{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T20:36:22Z","timestamp":1793133382245,"version":"4.5.0"},"publisher-location":"Berlin, Heidelberg","reference-count":22,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540205920","type":"print"},{"value":"9783540400615","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/978-3-540-40061-5_7","type":"book-chapter","created":{"date-parts":[[2010,9,5]],"date-time":"2010-09-05T19:06:00Z","timestamp":1283713560000},"page":"111-123","source":"Crossref","is-referenced-by-count":125,"title":["Tate Pairing Implementation for Hyperelliptic Curves y 2 = x p \u2013 x + d"],"prefix":"10.1007","author":[{"given":"Iwan","family":"Duursma","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Hyang-Sook","family":"Lee","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"7_CR1","unstructured":"The Pairing-Based Crypto Lounge, http:\/\/planeta.terra.com.br\/informatica\/paulobarreto\/pblounge.html"},{"key":"7_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"354","DOI":"10.1007\/3-540-45708-9_23","volume-title":"Advances in Cryptology - CRYPTO 2002","author":"P.S.L.M. Barreto","year":"2002","unstructured":"Barreto, P.S.L.M., Kim, H.Y., Lynn, B., Scott, M.: Efficient Algorithms for Pairing-Based Cryptosystems. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol.\u00a02442, pp. 354\u2013368. Springer, Heidelberg (2002)"},{"key":"7_CR3","doi-asserted-by":"crossref","unstructured":"Blake, I., Seroussi, G., Smart, N.P.: Elliptic curves in cryptography. London Mathematical Society. LNS, vol.\u00a0265. Cambridge University Press, Cambridge (1999) (reprinted 2000)","DOI":"10.1017\/CBO9781107360211"},{"key":"7_CR4","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"213","DOI":"10.1007\/3-540-44647-8_13","volume-title":"Advances in Cryptology - CRYPTO 2001","author":"D. Boneh","year":"2001","unstructured":"Boneh, D., Franklin, M.: Identity-based encryption from the Weil pairing. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol.\u00a02139, pp. 213\u2013229. Springer, Heidelberg (2001)"},{"key":"7_CR5","doi-asserted-by":"crossref","unstructured":"Boneh, D., Silverberg, A.: Applications of multilinear forms to cryptography. Contemporary Mathematics, vol.\u00a0324, pp. 71\u201390. American Mathematical Society (2003)","DOI":"10.1090\/conm\/324\/05731"},{"key":"7_CR6","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"18","DOI":"10.1007\/3-540-36288-6_2","volume-title":"Public Key Cryptography - PKC 2003","author":"J.C. Cha","year":"2002","unstructured":"Cha, J.C., Cheon, J.H.: An Identity-Based Signature from Gap DiffieHellman Groups. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol.\u00a02567, pp. 18\u201330. Springer, Heidelberg (2002)"},{"issue":"6","key":"7_CR7","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.: New direction in cryptography. IEEE Trans. Information Theory\u00a0IT-22(6), 644\u2013654 (1976)","journal-title":"IEEE Trans. Information Theory"},{"key":"7_CR8","first-page":"45","volume-title":"Arithmetic, Geometry and Coding Theory","author":"I. Duursma","year":"1996","unstructured":"Duursma, I.: Class numbers for hyperelliptic curves. In: Pellikaan, Perret, Vladuts (eds.) Arithmetic, Geometry and Coding Theory, pp. 45\u201352. deGruyter, Berlin (1996)"},{"key":"7_CR9","doi-asserted-by":"crossref","first-page":"73","DOI":"10.1007\/978-3-642-57189-3_6","volume-title":"Coding theory, cryptography and related areas (Guanajuato, 1998)","author":"I. Duursma","year":"2000","unstructured":"Duursma, I., Sakurai, K.: Efficient algorithms for the Jacobian variety of hyperelliptic curves y2 = xp? x + 1 over a finite field of odd characteristic p. In: Coding theory, cryptography and related areas (Guanajuato, 1998), pp. 73\u201389. Springer, Berlin (2000)"},{"issue":"206","key":"7_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. Math. Comp.\u00a062(206), 865\u2013874 (1994)","journal-title":"Math. Comp."},{"key":"7_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\u2013513. Springer, Heidelberg (2001)"},{"key":"7_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"324","DOI":"10.1007\/3-540-45455-1_26","volume-title":"Algorithmic Number Theory","author":"S.D. Galbraith","year":"2002","unstructured":"Galbraith, S.D., Harrison, K., Soldera, D.: Implementing the Tate pairing. In: Fieker, C., Kohel, D.R. (eds.) ANTS 2002. LNCS, vol.\u00a02369, pp. 324\u2013337. Springer, Heidelberg (2002)"},{"key":"7_CR13","doi-asserted-by":"crossref","unstructured":"Hess, F.: Exponent group signature schemes and efficient identity based signature schems based on pairing. In: Proceedings of the Workshop Selected Areas in Cryptology, SAC (August 2002)","DOI":"10.1007\/3-540-36492-7_20"},{"key":"7_CR14","unstructured":"Hess, F.: A Note on the Tate Pairing of Curves over Finite Fields (2002), Available on: http:\/\/www.math.tu-berlin.de\/~hess"},{"key":"7_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1007\/3-540-36552-4_20","volume-title":"Information Security and Cryptology - ICISC 2002","author":"T. Izu","year":"2003","unstructured":"Izu, T., Takagi, T.: Efficient computations of the tate pairingfor the large MOV degrees. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol.\u00a02587, pp. 283\u2013297. Springer, Heidelberg (2003)"},{"key":"7_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"385","DOI":"10.1007\/10722028_23","volume-title":"Algorithmic Number Theory","author":"A. Joux","year":"2000","unstructured":"Joux, A.: A one round protocol for tripartite Diffie-Hellman. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol.\u00a01838, pp. 385\u2013394. Springer, Heidelberg (2000)"},{"key":"7_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"327","DOI":"10.1007\/BFb0055739","volume-title":"Advances in Cryptology - CRYPTO \u201998","author":"N. Koblitz","year":"1998","unstructured":"Koblitz, N.: An elliptic curve implementation of the finite field digital signature algorithm. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol.\u00a01462, pp. 327\u2013337. Springer, Heidelberg (1998)"},{"key":"7_CR18","unstructured":"Miller, V.: Short Programs for Functions on Curves (1986) (unpublished manuscript)"},{"key":"7_CR19","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"A. Menezes","year":"1993","unstructured":"Menezes, A., Okamoto, T., Vanstone, S.: Reducing elliptic curve logarithms to logarithms in a finite field. IEEE Trans. on Inform. Theory\u00a039, 1639\u20131646 (1993)","journal-title":"IEEE Trans. on Inform. Theory"},{"issue":"18","key":"7_CR20","doi-asserted-by":"publisher","first-page":"1025","DOI":"10.1049\/el:20020682","volume":"38","author":"K.G. Paterson","year":"2002","unstructured":"Paterson, K.G.: ID-based signature from pairings on elliptic curves. Electronics Letters\u00a038(18), 1025\u20131026 (2002)","journal-title":"Electronics Letters"},{"key":"7_CR21","unstructured":"Sakai, R., Ohgishi, K., Kasahara, M.: Cryptosystems based on pairing. In: Symposium on cryptography and Information Security, Okinawa, Japan, pp. 26\u201328 (2000)"},{"key":"7_CR22","doi-asserted-by":"publisher","first-page":"630","DOI":"10.1049\/el:20020387","volume":"38","author":"N.P. Smart","year":"2002","unstructured":"Smart, N.P.: An identity based authentication key agreement protocol based on pairing. Electronics Letters\u00a038, 630\u2013632 (2002)","journal-title":"Electronics Letters"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology - ASIACRYPT 2003"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-540-40061-5_7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,6,3]],"date-time":"2019-06-03T17:20:48Z","timestamp":1559582448000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-540-40061-5_7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540205920","9783540400615"],"references-count":22,"URL":"https:\/\/doi.org\/10.1007\/978-3-540-40061-5_7","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2003]]}}}