{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,4]],"date-time":"2024-09-04T22:32:00Z","timestamp":1725489120944},"publisher-location":"Berlin, Heidelberg","reference-count":21,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540551881"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"DOI":"10.1007\/3-540-46766-1_21","type":"book-chapter","created":{"date-parts":[[2007,8,11]],"date-time":"2007-08-11T15:03:27Z","timestamp":1186844607000},"page":"267-278","source":"Crossref","is-referenced-by-count":4,"title":["Efficient Algorithms for the Construction of Hyperelliptic Cryptosystems"],"prefix":"10.1007","author":[{"given":"Tatsuaki","family":"Okamoto","sequence":"first","affiliation":[]},{"given":"Kouichi","family":"Sakurai","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"key":"21_CR1","doi-asserted-by":"publisher","first-page":"95","DOI":"10.2307\/2007876","volume":"48","author":"D. Cantor","year":"1987","unstructured":"D. Cantor, \u201cComputing in the Jacobian of a Hyperelliptic Curve\u201d, Math. Comp., 48, pp.95\u2013101 (1987).","journal-title":"Math. Comp."},{"key":"21_CR2","doi-asserted-by":"publisher","first-page":"587","DOI":"10.1109\/TIT.1984.1056941","volume":"IT-30","author":"D. Coppersmith","year":"1984","unstructured":"D. Coppersmith, \u201cFast evaluation of logarithms in fields of characteristic two\u201d, IEEE Transaction on Information Theory, IT-30, 587\u2013594 (1984).","journal-title":"IEEE Transaction on Information Theory"},{"key":"21_CR3","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01840433","volume":"1","author":"D. Coppersmith","year":"1986","unstructured":"D. Coppersmith, A. Odlyzko and R. Schroeppel, \u201cDiscrete logarithms in GF(p)\u201d, Algorithmica, 1 (1986), 1\u201315.","journal-title":"Algorithmica"},{"issue":"6","key":"21_CR4","doi-asserted-by":"publisher","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"IT-22","author":"W. Diffie","year":"1976","unstructured":"W. Diffie and M. E. Hellman, \u201cNew Directions in Cryptography\u201d, IEEE Transactions on Information Theory, Vol.IT-22, No. 6, pp.644\u2013654 (1976).","journal-title":"IEEE Transactions on Information Theory"},{"key":"21_CR5","doi-asserted-by":"publisher","first-page":"473","DOI":"10.1109\/TIT.1985.1057075","volume":"IT-31","author":"T. ElGamal","year":"1985","unstructured":"T. ElGamal, \u201cA subexponential-time algorithm for computing discrete logarithms over GF(p 2)\u201d, IEEE Transactions on Information Theory, IT-31, pp.473\u2013481 (1985).","journal-title":"IEEE Transactions on Information Theory"},{"key":"21_CR6","doi-asserted-by":"publisher","first-page":"159","DOI":"10.1016\/S0019-9958(84)80056-X","volume":"61","author":"S. Even","year":"1984","unstructured":"S. Even, A.L. Selman and Y. Yacobi, \u201cThe Complexity of Promise Problems with Applications to Public-Key Cryptography\u201d, Information and Control, 61, pp.159\u2013173 (1984).","journal-title":"Information and Control"},{"key":"21_CR7","volume-title":"Algebraic Curves","author":"W. Fulton","year":"1969","unstructured":"W. Fulton, \u201cAlgebraic Curves,\u201d Benjamin, New York, 1969."},{"key":"21_CR8","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1007\/3-540-47721-7_7","volume-title":"Advances in Cryptology: Proceedings of Crypto\u2019 86","author":"B. Kaliski","year":"1987","unstructured":"B. Kaliski, \u201cA pseudorandom bit generator based on elliptic logarithms\u201d, Advances in Cryptology: Proceedings of Crypto\u2019 86, Lecture Notes in Computer Science, 293, Springer-Verlag, pp.84\u2013103 (1987)."},{"key":"21_CR9","doi-asserted-by":"publisher","first-page":"203","DOI":"10.2307\/2007884","volume":"48","author":"N. Koblitz","year":"1987","unstructured":"N. Koblitz, \u201cElliptic Curve Cryptosystems\u201d, Math. Comp., 48, pp.203\u2013209 (1987).","journal-title":"Math. Comp."},{"key":"21_CR10","doi-asserted-by":"publisher","first-page":"139","DOI":"10.1007\/BF02252872","volume":"1","author":"N. Koblitz","year":"1989","unstructured":"N. Koblitz, \u201cHyperelliptic Cryptosystems\u201d, Journal of Cryptology, Vol.1, pp.139\u2013150 (1989).","journal-title":"Journal of Cryptology"},{"key":"21_CR11","volume-title":"The Art of Computer Programming","author":"D. Knuth","year":"1981","unstructured":"D. Knuth, The Art of Computer Programming, Vol. 2. Reading, MA: Addison-Wesley, 1981."},{"unstructured":"S. Lang, Abelian Varieties, Interscience, New York, 1959.","key":"21_CR12"},{"doi-asserted-by":"crossref","unstructured":"A.J. Menezes, T. Okamoto, S.A. Vanstone, \u201cReducing Elliptic Curve Logarithms to Logarithms in a Finite Field\u201d, Proc. of STOC\u201991, pp.80\u201389 (1991).","key":"21_CR13","DOI":"10.1145\/103418.103434"},{"doi-asserted-by":"crossref","unstructured":"V. Miller, \u201cUses of elliptic curves in cryptography\u201d, Proc. of Crypto\u2019 85, pp.417\u2013426 (1986).","key":"21_CR14","DOI":"10.1007\/3-540-39799-X_31"},{"unstructured":"V. Miller, \u201cShort programs for functions on curves\u201d, unpublished manuscript, 1986.","key":"21_CR15"},{"doi-asserted-by":"crossref","unstructured":"A. Odlyzko, \u201cDiscrete logarithms and their cryptographic significance\u201d, Proc. of Eurocrypt\u2019 84, pp.224\u2013314, (1985).","key":"21_CR16","DOI":"10.1007\/3-540-39757-4_20"},{"unstructured":"J. Pila, \u201cFrobenius Maps of Abelian Varieties and Finding Roots of Unity in Finite Fields\u201d, PhD Thesis of Stanford Univ., (1988)","key":"21_CR17"},{"key":"21_CR18","doi-asserted-by":"publisher","first-page":"483","DOI":"10.2307\/2007968","volume":"44","author":"R. Schoof","year":"1985","unstructured":"R. Schoof, \u201cElliptic curves over finite fields and the computation of square roots mod p\u201d, Mathematics of Computation, 44, pp.483\u2013494 (1985).","journal-title":"Mathematics of Computation"},{"key":"21_CR19","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/0097-3165(87)90003-3","volume":"A 46","author":"R. Schoof","year":"1987","unstructured":"R. Schoof, \u201cNonsingular plane cubic curves over finite fields\u201d, Journal of Combinatorial Theory, A 46, pp.183\u2013211 (1987).","journal-title":"Journal of Combinatorial Theory"},{"key":"21_CR20","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1920-8","volume-title":"The Arithmetic of Elliptic Curves","author":"J. Silverman","year":"1986","unstructured":"J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, New York, 1986."},{"unstructured":"H. Shizuya, T. Itoh, K. Sakurai, \u201cOn the Complexity of Hyperelliptic Discrete Logarithm Problem\u201d, to appear in Proc. of Eurocrypt\u2019 91.","key":"21_CR21"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2014 CRYPTO \u201991"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-46766-1_21.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T21:13:28Z","timestamp":1605647608000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-46766-1_21"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[null]]},"ISBN":["9783540551881"],"references-count":21,"URL":"https:\/\/doi.org\/10.1007\/3-540-46766-1_21","relation":{},"subject":[]}}