{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T11:54:28Z","timestamp":1791114868233,"version":"4.1.0"},"publisher-location":"Berlin, Heidelberg","reference-count":26,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642452383","type":"print"},{"value":"9783642452390","type":"electronic"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2013]]},"DOI":"10.1007\/978-3-642-45239-0_10","type":"book-chapter","created":{"date-parts":[[2013,12,11]],"date-time":"2013-12-11T03:20:44Z","timestamp":1386732044000},"page":"158-172","source":"Crossref","is-referenced-by-count":6,"title":["Recovering Private Keys Generated with Weak PRNGs"],"prefix":"10.1007","author":[{"given":"Pierre-Alain","family":"Fouque","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mehdi","family":"Tibouchi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jean-Christophe","family":"Zapalowicz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","reference":[{"key":"10_CR1","doi-asserted-by":"crossref","unstructured":"Barak, B., Halevi, S.: A model and architecture for pseudo-random generation with applications to \/dev\/random. In: ACM CCS, pp. 203\u2013212 (2005)","DOI":"10.1145\/1102120.1102148"},{"key":"10_CR2","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/BFb0052242","volume-title":"Advances in Cryptology - CRYPTO \u201997","author":"M. Bellare","year":"1997","unstructured":"Bellare, M., Goldwasser, S., Micciancio, D.: \u201cPseudo-random\u201d number generation within cryptographic algorithms: The DSS case. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol.\u00a01294, pp. 277\u2013291. Springer, Heidelberg (1997)"},{"key":"10_CR3","unstructured":"Bleichenbacher, D.: On the generation of one-time keys in DL signature schemes. Presentation at the IEEE P1363 Working Group Meeting (November 2000)"},{"issue":"2","key":"10_CR4","doi-asserted-by":"publisher","first-page":"364","DOI":"10.1137\/0215025","volume":"15","author":"L. Blum","year":"1986","unstructured":"Blum, L., Blum, M., Shub, M.: A simple unpredictable pseudo-random number generator. SIAM J. Comput.\u00a015(2), 364\u2013383 (1986)","journal-title":"SIAM J. Comput."},{"issue":"4","key":"10_CR5","doi-asserted-by":"publisher","first-page":"850","DOI":"10.1137\/0213053","volume":"13","author":"M. Blum","year":"1984","unstructured":"Blum, M., Micali, S.: How to generate cryptographically strong sequences of pseudo-random bits. SIAM J. Comput.\u00a013(4), 850\u2013864 (1984)","journal-title":"SIAM J. Comput."},{"issue":"1-3","key":"10_CR6","doi-asserted-by":"publisher","first-page":"223","DOI":"10.1016\/j.tcs.2004.09.002","volume":"329","author":"A. Bostan","year":"2004","unstructured":"Bostan, A., Schost, \u00c9.: On the complexities of multipoint evaluation and interpolation. Theor. Comput. Sci.\u00a0329(1-3), 223\u2013235 (2004)","journal-title":"Theor. Comput. Sci."},{"issue":"4","key":"10_CR7","doi-asserted-by":"publisher","first-page":"420","DOI":"10.1016\/j.jco.2004.09.009","volume":"21","author":"A. Bostan","year":"2005","unstructured":"Bostan, A., Schost, \u00c9.: Polynomial evaluation and interpolation on special sets of points. J. Complexity\u00a021(4), 420\u2013446 (2005)","journal-title":"J. Complexity"},{"issue":"3","key":"10_CR8","doi-asserted-by":"publisher","first-page":"177","DOI":"10.1007\/BF02252875","volume":"1","author":"J. Boyar","year":"1989","unstructured":"Boyar, J.: Inferring sequences produced by a linear congruential generator missing low-order bits. J. Cryptology\u00a01(3), 177\u2013184 (1989)","journal-title":"J. Cryptology"},{"issue":"1","key":"10_CR9","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1145\/58562.59305","volume":"36","author":"J. Boyar","year":"1989","unstructured":"Boyar, J.: Inferring sequences produced by pseudo-random number generators. J. ACM\u00a036(1), 129\u2013141 (1989)","journal-title":"J. ACM"},{"key":"10_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"358","DOI":"10.1007\/3-540-48071-4_26","volume-title":"Advances in Cryptology - CRYPTO \u201992","author":"J. Brandt","year":"1993","unstructured":"Brandt, J., Damg\u00e5rd, I.B.: On generation of probable primes by incremental search. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol.\u00a0740, pp. 358\u2013370. Springer, Heidelberg (1993)"},{"key":"10_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"502","DOI":"10.1007\/978-3-642-29011-4_30","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2012","author":"Y. Chen","year":"2012","unstructured":"Chen, Y., Nguyen, P.Q.: Faster algorithms for approximate common divisors: Breaking fully-homomorphic-encryption challenges over the integers. In: Pointcheval, D., Johansson, T. (eds.) EUROCRYPT 2012. LNCS, vol.\u00a07237, pp. 502\u2013519. Springer, Heidelberg (2012)"},{"key":"10_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1007\/11506157_5","volume-title":"Information Security and Privacy","author":"S. Contini","year":"2005","unstructured":"Contini, S., Shparlinski, I.E.: On stern\u2019s attack against secret truncated linear congruential generators. In: Boyd, C., Gonz\u00e1lez Nieto, J.M. (eds.) ACISP 2005. LNCS, vol.\u00a03574, pp. 52\u201360. Springer, Heidelberg (2005)"},{"key":"10_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/978-3-642-19379-8_9","volume-title":"Public Key Cryptography \u2013 PKC 2011","author":"J.-S. Coron","year":"2011","unstructured":"Coron, J.-S., Joux, A., Mandal, A., Naccache, D., Tibouchi, M.: Cryptanalysis of the RSA subgroup assumption from TCC 2005. In: Catalano, D., Fazio, N., Gennaro, R., Nicolosi, A. (eds.) PKC 2011. LNCS, vol.\u00a06571, pp. 147\u2013155. Springer, Heidelberg (2011)"},{"key":"10_CR14","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"368","DOI":"10.1007\/3-540-46035-7_24","volume-title":"Advances in Cryptology - EUROCRYPT 2002","author":"A. Desai","year":"2002","unstructured":"Desai, A., Hevia, A., Yin, Y.L.: A practice-oriented treatment of pseudorandom number generators. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol.\u00a02332, pp. 368\u2013383. Springer, Heidelberg (2002)"},{"key":"10_CR15","doi-asserted-by":"crossref","unstructured":"Fiduccia, C.M.: Polynomial evaluation via the division algorithm: The fast fourier transform revisited. In: STOC, pp. 88\u201393 (1972)","DOI":"10.1145\/800152.804900"},{"issue":"2","key":"10_CR16","doi-asserted-by":"publisher","first-page":"262","DOI":"10.1137\/0217016","volume":"17","author":"A.M. Frieze","year":"1988","unstructured":"Frieze, A.M., H\u00e5stad, J., Kannan, R., Lagarias, J.C., Shamir, A.: Reconstructing truncated integer variables satisfying linear congruences. SIAM J. Comput.\u00a017(2), 262\u2013280 (1988)","journal-title":"SIAM J. Comput."},{"key":"10_CR17","unstructured":"Heninger, N., Durumeric, Z., Wustrow, E., Alex Halderman, J.: Mining your Ps and Qs: Detection of widespread weak keys in network devices. In: Kohno, T. (ed.) USENIX Security 2012 (2012)"},{"issue":"3","key":"10_CR18","doi-asserted-by":"publisher","first-page":"283","DOI":"10.1023\/A:1011214926272","volume":"23","author":"N. Howgrave-Graham","year":"2001","unstructured":"Howgrave-Graham, N., Smart, N.P.: Lattice attacks on digital signature schemes. Des. Codes Cryptography\u00a023(3), 283\u2013290 (2001)","journal-title":"Des. Codes Cryptography"},{"issue":"3","key":"10_CR19","doi-asserted-by":"publisher","first-page":"161","DOI":"10.1007\/s001459900042","volume":"11","author":"A. Joux","year":"1998","unstructured":"Joux, A., Stern, J.: Lattice reduction: A toolbox for the cryptanalyst. J. Cryptology\u00a011(3), 161\u2013185 (1998)","journal-title":"J. Cryptology"},{"key":"10_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"626","DOI":"10.1007\/978-3-642-32009-5_37","volume-title":"Advances in Cryptology \u2013 CRYPTO 2012","author":"A.K. Lenstra","year":"2012","unstructured":"Lenstra, A.K., Hughes, J.P., Augier, M., Bos, J.W., Kleinjung, T., Wachter, C.: Public keys. In: Safavi-Naini, R., Canetti, R. (eds.) CRYPTO 2012. LNCS, vol.\u00a07417, pp. 626\u2013642. Springer, Heidelberg (2012)"},{"issue":"4","key":"10_CR21","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"A.K. Lenstra","year":"1982","unstructured":"Lenstra, A.K., Lenstra Jr., H.W., Lov\u00e1sz, L.: Factoring polynomials with rational coefficients. Math. Ann.\u00a0261(4), 515\u2013534 (1982)","journal-title":"Math. Ann."},{"key":"10_CR22","unstructured":"Menezes, A., Van Oorschot, P.C., Vanstone, S.A.: Handbook of Applied Cryptography (1996)"},{"issue":"3","key":"10_CR23","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1007\/BF00196909","volume":"3","author":"S. Micali","year":"1991","unstructured":"Micali, S., Schnorr, C.-P.: Efficient, perfect polynomial random number generators. J. Cryptology\u00a03(3), 157\u2013172 (1991)","journal-title":"J. Cryptology"},{"issue":"3","key":"10_CR24","doi-asserted-by":"publisher","first-page":"151","DOI":"10.1007\/s00145-002-0021-3","volume":"15","author":"P.Q. Nguyen","year":"2002","unstructured":"Nguyen, P.Q., Shparlinski, I.: The insecurity of the digital signature algorithm with partially known nonces. J. Cryptology\u00a015(3), 151\u2013176 (2002)","journal-title":"J. Cryptology"},{"key":"10_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"544","DOI":"10.1007\/3-540-10843-2_43","volume-title":"Automata, Languages and Programming","author":"A. Shamir","year":"1981","unstructured":"Shamir, A.: On the generation of cryptographically strong pseudo-random sequences. In: Even, S., Kariv, O. (eds.) ICALP 1981. LNCS, vol.\u00a0115, pp. 544\u2013550. Springer, Heidelberg (1981); U. C. Santa Barbara, Dept. of Elec. and Computer Eng., ECE Report No 82-04"},{"key":"10_CR26","doi-asserted-by":"crossref","unstructured":"Stern, J.: Secret linear congruential generators are not cryptographically secure. In: FOCS, pp. 421\u2013426. IEEE Computer Society (1987)","DOI":"10.1109\/SFCS.1987.51"}],"container-title":["Lecture Notes in Computer Science","Cryptography and Coding"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-45239-0_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,25]],"date-time":"2019-05-25T07:45:21Z","timestamp":1558770321000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-45239-0_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"ISBN":["9783642452383","9783642452390"],"references-count":26,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-45239-0_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013]]}}}