{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,28]],"date-time":"2025-11-28T04:46:43Z","timestamp":1764305203398},"publisher-location":"Berlin, Heidelberg","reference-count":42,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540408338"},{"type":"electronic","value":"9783540452386"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/978-3-540-45238-6_28","type":"book-chapter","created":{"date-parts":[[2010,6,23]],"date-time":"2010-06-23T20:04:43Z","timestamp":1277323483000},"page":"351-365","source":"Crossref","is-referenced-by-count":48,"title":["Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves"],"prefix":"10.1007","author":[{"given":"Jan","family":"Pelzl","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Thomas","family":"Wollinger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jorge","family":"Guajardo","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Christof","family":"Paar","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"key":"28_CR1","unstructured":"ANSI X9.62-1999. The Elliptic Curve Digital Signature Algorithm. Technical report, ANSI (1999)"},{"key":"28_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"400","DOI":"10.1007\/3-540-36400-5_29","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2002","author":"N. Boston","year":"2003","unstructured":"Boston, N., Clancy, T., Liow, Y., Webster, J.: Genus Two Hyperelliptic Curve Coprocessor. In: Kaliski Jr., B.S., Ko\u00e7, \u00c7.K., Paar, C. (eds.) CHES 2002. LNCS, vol.\u00a02523, pp. 400\u2013414. Springer, Heidelberg (2003)"},{"key":"28_CR3","series-title":"London Mathematical Society Lecture Notes Series","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781107360211","volume-title":"Elliptic Curves in Cryptography","author":"I.F. Blake","year":"1999","unstructured":"Blake, I.F., Seroussi, G., Smart, N.P.: Elliptic Curves in Cryptography. London Mathematical Society Lecture Notes Series, vol.\u00a0265. Cambridge University Press, Reading (1999)"},{"issue":"177","key":"28_CR4","doi-asserted-by":"publisher","first-page":"95","DOI":"10.1090\/S0025-5718-1987-0866101-0","volume":"48","author":"D.G. Cantor","year":"1987","unstructured":"Cantor, D.G.: Computing in Jacobian of a Hyperelliptic Curve. Mathematics of Computation\u00a048(177), 95\u2013101 (1987)","journal-title":"Mathematics of Computation"},{"key":"28_CR5","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1016\/0196-8858(86)90023-0","volume":"7","author":"D.V. Chudnovsky","year":"1987","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, 385\u2013434 (1987)","journal-title":"Advances in Applied Mathematics"},{"key":"28_CR6","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":"28_CR7","doi-asserted-by":"crossref","unstructured":"Cohen, H.: A course in computational number theory. Graduate Texts in Math., vol.\u00a0138. Springer, Berlin (1993), Third corrected printing (1996)","DOI":"10.1007\/978-3-662-02945-9"},{"key":"28_CR8","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"IT-22","author":"W. Diffie","year":"1976","unstructured":"Diffie, W., Hellman, M.E.: New directions in cryptography. IEEE Transactions on Information Theory,\u00a0IT-22, 644\u2013654 (1976)","journal-title":"IEEE Transactions on Information Theory,"},{"key":"28_CR9","unstructured":"Enge, A.: The extended Euclidean algorithm on polynomials, and the computational efficiency of hyperelliptic cryptosystems (November 1999) (preprint)"},{"issue":"206","key":"28_CR10","first-page":"865","volume":"62","author":"G. Frey","year":"1994","unstructured":"Frey, G., R\u00fcck, H.-G.: A remark concerning m-divisibility and the discrete logarithm in the divisor class group of curves. Mathematics of Computation\u00a062(206), 865\u2013874 (1994)","journal-title":"Mathematics of Computation"},{"key":"28_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"495","DOI":"10.1007\/3-540-45682-1_29","volume-title":"Advances in Cryptology - ASIACRYPT 2001","author":"S.D. Galbraith","year":"2001","unstructured":"Galbraith, S.D.: Supersingular curves in cryptography. In: Boyd, C. (ed.) ASIACRYPT 2001. LNCS, vol.\u00a02248, pp. 495\u2013517. Springer, Heidelberg (2001)"},{"key":"28_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"19","DOI":"10.1007\/3-540-45539-6_2","volume-title":"Advances in Cryptology - EUROCRYPT 2000","author":"P. Gaudry","year":"2000","unstructured":"Gaudry, P.: An algorithm for solving the discrete log problem on hyperelliptic curves. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol.\u00a01807, pp. 19\u201334. Springer, Heidelberg (2000)"},{"key":"28_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"297","DOI":"10.1007\/10722028_18","volume-title":"Algorithmic Number Theory","author":"P. Gaudry","year":"2000","unstructured":"Gaudry, P., Harley, R.: Counting Points on Hyperelliptic Curves over Finite Fields. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol.\u00a01838, pp. 297\u2013312. Springer, Heidelberg (2000)"},{"key":"28_CR14","unstructured":"Harley, R.: Fast Arithmetic on Genus Two Curves (2000), Available at \n                    \n                      http:\/\/cristal.inria.fr\/~harley\/hyper\/"},{"key":"28_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-44499-8_1","volume-title":"Cryptographic Hardware and Embedded Systems - CHES 2000","author":"D. Hankerson","year":"2000","unstructured":"Hankerson, D., L\u00f3pez Hernandez, J., Menezes, A.: Software Implementation of Elliptic Curve Cryptography Over Binary Fields. In: Paar, C., Ko\u00e7, \u00c7.K. (eds.) CHES 2000. LNCS, vol.\u00a01965, pp. 1\u201324. Springer, Heidelberg (2000)"},{"key":"28_CR16","unstructured":"Kuroki, J., Gonda, M., Matsuo, K., Chao, J., Tsujii, S.: Fast Genus Three Hyperelliptic Curve Cryptosystems. In: The 2002 Symposium on Cryptography and Information Security, Japan \u2013 SCIS 2002, January 29-February 1 (2002)"},{"issue":"7","key":"28_CR17","first-page":"595","volume":"7","author":"A. Karatsuba","year":"1963","unstructured":"Karatsuba, A., Ofman, Y.: Multiplication of multidigit numbers on automata. Sov. Phys. Dokl (English translation)\u00a07(7), 595\u2013596 (1963)","journal-title":"Sov. Phys. Dokl. (English translation)"},{"key":"28_CR18","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. Mathematics of Computation\u00a048, 203\u2013209 (1987)","journal-title":"Mathematics of Computation"},{"key":"28_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"94","DOI":"10.1007\/0-387-34799-2_8","volume-title":"Advances in Cryptology - CRYPTO \u201988","author":"N. Koblitz","year":"1990","unstructured":"Koblitz, N.: A Family of Jacobians Suitable for Discrete Log Cryptosystems. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol.\u00a0403, pp. 94\u201399. Springer, Heidelberg (1990)"},{"key":"28_CR20","doi-asserted-by":"crossref","unstructured":"Koblitz, N.: Hyperelliptic Cryptosystems. In: Brickell, E.F. (ed.) Journal of Cryptology, pp. 139\u2013150 (1989)","DOI":"10.1007\/BF02252872"},{"key":"28_CR21","series-title":"Algorithms and Computation in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-03642-6","volume-title":"Algebraic Aspects of Cryptography","author":"N. Koblitz","year":"1998","unstructured":"Koblitz, N.: Algebraic Aspects of Cryptography. Algorithms and Computation in Mathematics. Springer, Heidelberg (1998)"},{"key":"28_CR22","unstructured":"Krieger, U.: signature.c, Diplomarbeit, Universit\u00e4t Essen, Fachbereich 6 (Mathematik und Informatik) (February 1997)"},{"key":"28_CR23","unstructured":"Lange, T.: Efficient Arithmetic on Genus 2 Hyperelliptic Curves over Finite Fields via Explicit Formulae. Cryptology ePrint Archive, Report 2002\/121 (2002), \n                    \n                      http:\/\/eprint.iacr.org\/"},{"key":"28_CR24","unstructured":"Lange, T.: Inversion-Free Arithmetic on Genus 2 Hyperelliptic Curves. Cryptology ePrint Archive, Report 2002\/147 (2002), \n                    \n                      http:\/\/eprint.iacr.org\/"},{"key":"28_CR25","unstructured":"Lange, T.: Weighted Coordinates on Genus 2 Hyperelliptic Curves. Cryptology ePrint Archive, Report 2002\/153 (2002), \n                    \n                      http:\/\/eprint.iacr.org\/"},{"key":"28_CR26","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1007\/3-540-48892-8_16","volume-title":"Selected Areas in Cryptography","author":"J. L\u00f3pez","year":"1999","unstructured":"L\u00f3pez, J., Dahab, R.: Improved algorithms for elliptic curve arithmetic in GF(2\n                    n\n                  ). In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol.\u00a01556, pp. 201\u2013212. Springer, Heidelberg (1999)"},{"key":"28_CR27","doi-asserted-by":"crossref","unstructured":"Lopez, J., Dahab, R.: High-speed software multiplication in \n                    \n                      \n                    \n                    $$\n\\mathbb{F}_2 \n$$\n                  \n                  \n                    m\n                  . In: Roy, B., Okamoto, E. (eds.) INDOCRYPT 2000. LNCS, vol.\u00a01977, pp. 203\u2013212. Springer, Heidelberg (2000)","DOI":"10.1007\/3-540-44495-5_18"},{"key":"28_CR28","unstructured":"Matsuo, K., Chao, J., Tsujii, S.: Fast Genus Two Hyperelliptic Curve Cryptosystems. In: ISEC2001-31, IEICE (2001)"},{"key":"28_CR29","unstructured":"Miyamoto, Y., Doi, H., Matsuo, K., Chao, J., Tsuji, S.: A Fast Addition Algorithm of Genus Two Hyperelliptic Curve. In: SCIS, IEICE Japan, pp. 497\u2013502 (2002) (in Japanese)"},{"key":"28_CR30","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":"V. Miller","year":"1986","unstructured":"Miller, V.: Uses of elliptic curves in cryptography. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol.\u00a0218, pp. 417\u2013426. Springer, Heidelberg (1986)"},{"key":"28_CR31","volume-title":"Prog. Math.","author":"D. Mumford","year":"1984","unstructured":"Mumford, D.: Tata lectures on theta II. In: Mumford, D. (ed.) Prog. Math., vol.\u00a043, Birkh\u00e4user, Basel (1984)"},{"key":"28_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"439","DOI":"10.1007\/10722028_28","volume-title":"Algorithmic Number Theory","author":"K. Nagao","year":"2000","unstructured":"Nagao, K.: Improving group law algorithms for Jacobians of hyperelliptic curves. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol.\u00a01838, pp. 439\u2013448. Springer, Heidelberg (2000)"},{"key":"28_CR33","unstructured":"IEEE P1363 Standard Specifications for Public Key Cryptography, Last Preliminary Draft (November 1999)"},{"issue":"143","key":"28_CR34","first-page":"918","volume":"32","author":"J.M. Pollard","year":"1978","unstructured":"Pollard, J.M.: Monte carlo methods for index computation mod p. Mathematics of Computation\u00a032(143), 918\u2013924 (1978)","journal-title":"Mathematics of Computation"},{"key":"28_CR35","doi-asserted-by":"crossref","unstructured":"Pelzl, J., Wollinger, T., Guajardo, J., Paar, C.: Hyperelliptic Curve Cryptosystems: Closing the Performance Gap to Elliptic Curves (Update). Cryptology ePrint Archive, Report 2003\/026 (2003), \n                    \n                      http:\/\/eprint.iacr.org\/","DOI":"10.1007\/978-3-540-45238-6_28"},{"key":"28_CR36","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1007\/3-540-48910-X_12","volume-title":"Advances in Cryptology - EUROCRYPT \u201999","author":"N.P. Smart","year":"1999","unstructured":"Smart, N.P.: On the Performance of Hyperelliptic Cryptosystems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol.\u00a01592, pp. 165\u2013175. Springer, Heidelberg (1999)"},{"key":"28_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"80","DOI":"10.1007\/3-540-49649-1_8","volume-title":"Advances in Cryptology - ASIACRYPT\u201998","author":"Y. Sakai","year":"1998","unstructured":"Sakai, Y., Sakurai, K.: Design of Hyperelliptic Cryptosystems in small Characteristic and a Software Implementation over \n                    \n                      \n                    \n                    $$\n\\mathbb{F}_{2^n } \n$$\n                  . In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol.\u00a01514, pp. 80\u201394. Springer, Heidelberg (1998)"},{"key":"28_CR38","unstructured":"Sakai, Y., Sakurai, K.: On the Practical Performance of Hyperelliptic Curve Cryptosystems in Software Implementation. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences E83-A (4), 692\u2013703 (2000)"},{"key":"28_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"164","DOI":"10.1007\/BFb0054023","volume-title":"Public Key Cryptography","author":"Y. Sakai","year":"1998","unstructured":"Sakai, Y., Sakurai, K., Ishizuka, H.: Secure Hyperelliptic Cryptosystems and their Performance. In: Imai, H., Zheng, Y. (eds.) PKC 1998. LNCS, vol.\u00a01431, pp. 164\u2013181. Springer, Heidelberg (1998)"},{"key":"28_CR40","unstructured":"Takahashi, M.: Improving Harley Algorithms for Jacobians of Genus 2 Hyperelliptic Curves. In: SCIS, IEICE, Japan (2002) (in Japanese)"},{"issue":"1","key":"28_CR41","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/PL00003816","volume":"12","author":"P.C. Oorschot","year":"1999","unstructured":"van Oorschot, P.C., Wiener, M.J.: Parallel collision search with cryptanalytic applications. Journal of Cryptology\u00a012(1), 1\u201328 (Winter 1999)","journal-title":"Journal of Cryptology"},{"key":"28_CR42","unstructured":"Wollinger, T.: Computer Architectures for Cryptosystems Based on Hyperelliptic Curves, Master Thesis, Worcester Polytechnic Institute (2001)"}],"container-title":["Lecture Notes in Computer Science","Cryptographic Hardware and Embedded Systems - CHES 2003"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-45238-6_28","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,21]],"date-time":"2019-05-21T07:38:43Z","timestamp":1558424323000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-45238-6_28"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540408338","9783540452386"],"references-count":42,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-45238-6_28","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2003]]}}}