-speed $$GF(2^{m})$$ elliptic curve scalar multiplication on FPGAs. In: Prouff, E., Schaumont, P. (eds.) CHES 2012. LNCS, vol. 7428, pp. 494\u2013511. Springer, Heidelberg (2012)"},{"key":"25_CR27","doi-asserted-by":"crossref","unstructured":"Roy, D.B., Mukhopadhyay, D., Izumi, M., Takahashi, J.: Tile before multiplication: an efficient strategy to optimize DSP multiplier for accelerating prime field ECC for NIST curves. In: Proceedings of the 51st Annual Design Automation Conference\u2013DAC 2014, pp. 177: 1\u2013177: 6. ACM (2014)","DOI":"10.1145\/2593069.2593234"},{"key":"25_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1007\/978-3-319-05960-0_3","volume-title":"Reconfigurable Computing: Architectures, Tools, and Applications","author":"P Sasdrich","year":"2014","unstructured":"Sasdrich, P., G\u00fcneysu, T.: Efficient elliptic-curve cryptography using Curve25519 on reconfigurable devices. In: Goehringer, D., Santambrogio, M.D., Cardoso, J.M.P., Bertels, K. (eds.) ARC 2014. LNCS, vol. 8405, pp. 25\u201336. Springer, Heidelberg (2014)"},{"issue":"1","key":"25_CR29","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/2700834","volume":"9","author":"Pascal Sasdrich","year":"2015","unstructured":"Sasdrich, P., G\u00fcneysu, T.: Implementing Curve25519 for side-channel-protected elliptic curve cryptography. ACM Trans. Reconfigurable Technol. Syst. 9(1), (2015). Article 3","journal-title":"ACM Transactions on Reconfigurable Technology and Systems"},{"key":"25_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"61","DOI":"10.1007\/978-3-642-42033-7_4","volume-title":"Advances in Cryptology - ASIACRYPT 2013","author":"B Smith","year":"2013","unstructured":"Smith, B.: Families of fast elliptic curves from $$\\mathbb{Q}$$-curves. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part I. LNCS, vol. 8269, pp. 61\u201378. Springer, Heidelberg (2013)"},{"issue":"1","key":"25_CR31","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1109\/TIE.2012.2186104","volume":"60","author":"GD Sutter","year":"2013","unstructured":"Sutter, G.D., Deschamps, J.P., Ima\u00f1a, J.L.: Efficient elliptic curve point multiplication using digit-serial binary field operations. IEEE Trans. Industr. Electron. 60(1), 217\u2013225 (2013)","journal-title":"IEEE Trans. Industr. Electron."}],"container-title":["Lecture Notes in Computer Science","Cryptographic Hardware and Embedded Systems \u2013 CHES 2016"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-53140-2_25","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,3]],"date-time":"2020-08-03T00:05:42Z","timestamp":1596413142000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-53140-2_25"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016]]},"ISBN":["9783662531396","9783662531402"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-53140-2_25","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016]]},"assertion":[{"value":"4 August 2016","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}},{"value":"CHES","order":1,"name":"conference_acronym","label":"Conference Acronym","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"International Conference on Cryptographic Hardware and Embedded Systems","order":2,"name":"conference_name","label":"Conference Name","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"Santa Barbara","order":3,"name":"conference_city","label":"Conference City","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"USA","order":4,"name":"conference_country","label":"Conference Country","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"2016","order":5,"name":"conference_year","label":"Conference Year","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"17 August 2016","order":7,"name":"conference_start_date","label":"Conference Start Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"19 August 2016","order":8,"name":"conference_end_date","label":"Conference End Date","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"18","order":9,"name":"conference_number","label":"Conference Number","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"ches2016","order":10,"name":"conference_id","label":"Conference ID","group":{"name":"ConferenceInfo","label":"Conference Information"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}