{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,13]],"date-time":"2025-10-13T19:43:25Z","timestamp":1760384605744},"publisher-location":"Berlin, Heidelberg","reference-count":24,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540648925"},{"type":"electronic","value":"9783540684626"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1998]]},"DOI":"10.1007\/bfb0055739","type":"book-chapter","created":{"date-parts":[[2006,7,27]],"date-time":"2006-07-27T17:12:36Z","timestamp":1154020356000},"page":"327-337","source":"Crossref","is-referenced-by-count":39,"title":["An elliptic curve implementation of the finite field digital signature algorithm"],"prefix":"10.1007","author":[{"given":"Neal","family":"Koblitz","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2006,5,28]]},"reference":[{"key":"24_CR1","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1007\/s001459900040","volume":"11","author":"R. Balasubramanian","year":"1998","unstructured":"R. Balasubramanian and N. Koblitz, The improbability than an elliptic curve has subexponential discrete log problem under the Menezes-Okamoto-Vanstone algorithm, J. Cryptology 11 (1998), 141\u2013145.","journal-title":"J. Cryptology"},{"key":"24_CR2","doi-asserted-by":"crossref","unstructured":"I. Blake, X. H. Gao, R. C. Mullin, S. A. Vanstone, and T. Yaghoobian, Applications of Finite Fields, Kluwer Acad. Publ., 1993.","DOI":"10.1007\/978-1-4757-2226-0"},{"key":"24_CR3","doi-asserted-by":"publisher","first-page":"315","DOI":"10.1007\/BF00125200","volume":"2","author":"S. Gao","year":"1992","unstructured":"S. Gao and H. W. Lenstra, Jr., Optimal normal bases, Designs, Codes and Cryptography 2 (1992), 315\u2013323.","journal-title":"Designs, Codes and Cryptography"},{"key":"24_CR4","doi-asserted-by":"crossref","unstructured":"K. Ireland and M. I. Rosen, A Classical Introduction to Modern Number Theory, 2nd ed., Springer-Verlag, 1990.","DOI":"10.1007\/978-1-4757-2103-4"},{"key":"24_CR5","doi-asserted-by":"publisher","first-page":"203","DOI":"10.2307\/2007884","volume":"48","author":"N. Koblitz","year":"1987","unstructured":"N. Koblitz, Elliptic curve cryptosystems, Math. Comp. 48 (1987), 203\u2013209.","journal-title":"Math. Comp."},{"key":"24_CR6","doi-asserted-by":"crossref","unstructured":"N. Koblitz, CM-curves with good cryptographic properties, Advances in Cryptology \u2014 Crypto '91, Springer-Verlag, 1992, 279\u2013287.","DOI":"10.1007\/3-540-46766-1_22"},{"key":"24_CR7","doi-asserted-by":"crossref","unstructured":"N. Koblitz, A Course in Number Theory and Cryptography, 2nd ed., Springer-Verlag, 1994.","DOI":"10.1007\/978-1-4419-8592-7"},{"key":"24_CR8","doi-asserted-by":"crossref","unstructured":"N. Koblitz, Algebraic Aspects of Cryptography, Springer-Verlag, 1998.","DOI":"10.1007\/978-3-662-03642-6"},{"key":"24_CR9","unstructured":"N. Koblitz, A. Menezes, and S. A. Vanstone, The state of elliptic curve cryptography, to appear in Designs, Codes and Cryptography."},{"key":"24_CR10","doi-asserted-by":"crossref","unstructured":"W. Meier and O. Staffelbach, Efficient multiplication on certain non-supersingular elliptic curves, Advances in Cryptology \u2014 Crypto '92, Springer-Verlag, 1993, 333\u2013344.","DOI":"10.1007\/3-540-48071-4_24"},{"key":"24_CR11","doi-asserted-by":"crossref","unstructured":"A. Menezes, Elliptic Curve Public Key Cryptosystems, Kluwer Acad. Publ., 1993.","DOI":"10.1007\/978-1-4615-3198-2"},{"key":"24_CR12","doi-asserted-by":"publisher","first-page":"1639","DOI":"10.1109\/18.259647","volume":"39","author":"A. Menezes","year":"1993","unstructured":"A. Menezes, T. Okamoto, and S. A. Vanstone, Reducing elliptic curve logarithms to logarithms in a finite field, IEEE Trans. Information Theory 39 (1993), 1639\u20131646.","journal-title":"IEEE Trans. Information Theory"},{"key":"24_CR13","doi-asserted-by":"publisher","first-page":"209","DOI":"10.1007\/BF00203817","volume":"6","author":"A. Menezes","year":"1993","unstructured":"A. Menezes and S. A. Vanstone, Elliptic curve cryptosystems and their implementation, J. Cryptology 6 (1993), 209\u2013224.","journal-title":"J. Cryptology"},{"key":"24_CR14","doi-asserted-by":"crossref","unstructured":"V. Miller, Uses of elliptic curves in cryptography, Advances in Cryptology \u2014 Crypto '85, Springer-Verlag, 1986, 417\u2013426.","DOI":"10.1007\/3-540-39799-X_31"},{"key":"24_CR15","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1016\/0166-218X(88)90090-X","volume":"22","author":"R. Mullin","year":"1988\/89","unstructured":"R. Mullin, I. Onyszchuk, S. A. Vanstone, and R. Wilson, Optimal normal bases in GF(p n ), Discrete Applied Math. 22 (1988\/89), 149\u2013161.","journal-title":"Discrete Applied Math."},{"key":"24_CR16","unstructured":"National Institute for Standards and Technology, Digital signature standard, FIPS Publication 186, 1993."},{"key":"24_CR17","unstructured":"T. Satoh and K. Araki, Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves, preprint."},{"key":"24_CR18","unstructured":"R. Schroeppel, personal communication, Dec. 2, 1997."},{"key":"24_CR19","doi-asserted-by":"crossref","unstructured":"R. Schroeppel, H. Orman, S. O'Malley, and O. Spatscheck, Fast key exchange with elliptic curve systems, Advances in Cryptology \u2014 Crypto '95, Springer-Verlag, 1995, 43\u201356.","DOI":"10.1007\/3-540-44750-4_4"},{"key":"24_CR20","doi-asserted-by":"publisher","first-page":"353","DOI":"10.1090\/S0025-5718-98-00887-4","volume":"67","author":"I. A. Semaev","year":"1998","unstructured":"I. A. Semaev, Evaluation of discrete logarithms in a group of p-torsion points of an elliptic curve in characteristic p, Math. Comp. 67 (1998), 353\u2013356.","journal-title":"Math. Comp."},{"key":"24_CR21","doi-asserted-by":"crossref","unstructured":"J. Silverman, The Arithmetic of Elliptic Curves, Springer-Verlag, 1986.","DOI":"10.1007\/978-1-4757-1920-8"},{"key":"24_CR22","unstructured":"N. Smart, The discrete log problem on elliptic curves of trace 1, preprint."},{"key":"24_CR23","doi-asserted-by":"crossref","unstructured":"J. Solinas, An improved algorithm for arithmetic on a family of elliptic curves, Advances in Cryptology \u2014 Crypto '97, Springer-Verlag, 1997, 357\u2013371.","DOI":"10.1007\/BFb0052248"},{"key":"24_CR24","doi-asserted-by":"crossref","unstructured":"E. De Win, A. Bosselaers, S. Vandenberghe, P. De Gersem, and J. Vandewalle, A fast software implementation for arithmetic operations in GF(2n), Advances in Cryptology \u2014 Asiacrypt '96, Springer-Verlag, 1996, 65\u201376.","DOI":"10.1007\/BFb0034836"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology \u2014 CRYPTO '98"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0055739","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,4,20]],"date-time":"2019-04-20T05:09:08Z","timestamp":1555736948000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0055739"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"ISBN":["9783540648925","9783540684626"],"references-count":24,"URL":"https:\/\/doi.org\/10.1007\/bfb0055739","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1998]]}}}