{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,15]],"date-time":"2026-06-15T03:41:41Z","timestamp":1781494901400,"version":"3.54.1"},"publisher-location":"Berlin, Heidelberg","reference-count":16,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783540414551","type":"print"},{"value":"9783540444992","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2000]]},"DOI":"10.1007\/3-540-44499-8_27","type":"book-chapter","created":{"date-parts":[[2007,8,28]],"date-time":"2007-08-28T10:14:13Z","timestamp":1188296053000},"page":"340-354","source":"Crossref","is-referenced-by-count":34,"title":["Efficient Generation of Prime Numbers"],"prefix":"10.1007","author":[{"given":"Marc","family":"Joye","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Pascal","family":"Paillier","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Serge","family":"Vaudenay","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2002,1,29]]},"reference":[{"key":"27_CR1","unstructured":"ANSI X9.31. Public-key cryptography using RSA for the financial services industry. American National Standard for Financial Services, draft, 1995."},{"key":"27_CR2","doi-asserted-by":"publisher","first-page":"29","DOI":"10.2307\/2152935","volume":"61","author":"A.O.L. Atkin","year":"1993","unstructured":"A.O.L. Atkin and F. Morain. Elliptic curves and primality proving. Mathematics of Computation, vol. 61, pp. 29\u201368, 1993.","journal-title":"Mathematics of Computation"},{"key":"27_CR3","series-title":"Lect Notes Comput Sci","doi-asserted-by":"publisher","first-page":"425","DOI":"10.1007\/BFb0052253","volume-title":"Advances in Cryptology-CRYPTO\u201997","author":"D. Boneh","year":"1997","unstructured":"D. Boneh and M. Franklin. Efficient generation of shared RSA keys. In Advances in Cryptology-CRYPTO\u201997, vol. 1294 of Lecture Notes in Computer Science, pp. 425\u2013439, Springer-Verlag, 1997."},{"key":"27_CR4","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"652","DOI":"10.1007\/3-540-46885-4_62","volume-title":"Advances in Cryptology-CRYPTO\u201989","author":"W. Bosma","year":"1990","unstructured":"W. Bosma and M.-P. van der Hulst. Faster primality testing. In Advances in Cryptology-CRYPTO\u201989, vol. 435 of Lecture Notes in Computer Science, pp. 652\u2013656, Springer-Verlag, 1990."},{"key":"27_CR5","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1007\/3-540-48071-4_26","volume-title":"Advances in Cryptology-CRYPTO\u2019 92","author":"J. Brandt","year":"1993","unstructured":"J. Brandt and I. Damg\u2222rd. On generation of probable primes by incremental search. In Advances in Cryptology-CRYPTO\u2019 92, vol. 740 of Lecture Notes in Computer Science, pp. 358\u2013370, Springer-Verlag, 1993."},{"key":"27_CR6","series-title":"Lect Notes Comput Sci","first-page":"440","volume-title":"Advances in Cryptology-ASIACRYPT\u201991","author":"J. Brandt","year":"1991","unstructured":"J. Brandt, I. Damg\u2222rd, and P. Landrock. Speeding up prime number generation. In Advances in Cryptology-ASIACRYPT\u201991, vol. 739 of Lecture Notes in Computer Science, pp. 440\u2013449, Springer-Verlag, 1991."},{"key":"27_CR7","first-page":"231","volume":"37","author":"C. Couvreur","year":"1982","unstructured":"C. Couvreur and J.-J. Quisquater. An introduction to fast generation of large prime numbers. Philips Journal of Research, vol. 37, pp. 231\u2013264, 1982.","journal-title":"Philips Journal of Research"},{"key":"27_CR8","doi-asserted-by":"crossref","unstructured":"C. Ding, D. Pei, and A. Salomaa. Chinese Remainder Theorem, Word Scientific, 1996.","DOI":"10.1142\/3254"},{"key":"27_CR9","unstructured":"FIPS 186. Digital signature standard. Federal Information Processing Standards Publication 186, US Department of Commerce\/N.I.S.T., 1994."},{"key":"27_CR10","unstructured":"D.E. Knuth. The Art of Computer Programming-Seminumerical Algorithms, vol. 2, Addison-Wesley, 2nd ed., 1981."},{"key":"27_CR11","unstructured":"A.J. Menezes, P.C. van Oorschot, and S.A. Vanstone. Handbook of Applied Cryptography, CRC Press, 1997."},{"key":"27_CR12","unstructured":"H.C. Pocklington. The determination of the prime or composite nature of large numbers by Fermat\u2019s theorem. Proc. of the Cambridge Philosophical Society, vol. 18, pp. 29\u201330, 1914."},{"key":"27_CR13","doi-asserted-by":"crossref","unstructured":"H. Riesel. Prime Numbers and Computer Methods for Factorization, Birkh\u00e4user, 1985.","DOI":"10.1007\/978-1-4757-1089-2"},{"key":"27_CR14","doi-asserted-by":"publisher","first-page":"62","DOI":"10.1080\/0161-117891852785","volume":"2","author":"R.L. Rivest","year":"1978","unstructured":"R.L. Rivest. Remarks on a proposed cryptanalytic attack on the M.I.T. public-key cryptosystem. Cryptologia, vol. 2, pp. 62\u201365, 1978.","journal-title":"Cryptologia"},{"key":"27_CR15","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.M. Adleman. A method for obtaining digital signatures and public-key cryptosystems. Communications of the ACM, vol. 21, pp. 120\u2013126, 1978.","journal-title":"Communications of the ACM"},{"key":"27_CR16","doi-asserted-by":"publisher","first-page":"84","DOI":"10.1137\/0206006","volume":"6","author":"R. Solovay","year":"1977","unstructured":"R. Solovay and V. Strassen. A fast Monte-Carlo test for primality. SIAM Journal on Computing, vol. 6, pp. 84\u201385, 1977.","journal-title":"SIAM Journal on Computing"}],"container-title":["Lecture Notes in Computer Science","Cryptographic Hardware and Embedded Systems \u2014 CHES 2000"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-44499-8_27","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,2,22]],"date-time":"2019-02-22T22:47:40Z","timestamp":1550875660000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-44499-8_27"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2000]]},"ISBN":["9783540414551","9783540444992"],"references-count":16,"URL":"https:\/\/doi.org\/10.1007\/3-540-44499-8_27","relation":{},"ISSN":["0302-9743"],"issn-type":[{"value":"0302-9743","type":"print"}],"subject":[],"published":{"date-parts":[[2000]]}}}