{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T15:09:23Z","timestamp":1753888163251},"publisher-location":"Berlin, Heidelberg","reference-count":28,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540639275"},{"type":"electronic","value":"9783540696681"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[1997]]},"DOI":"10.1007\/bfb0024472","type":"book-chapter","created":{"date-parts":[[2005,11,19]],"date-time":"2005-11-19T03:06:58Z","timestamp":1132369618000},"page":"265-269","source":"Crossref","is-referenced-by-count":3,"title":["On using Carmichael numbers for public key encryption systems"],"prefix":"10.1007","author":[{"given":"R. G. E.","family":"Pinch","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2005,6,17]]},"reference":[{"key":"29_CR1","series-title":"Lecture notes in Computer Science","volume-title":"Algorithmic number theory","year":"1994","unstructured":"L.M. Adleman and M.-D.A. Huang (eds.), Algorithmic number theory, Lecture notes in Computer Science, vol. 877, Berlin, Springer-Verlag, 1994, Proceedings, first international symposium, Ithaca, NY, May 1994."},{"key":"29_CR2","doi-asserted-by":"crossref","first-page":"173","DOI":"10.2307\/2006975","volume":"17","author":"L.M. Adleman","year":"1983","unstructured":"L.M. Adleman, C. Pomerance, and R. Rumely, On distinguishing prime numbers from composite numbers, Ann. Math. 17 (1983), 173\u2013206.","journal-title":"Ann. Math."},{"key":"29_CR3","doi-asserted-by":"crossref","first-page":"29","DOI":"10.1090\/S0025-5718-1993-1199989-X","volume":"61","author":"A.O.L. Atkin","year":"1993","unstructured":"A.O.L. Atkin and F. Morain, Elliptic curves and primality proving, Math. Comp. 61 (1993), 29\u201368, Lehmer memorial issue.","journal-title":"Math. Comp."},{"issue":"220","key":"29_CR4","doi-asserted-by":"publisher","first-page":"1705","DOI":"10.1090\/S0025-5718-97-00857-0","volume":"66","author":"R. Balasubramanian","year":"1997","unstructured":"R. Balasubramanian and S.V. Nagaraj, Density of Carmichael numbers with three prime factors, Math. Comp. 66 (1997), no. 220, 1705\u20131708.","journal-title":"Math. Comp."},{"issue":"154","key":"29_CR5","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1090\/S0025-5718-1981-0606520-5","volume":"36","author":"R.P. Brent","year":"1981","unstructured":"R.P. Brent and J.M. Pollard, Factorization of the eighth Fermat number, Math. Comp. 36 (1981), no. 154, 627\u2013630.","journal-title":"Math. Comp."},{"key":"29_CR6","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1090\/S0002-9904-1939-06953-X","volume":"45","author":"J. Chernick","year":"1939","unstructured":"J. Chernick, On Fermat's simple theorem, Bull. Amer. Math. Soc. 45 (1939), 269\u2013274.","journal-title":"Bull. Amer. Math. Soc."},{"key":"29_CR7","unstructured":"I. Damg\u00e5rd and P. Landrock, Improved bounds for the Rabin primality test, Cryptography and coding III (M. Ganley, ed.), IMA conference series (n.s.), vol. 45, Institute of Mathematics and its Applications, Oxford University Press, 1993, Proceedings, 3rd IMA conference on cryptography and coding, Cirencester, December 1991., pp. 117\u2013128."},{"key":"29_CR8","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1090\/S0025-5718-1993-1189518-9","volume":"61","author":"I. Damg\u00e5rd","year":"1993","unstructured":"I. Damg\u00e5rd, P. Landrock, and C. Pomerance, Average case error estimates for the strong probable prime test, Math. Comp. 61 (1993), 177\u2013194, Lehmer memorial issue.","journal-title":"Math. Comp."},{"key":"29_CR9","unstructured":"M. Del\u00e9glise and J. Rivat, Computing \u03c0(x), M(x) and \u03a8(x), In Adleman and Huang [1], Proceedings, first international symposium, Ithaca, NY, May 1994, p. 264."},{"issue":"213","key":"29_CR10","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1090\/S0025-5718-96-00674-6","volume":"65","author":"M. Del\u00e9glise","year":"1996","unstructured":"-, Computing \u03c0(x): the Meissel, Lehmer, Lagarias, Miller, Odlyzko method, Math. Comp. 65 (1996), no. 213, 235\u2013245.","journal-title":"Math. Comp."},{"key":"29_CR11","first-page":"155","volume":"33","author":"L.E. Dickson","year":"1904","unstructured":"L.E. Dickson, A new extension of dirichlet's theorem on prime numbers, Messenger of Mathematics 33 (1904), 155\u2013161.","journal-title":"Messenger of Mathematics"},{"issue":"3","key":"29_CR12","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1016\/0893-9659(88)90081-X","volume":"1","author":"E.D. Huthnance","year":"1988","unstructured":"E.D. Huthnance and J. Warndof, On using primes for public key encryption systems, Appl. Math. Lett. 1 (1988), no. 3, 225\u2013227.","journal-title":"Appl. Math. Lett."},{"key":"29_CR13","unstructured":"B.S. Kaliski jr, How RSA's toolkits generate primes, Tech. Report 003-903028-100000-000, RSA Laboratories, Redwood City, CA, 18 Feb 1994."},{"key":"29_CR14","unstructured":"P. Landrock, Proper key generation, Cryptomathic Bull. 1 (1996), at URL http:\/\/www.cryptomathic.dk\/ matt\/news.html."},{"key":"29_CR15","doi-asserted-by":"crossref","first-page":"649","DOI":"10.2307\/1971363","volume":"126","author":"H.W. Lenstra Jr","year":"1987","unstructured":"H.W. Lenstra jr, Factoring integers with elliptic curves, Annals of Math. 126 (1987),649\u2013673.","journal-title":"Annals of Math."},{"key":"29_CR16","series-title":"Lecture notes in Computer Science","volume-title":"Advances in cryptology \u2014 Crypto '90","year":"1991","unstructured":"A.J. Menezes and S.A. Vanstone (eds.), Advances in cryptology \u2014\nCrypto '90, Lecture notes in Computer Science, vol. 537, Berlin, Springer-Verlag, 1991."},{"key":"29_CR17","first-page":"381","volume":"61","author":"R.G.E. Pinch","year":"1993","unstructured":"R.G.E. Pinch, The Carmichael numbers up to 10\n15, Math. Comp. 61 (1993), 381\u2013391, Lehmer memorial issue.","journal-title":"Math. Comp."},{"issue":"9","key":"29_CR18","first-page":"1203","volume":"40","author":"R.G.E. Pinch","year":"1993","unstructured":"\u2014, Some primality testing algorithms, Notices Amer. Math. Soc. 40 (1993), no. 9, 1203\u20131210.","journal-title":"Notices Amer. Math. Soc."},{"key":"29_CR19","unstructured":"\u2014, Some primality testing algorithms, The Rhine workshop on computer algebra, Karlsruhe, March, 1994 proceedings (J. Calmet, ed.), February 1994, pp. 2\u201313."},{"key":"29_CR20","doi-asserted-by":"crossref","first-page":"521","DOI":"10.1017\/S0305004100049252","volume":"76","author":"J.M. Pollard","year":"1974","unstructured":"J.M. Pollard, Theorems on factorization and primality testing, Proc. Cambridge Philos. Soc. 76 (1974), 521\u2013528.","journal-title":"Proc. Cambridge Philos. Soc."},{"key":"29_CR21","doi-asserted-by":"publisher","first-page":"331","DOI":"10.1007\/BF01933667","volume":"15","author":"J.M. Pollard","year":"1975","unstructured":"-, A Monte Carlo method for factorization, BIT 15 (1975), 331\u2013334.","journal-title":"BIT"},{"key":"29_CR22","series-title":"Lecture notes in Computer Science","doi-asserted-by":"crossref","first-page":"625","DOI":"10.1007\/3-540-38424-3_45","volume-title":"Menezes and Vanstone","author":"R.L. Rivest","year":"1991","unstructured":"R.L. Rivest, Finding four million large random primes, In Menezes and Vanstone [16], pp. 625\u2013626."},{"issue":"2","key":"29_CR23","doi-asserted-by":"publisher","first-page":"120","DOI":"10.1145\/359340.359342","volume":"21","author":"R.L. Rivest","year":"1978","unstructured":"R.L. Rivest, A. Shamir, and L. Adleman, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM 21 (1978), no. 2, 120\u2013126, Reprinted as [24].","journal-title":"Communications of the ACM"},{"issue":"1","key":"29_CR24","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1145\/357980.358017","volume":"26","author":"R.L. Rivest","year":"1983","unstructured":"-, A method for obtaining digital signatures and public-key cryptosystems, Communications of the ACM 26 (1983), no. 1, 96\u201399, Reprint of [23].","journal-title":"Communications of the ACM"},{"issue":"1","key":"29_CR25","first-page":"9","volume":"3","author":"R.D. Silverman","year":"1997","unstructured":"R.D. Silverman, Fast generation of random, strong RSA primes, Cryptobytes 3 (1997), no. 1, 9\u201313.","journal-title":"Cryptobytes"},{"key":"29_CR26","first-page":"225","volume":"39","author":"H.C. Williams","year":"1982","unstructured":"H.C. Williams, A p + 1 method of factoring, Math. Comp. 39 (1982), 225\u2013234.","journal-title":"Math. Comp."},{"key":"29_CR27","unstructured":"P.R. Zimmerman, The official PGP user's guide, MIT Press, 1995, 0-262-74017-6."},{"key":"29_CR28","unstructured":"\u2014, PGP source code and internals, MIT Press, 1995."}],"container-title":["Lecture Notes in Computer Science","Crytography and Coding"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/BFb0024472","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,4]],"date-time":"2019-02-04T21:04:26Z","timestamp":1549314266000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/BFb0024472"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1997]]},"ISBN":["9783540639275","9783540696681"],"references-count":28,"URL":"https:\/\/doi.org\/10.1007\/bfb0024472","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[1997]]}}}