{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,19]],"date-time":"2025-09-19T08:16:19Z","timestamp":1758269779038},"publisher-location":"Berlin, Heidelberg","reference-count":23,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783540006466"},{"type":"electronic","value":"9783540365044"}],"license":[{"start":{"date-parts":[[2003,1,1]],"date-time":"2003-01-01T00:00:00Z","timestamp":1041379200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2003]]},"DOI":"10.1007\/3-540-36504-4_10","type":"book-chapter","created":{"date-parts":[[2007,7,20]],"date-time":"2007-07-20T14:48:45Z","timestamp":1184942925000},"page":"136-146","source":"Crossref","is-referenced-by-count":31,"title":["CryptoComputing with Rationals"],"prefix":"10.1007","author":[{"given":"Pierre-Alain","family":"Fouque","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jacques","family":"Stern","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Geert-Jan","family":"Wackers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"1","key":"10_CR1","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02252866","volume":"2","author":"M. Abadi","year":"1990","unstructured":"M. Abadi and J. Feigenbaum. Secure circuit evaluation: a protocol based on hiding information from an oracle. Journal of Cryptology, 2(1):1\u201312, 1990.","journal-title":"Journal of Cryptology"},{"key":"10_CR2","doi-asserted-by":"crossref","unstructured":"O. Baudron, P.A. Fouque, D. Pointcheval, G. Poupard, and J. Stern. Practical Multi-Candidate Election System. In PODC\u2019 01. ACM, 2001.","DOI":"10.1145\/383962.384044"},{"key":"10_CR3","series-title":"Lect Notes Comput Sci","volume-title":"Financial Crypto\u2019 01","author":"O. Baudron","year":"2001","unstructured":"O. Baudron and J. Stern. Non-interactive Private Auctions. In Financial Crypto\u2019 01, LNCS. Springer-Verlag, Berlin, 2001."},{"key":"10_CR4","unstructured":"J. Benaloh. Verifiable Secret-Ballot Elections. PhD thesis, Yale University, 1987."},{"key":"10_CR5","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1007\/3-540-68697-5_22","volume-title":"Crypto\u2019 96","author":"D. Boneh","year":"1996","unstructured":"D. Boneh and R. Lipton. Searching for Elements in Black-Box Fields and Applications. In Crypto\u2019 96, LNCS 1109, pages 283\u2013297. Springer-Verlag, 1996."},{"key":"10_CR6","doi-asserted-by":"crossref","unstructured":"H. Cohen. A Course in Computational Algebraic Number Theory. Graduate Texts in Mathematics 138. Springer-Verlag, 1993.","DOI":"10.1007\/978-3-662-02945-9"},{"key":"10_CR7","doi-asserted-by":"crossref","unstructured":"J. Cohen and M. Fisher. A robust and verifiable cryptographically secure election scheme. In Symposium on Foundations of Computer Science. IEEE, 1985.","DOI":"10.1109\/SFCS.1985.2"},{"key":"10_CR8","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"280","DOI":"10.1007\/3-540-44987-6_18","volume-title":"Eurocrypt\u2019 01","author":"R. Cramer","year":"2001","unstructured":"R. Cramer, I. Damg\u00e5rd, and J. B. Nielsen. Multiparty computation from threshold homomorphic encryption. In Eurocrypt\u2019 01, LNCS 2045, pages 280\u2013300. Springer-Verlag, 2001."},{"key":"10_CR9","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/3-540-44586-2_9","volume-title":"PKC\u2019 01","author":"I. Damg\u00e5rd","year":"2001","unstructured":"I. Damg\u00e5rd and M. Jurik. Efficient Protocols based on Probabilistic Encryption using Composite Degree Residue Classes. In PKC\u2019 01, LNCS 1992, pages 119\u2013136. Springer-Verlag, 2001."},{"issue":"4","key":"10_CR10","doi-asserted-by":"publisher","first-page":"397","DOI":"10.1017\/S0963548397003258","volume":"6","author":"H. Daud\u00e9","year":"1997","unstructured":"H. Daud\u00e9, P; Flajolet, and B. Vall\u00e9e. An average-case analysis of the gaussian algorithm for lattice reduction. Combin. Probab. Comput, 6(4):397\u2013433, 1997.","journal-title":"Combin. Probab. Comput"},{"key":"10_CR11","first-page":"1","volume":"2","author":"J. Feigenbaum","year":"1991","unstructured":"J. Feigenbaum and M. Merritt. Open Questions, Talks Abstracts, and Summary of Discussions. DIM ACS Series in Discrete Mathematics and Theoretical Computer Science, 2:1\u201345, 1991.","journal-title":"DIM ACS Series in Discrete Mathematics and Theoretical Computer Science"},{"key":"10_CR12","series-title":"Lect Notes Comput Sci","volume-title":"Financial Crypto\u2019 00","author":"P. A. Fouque","year":"2000","unstructured":"P. A. Fouque, G. Poupard, and J. Stern. Sharing Decryption in the Context of Voting or Lotteries. In Financial Crypto\u2019 00, LNCS. Springer-Verlag, 2000."},{"key":"10_CR13","doi-asserted-by":"crossref","unstructured":"S. Goldwasser and S. Micali. Probabilistic encryption. Journal of Computer and System Sciences, 28, 1984.","DOI":"10.1016\/0022-0000(84)90070-9"},{"key":"10_CR14","unstructured":"A. Joux. La R\u00e9duction des R\u00e9seaux en Cryptographie. PhD thesis, \u00c9cole polytechnique, 1993."},{"key":"10_CR15","doi-asserted-by":"crossref","unstructured":"D. Naccache and J. Stern. A New Public Key Cryptosystem Based on Higher Residues. In Proc. of the 5th CCCS, pages 59\u201366. ACM press, 1998.","DOI":"10.1145\/288090.288106"},{"key":"10_CR16","series-title":"Lect Notes Comput Sci","doi-asserted-by":"publisher","first-page":"308","DOI":"10.1007\/BFb0054135","volume-title":"Eurocrypt\u2019 98","author":"T. Okamoto","year":"1998","unstructured":"T. Okamoto and S. Uchiyama. A New Public-Key Cryptosystem as Secure as Factoring. In Eurocrypt\u2019 98, LNCS 1403, pages 308\u2013318. Springer-Verlag, 1998."},{"key":"10_CR17","series-title":"Lect Notes Comput Sci","first-page":"223","volume-title":"Eurocrypt\u2019 99","author":"P. Paillier","year":"1999","unstructured":"P. Paillier. Public-Key Cryptosystems Based on Composite Degree Residuosity Classes. In Eurocrypt\u2019 99, LNCS 1592, pages 223\u2013238. Springer-Verlag, 1999."},{"key":"10_CR18","series-title":"Lect Notes Comput Sci","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1007\/3-540-45539-6_13","volume-title":"Proceedings of Eurocrypt 2000","author":"G. Poupard","year":"2000","unstructured":"G. Poupard and J. Stern. Fair Encryption of RSA Keys. In Proceedings of Eurocrypt 2000, Lecture Notes in Computer Science, pages 172\u2013189. Springer-Verlag, 2000."},{"key":"10_CR19","unstructured":"R. Rivest, L. Adleman, and M. L. Dertouzos. On Data Banks and Privacy Homomorphisms. In Foundations of Secure Computation, pages 169\u2013179. Academic Press, 1978."},{"key":"10_CR20","unstructured":"T. Sander, A. Young, and M. Yung. Non-Interactive CryptoComputing for NC\n                1. In Proc. of the 31st STOC. ACM, 1999."},{"key":"10_CR21","unstructured":"V. Shoup. Number Theory Library (NTL). Can be obtained at \n                  http:\/\/www.shoup.net."},{"key":"10_CR22","doi-asserted-by":"publisher","first-page":"556","DOI":"10.1016\/0196-6774(91)90033-U","volume":"12","author":"B. Vall\u00e9e","year":"1991","unstructured":"B. Vall\u00e9e. Gauss\u2019 algorithm revisited. J. Algorithms, 12:556\u2013572, 1991.","journal-title":"J. Algorithms"},{"key":"10_CR23","doi-asserted-by":"crossref","unstructured":"S. Vanstone and R. Zuccherato. Elliptic Curve Cryptosystem Using Curves of Smooth Order Over the Ring Z\n                n. IEEE Transaction on Information Theory, IT-43, 1997.","DOI":"10.1109\/18.605586"}],"container-title":["Lecture Notes in Computer Science","Financial Cryptography"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/3-540-36504-4_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,21]],"date-time":"2019-05-21T20:00:14Z","timestamp":1558468814000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/3-540-36504-4_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003]]},"ISBN":["9783540006466","9783540365044"],"references-count":23,"URL":"https:\/\/doi.org\/10.1007\/3-540-36504-4_10","relation":{},"ISSN":["0302-9743"],"issn-type":[{"type":"print","value":"0302-9743"}],"subject":[],"published":{"date-parts":[[2003]]}}}