{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T23:02:43Z","timestamp":1725663763488},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540545224"},{"type":"electronic","value":"9783540384366"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1991]]},"DOI":"10.1007\/3-540-54522-0_97","type":"book-chapter","created":{"date-parts":[[2012,2,25]],"date-time":"2012-02-25T22:59:47Z","timestamp":1330210787000},"page":"74-81","source":"Crossref","is-referenced-by-count":0,"title":["Arithmetic on non supersingular elliptic curves"],"prefix":"10.1007","author":[{"given":"T.","family":"Beth","sequence":"first","affiliation":[]},{"given":"F.","family":"Schaefer","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,6,7]]},"reference":[{"issue":"4","key":"7_CR1","doi-asserted-by":"crossref","first-page":"458","DOI":"10.1109\/49.17708","volume":"7","author":"T. Beth","year":"1989","unstructured":"T. Beth, D. Gollmann; Algorithm Engineering for Public Key Algorithms; IEEE Journal on Selected Areas in Comm., Vol. 7, No. 4, 1989, pp 458\u2013466.","journal-title":"IEEE Journal on Selected Areas in Comm."},{"key":"7_CR2","unstructured":"T. Beth, W. Geiselmann, F. Schaefer; Arithmetics on Elliptic Curves; Algebraic and Combinatorial Coding Theory, 2nd Int. Workshop, Leningrad, 1990, pp 28\u201333."},{"key":"7_CR3","unstructured":"T. Beth, F. Schaefer; Non Supersingular Elliptic Curves for Public Key Cryptosystems; to appear in Proc. of EUROCRYPT'91."},{"key":"7_CR4","doi-asserted-by":"crossref","first-page":"587","DOI":"10.1109\/TIT.1984.1056941","volume":"30","author":"D. Coppersmith","year":"1984","unstructured":"D. Coppersmith; Fast evaluation of logarithms in fields of characteristic two; IEEE Trans. Inform. Theory, IT 30, 1984, pp 587\u2013594.","journal-title":"IEEE Trans. Inform. Theory, IT"},{"key":"7_CR5","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1007\/BF02940746","volume":"14","author":"M. Deuring","year":"1941","unstructured":"M. Deuring; Die Typen der Multiplikatorenringe elliptischer Funktionenk\u00f6rper; Abh. Math. Sem. Hamburg, Bd. 14, 1941, pp 197\u2013272.","journal-title":"Abh. Math. Sem. Hamburg, Bd."},{"key":"7_CR6","doi-asserted-by":"crossref","first-page":"644","DOI":"10.1109\/TIT.1976.1055638","volume":"22","author":"W. Diffie","year":"1976","unstructured":"W. Diffie, M. Hellman; New directions in cryptography; IEEE Trans. Inform. Theory, IT 22, 1976, pp 644\u2013654.","journal-title":"IEEE Trans. Inform. Theory, IT"},{"key":"7_CR7","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1109\/TIT.1985.1057074","volume":"31","author":"T. ElGamal","year":"1985","unstructured":"T. ElGamal; A public key cryptosystem and a signature scheme based on discrete logarithms; IEEE Trans. Inform. Theory, IT 31, 1985, pp 469\u2013472.","journal-title":"IEEE Trans. Inform. Theory, IT"},{"issue":"177","key":"7_CR8","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1090\/S0025-5718-1987-0866109-5","volume":"48","author":"N. Koblitz","year":"1987","unstructured":"N. Koblitz; Elliptic Curve Cryptosystems; Mathematics of Computation, Vol. 48, No177, 1987, pp 203\u2013209.","journal-title":"Mathematics of Computation"},{"key":"7_CR9","first-page":"2","volume":"453","author":"A. Menezes","year":"1990","unstructured":"A. Menezes, S. A. Vanstone; The Implementation fo Elliptic Curve Cryptosystems; Advances in Cryptology-AUSCRYPT90, Springer LNCS 453, 1990, pp 2\u201313.","journal-title":"Advances in Cryptology-AUSCRYPT90, Springer LNCS"},{"key":"7_CR10","doi-asserted-by":"crossref","unstructured":"A. Menezes, T. Okamoto, S. A. Vanstone; Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field; Proc. of the 22nd Annual ACM Symposium on the Theory of Comp., 80\u201389, 1991.","DOI":"10.1145\/103418.103434"},{"key":"7_CR11","first-page":"417","volume":"218","author":"V. S. Miller","year":"1986","unstructured":"V. S. Miller; Use of Elliptic Curves in Cryptography; Advances in Cryptology: Proceedings of Crypto 85, Springer LNCS 218, 1986, pp 417\u2013426.","journal-title":"Springer LNCS"},{"key":"7_CR12","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1090\/S0025-5718-1987-0866113-7","volume":"48","author":"P. Montgomery","year":"1977","unstructured":"P. Montgomery; Speeding the Pollard and elliptic curve methods of factorization; Math. Comp., Vol. 48, 1977, pp 243\u2013264.","journal-title":"Math. Comp."},{"issue":"170","key":"7_CR13","first-page":"483","volume":"44","author":"R. Schoof","year":"1985","unstructured":"R. Schoof; Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p; Math. Of Comp., Vol. 44, No. 170, 1985, pp 483\u2013494.","journal-title":"Math. Of Comp."},{"key":"7_CR14","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4757-1920-8","volume-title":"The Arithmetic of Elliptic Curves","author":"J. H. Silverman","year":"1986","unstructured":"J. H. Silverman; The Arithmetic of Elliptic Curves; Springer-Verlag, New York, 1986."},{"key":"7_CR15","doi-asserted-by":"crossref","unstructured":"J. T. Tate; The Arithmetic of Elliptic Curves; Inventiones Math. 23, Springer-Verlag, 1974, pp 179\u2013206.","DOI":"10.1007\/BF01389745"},{"key":"7_CR16","doi-asserted-by":"crossref","unstructured":"W. C. Waterhouse; Abelian Varieties over finite fields; Ann. Scient. Ec. Norm. Sup., 4th serie, 1969, pp 521\u2013560.","DOI":"10.24033\/asens.1183"}],"container-title":["Lecture Notes in Computer Science","Applied Algebra, Algebraic Algorithms and Error-Correcting Codes"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-54522-0_97.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,17]],"date-time":"2020-11-17T20:55:31Z","timestamp":1605646531000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-54522-0_97"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1991]]},"ISBN":["9783540545224","9783540384366"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/3-540-54522-0_97","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1991]]}}}