{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,20]],"date-time":"2025-10-20T18:00:04Z","timestamp":1760983204708},"publisher-location":"Berlin, Heidelberg","reference-count":31,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642054433"},{"type":"electronic","value":"9783642054457"}],"license":[{"start":{"date-parts":[[2009,1,1]],"date-time":"2009-01-01T00:00:00Z","timestamp":1230768000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2009]]},"DOI":"10.1007\/978-3-642-05445-7_22","type":"book-chapter","created":{"date-parts":[[2009,11,3]],"date-time":"2009-11-03T10:03:23Z","timestamp":1257242603000},"page":"350-363","source":"Crossref","is-referenced-by-count":24,"title":["Highly Regular m-Ary Powering Ladders"],"prefix":"10.1007","author":[{"given":"Marc","family":"Joye","sequence":"first","affiliation":[]}],"member":"297","reference":[{"key":"22_CR1","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"203","DOI":"10.1007\/978-3-540-74462-7_15","volume-title":"Selected Areas in Cryptography","author":"R.M. Avanzi","year":"2007","unstructured":"Avanzi, R.M.: Delaying and merging operations in scalar multiplication: Applications to curve-based cryptosystems. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol.\u00a04356, pp. 203\u2013219. Springer, Heidelberg (2007)"},{"key":"22_CR2","unstructured":"Bar-El, H., Choukri, H., Naccache, D., Tunstall, M., Whelan, C.: The sorcerer\u2019s apprentice guide to fault attacks. Proceedings the IEEE\u00a094(2), 370\u2013382 (2004); Earlier version in Proc. of FDTC\u00a02004"},{"key":"22_CR3","unstructured":"Bernstein, D.J., Lange, T.: Explicit-formulas database, \n                    \n                      http:\/\/www.hyperelliptic.org\/EFD\/jacobian.html"},{"key":"22_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/978-3-540-76900-2_3","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2007","author":"D.J. Bernstein","year":"2007","unstructured":"Bernstein, D.J., Lange, T.: Faster addition and doubling on elliptic curves. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol.\u00a04833, pp. 29\u201350. Springer, Heidelberg (2007)"},{"issue":"2","key":"22_CR5","doi-asserted-by":"crossref","first-page":"110","DOI":"10.1007\/s001450010016","volume":"14","author":"D. Boneh","year":"2001","unstructured":"Boneh, D., DeMillo, R.A., Lipton, R.J.: On the importance of eliminating errors in cryptographic computations. Journal of Cryptology\u00a014(2), 110\u2013119 (2001); Extended abstract in Proc. of EUROCRYPT 1997","journal-title":"Journal of Cryptology"},{"volume-title":"Cryptographic Engineering","year":"2009","key":"22_CR6","unstructured":"Ko\u00e7, \u00c7.K. (ed.): Cryptographic Engineering. Springer, Heidelberg (2009)"},{"issue":"4","key":"22_CR7","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/0196-8858(86)90023-0","volume":"7","author":"D.V. Chudnovsky","year":"1986","unstructured":"Chudnovsky, D.V., Chudnovsky, G.V.: Sequences of numbers generated by addition in formal groups and new primality and factorization tests. Advances in Applied Mathematics\u00a07(4), 385\u2013434 (1986)","journal-title":"Advances in Applied Mathematics"},{"key":"22_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"51","DOI":"10.1007\/3-540-49649-1_6","volume-title":"Advances in Cryptology - ASIACRYPT\u201998","author":"H. Cohen","year":"1998","unstructured":"Cohen, H., Miyaji, A., Ono, T.: Efficient elliptic curve exponentiation using mixed coordinates. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol.\u00a01514, pp. 51\u201365. Springer, Heidelberg (1998)"},{"key":"22_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"292","DOI":"10.1007\/3-540-48059-5_25","volume-title":"Cryptographic Hardware and Embedded Systems","author":"J.-S. Coron","year":"1999","unstructured":"Coron, J.-S.: Resistance against differential power analysis for elliptic curve cryptosystems. In: Ko\u00e7, \u00c7.K., Paar, C. (eds.) CHES 1999. LNCS, vol.\u00a01717, pp. 292\u2013302. Springer, Heidelberg (1999)"},{"key":"22_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"251","DOI":"10.1007\/3-540-44709-1_21","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2001","author":"K. Gandolfi","year":"2001","unstructured":"Gandolfi, K., Mourtel, C., Olivier, F.: Electromagnetic analysis: Concrete results. In: Ko\u00e7, \u00c7.K., Naccache, D., Paar, C. (eds.) CHES 2001. LNCS, vol.\u00a02162, pp. 251\u2013261. Springer, Heidelberg (2001)"},{"key":"22_CR11","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1007\/1-4020-8147-2_11","volume-title":"Smart Card Research and Advanced Applications VI (CARDIS\u00a02004)","author":"C. Giraud","year":"2004","unstructured":"Giraud, C., Thiebeauld, H.: A survey on fault attacks. In: Quisquater, J.-J., et al. (eds.) Smart Card Research and Advanced Applications VI (CARDIS\u00a02004), pp. 159\u2013176. Kluwer, Dordrecht (2004)"},{"key":"22_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"135","DOI":"10.1007\/978-3-540-74735-2_10","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2007","author":"M. Joye","year":"2007","unstructured":"Joye, M.: Highly regular right-to-left algorithms for scalar multiplication. In: Paillier, P., Verbauwhede, I. (eds.) CHES 2007. LNCS, vol.\u00a04727, pp. 135\u2013147. Springer, Heidelberg (2007)"},{"key":"22_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"36","DOI":"10.1007\/978-3-540-69499-1_4","volume-title":"Arithmetic of Finite Fields","author":"M. Joye","year":"2008","unstructured":"Joye, M.: Fast point multiplication on elliptic curves without precomputation. In: von zur Gathen, J., Ima\u00f1a, J.L., Ko\u00e7, \u00c7.K. (eds.) WAIFI 2008. LNCS, vol.\u00a05130, pp. 36\u201346. Springer, Heidelberg (2008)"},{"key":"22_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"291","DOI":"10.1007\/3-540-36400-5_22","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2002","author":"M. Joye","year":"2003","unstructured":"Joye, M., Yen, S.-M.: The Montgomery powering ladder. In: Kaliski Jr., B.S., Ko\u00e7, \u00c7.K., Paar, C. (eds.) CHES 2002. LNCS, vol.\u00a02523, pp. 291\u2013302. Springer, Heidelberg (2003)"},{"key":"22_CR15","series-title":"Seminumerical Algorithms","volume-title":"The Art of Computer Programming","author":"D.E. Knuth","year":"1981","unstructured":"Knuth, D.E.: The Art of Computer Programming, 2nd edn. Seminumerical Algorithms, vol.\u00a02. Addison-Wesley, Reading (1981)","edition":"2"},{"key":"22_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"388","DOI":"10.1007\/3-540-48405-1_25","volume-title":"Advances in Cryptology - CRYPTO \u201999","author":"P. Kocher","year":"1999","unstructured":"Kocher, P., Jaffe, J., Jun, B.: Differential power analysis. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol.\u00a01666, pp. 388\u2013397. Springer, Heidelberg (1999)"},{"key":"22_CR17","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":"P.C. 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.\u00a01109, pp. 104\u2013113. Springer, Heidelberg (1996)"},{"key":"22_CR18","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"229","DOI":"10.1007\/978-3-540-78440-1_14","volume-title":"Public Key Cryptography \u2013 PKC 2008","author":"P. Longa","year":"2008","unstructured":"Longa, P., Miri, A.: New composite operations and precomputation scheme for elliptic curve cryptosystems over prime fields. In: Cramer, R. (ed.) PKC 2008. LNCS, vol.\u00a04939, pp. 229\u2013247. Springer, Heidelberg (2008)"},{"key":"22_CR19","volume-title":"Power Analysis Attacks: Revealing the Secrets of Smart Cards","author":"S. Mangard","year":"2007","unstructured":"Mangard, S., Oswald, E., Popp, T.: Power Analysis Attacks: Revealing the Secrets of Smart Cards. Springer, Heidelberg (2007)"},{"key":"22_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"189","DOI":"10.1007\/978-3-540-73074-3_15","volume-title":"Arithmetic of Finite Fields","author":"N. Meloni","year":"2007","unstructured":"Meloni, N.: New point addition formul\u00e6 for ECC applications. In: Carlet, C., Sunar, B. (eds.) WAIFI 2007. LNCS, vol.\u00a04547, pp. 189\u2013201. Springer, Heidelberg (2007)"},{"key":"22_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1007\/3-540-45439-X_22","volume-title":"Information Security","author":"B. M\u00f6ller","year":"2001","unstructured":"M\u00f6ller, B.: Securing elliptic curve point multiplication against side-channel attacks. In: Davida, G.I., Frankel, Y. (eds.) ISC 2001. LNCS, vol.\u00a02200, pp. 324\u2013334. Springer, Heidelberg (2001)"},{"issue":"177","key":"22_CR22","doi-asserted-by":"publisher","first-page":"243","DOI":"10.2307\/2007888","volume":"48","author":"P.L. Montgomery","year":"1987","unstructured":"Montgomery, P.L.: Speeding the Pollard and elliptic curve methods of factorization. Mathematics of Computation\u00a048(177), 243\u2013264 (1987)","journal-title":"Mathematics of Computation"},{"key":"22_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"328","DOI":"10.1007\/3-540-36563-X_23","volume-title":"Topics in Cryptology - CT-RSA 2003","author":"K. Okeya","year":"2003","unstructured":"Okeya, K., Takagi, T.: The width-w NAF method provides small memory and fast elliptic scalar multiplications secure against side channel attacks. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol.\u00a02612, pp. 328\u2013342. Springer, Heidelberg (2003)"},{"key":"22_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"200","DOI":"10.1007\/3-540-45418-7_17","volume-title":"Smart Card Programming and Security","author":"J.-J. Quisquater","year":"2001","unstructured":"Quisquater, J.-J., Samyde, D.: Electromagnetic analysis (EMA): Measures and counter-measures for smart cards. In: Attali, S., Jensen, T. (eds.) E-smart 2001. LNCS, vol.\u00a02140, pp. 200\u2013210. Springer, Heidelberg (2001)"},{"issue":"2","key":"22_CR25","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R.L. Rivest","year":"1978","unstructured":"Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM\u00a021(2), 120\u2013126 (1978)","journal-title":"Communications of the ACM"},{"key":"22_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"298","DOI":"10.1007\/978-3-540-28632-5_22","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2004","author":"Y. Sakai","year":"2004","unstructured":"Sakai, Y., Sakurai, K.: A new attack with side channel leakage during exponent recoding computations. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol.\u00a03156, pp. 298\u2013311. Springer, Heidelberg (2004)"},{"key":"22_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1007\/11693383_24","volume-title":"Selected Areas in Cryptography","author":"N. Th\u00e9riault","year":"2006","unstructured":"Th\u00e9riault, N.: SPA resistant left-to-right integer recodings. In: Preneel, B., Tavares, S. (eds.) SAC 2005. LNCS, vol.\u00a03897, pp. 345\u2013358. Springer, Heidelberg (2006)"},{"key":"22_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"268","DOI":"10.1007\/11767480_18","volume-title":"Applied Cryptography and Network Security","author":"C. Vuillaume","year":"2006","unstructured":"Vuillaume, C., Okeya, K.: Flexible exponentiation with resistance to side channel attacks. In: Zhou, J., Yung, M., Bao, F. (eds.) ACNS 2006. LNCS, vol.\u00a03989, pp. 268\u2013283. Springer, Heidelberg (2006)"},{"issue":"1","key":"22_CR29","doi-asserted-by":"publisher","first-page":"100","DOI":"10.1137\/0205008","volume":"5","author":"A.C. Yao","year":"1976","unstructured":"Yao, A.C.: On the evaluation of powers. SIAM Journal on Computing\u00a05(1), 100\u2013103 (1976)","journal-title":"SIAM Journal on Computing"},{"issue":"9","key":"22_CR30","doi-asserted-by":"publisher","first-page":"967","DOI":"10.1109\/12.869328","volume":"49","author":"S.-M. Yen","year":"2000","unstructured":"Yen, S.-M., Joye, M.: Checking before output may not be enough against fault-based cryptanalysis. IEEE Transactions on Computers\u00a049(9), 967\u2013970 (2000)","journal-title":"IEEE Transactions on Computers"},{"key":"22_CR31","series-title":"Lecture Notes in Computer Science","first-page":"414","volume-title":"Information Security and Cryptology - ICISC 2001","author":"S.-M. Yen","year":"2002","unstructured":"Yen, S.-M., Kim, S.-J., Lim, S.-G., Moon, S.-J.: A countermeasure against one physical cryptanalysis may benefit another attack. In: Kim, K.-c. (ed.) ICISC 2001. LNCS, vol.\u00a02288, pp. 414\u2013427. Springer, Heidelberg (2002)"}],"container-title":["Lecture Notes in Computer Science","Selected Areas in Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-05445-7_22","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,29]],"date-time":"2020-01-29T11:36:16Z","timestamp":1580297776000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-05445-7_22"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009]]},"ISBN":["9783642054433","9783642054457"],"references-count":31,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-05445-7_22","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2009]]}}}