{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T12:58:02Z","timestamp":1772283482312,"version":"3.50.1"},"publisher-location":"Cham","reference-count":20,"publisher":"Springer International Publishing","isbn-type":[{"value":"9783319224244","type":"print"},{"value":"9783319224251","type":"electronic"}],"license":[{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"},{"start":{"date-parts":[[2015,1,1]],"date-time":"2015-01-01T00:00:00Z","timestamp":1420070400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springernature.com\/gp\/researchers\/text-and-data-mining"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-319-22425-1_5","type":"book-chapter","created":{"date-parts":[[2015,8,19]],"date-time":"2015-08-19T14:42:31Z","timestamp":1439995351000},"page":"67-76","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Implicit Factorization of RSA Moduli Revisited (Short Paper)"],"prefix":"10.1007","author":[{"given":"Liqiang","family":"Peng","sequence":"first","affiliation":[]},{"given":"Lei","family":"Hu","sequence":"additional","affiliation":[]},{"given":"Yao","family":"Lu","sequence":"additional","affiliation":[]},{"given":"Zhangjie","family":"Huang","sequence":"additional","affiliation":[]},{"given":"Jun","family":"Xu","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,8,20]]},"reference":[{"key":"5_CR1","unstructured":"Ajtai, M.: Generating random lattices according to the invariant distribution. Draft of March (2006)"},{"key":"5_CR2","doi-asserted-by":"crossref","unstructured":"Ajtai, M.: The shortest vector problem in $$L_2$$ is $$NP$$-hard for randomized reductions (extended abstract). In: Vitter, J.S. (ed.) STOC 1998. pp. 10\u201319. ACM (1998)","DOI":"10.1145\/276698.276705"},{"key":"5_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"341","DOI":"10.1007\/978-3-642-42045-0_18","volume-title":"Advances in Cryptology - ASIACRYPT 2013","author":"DJ Bernstein","year":"2013","unstructured":"Bernstein, D.J., Chang, Y.-A., Cheng, C.-M., Chou, L.-P., Heninger, N., Lange, T., van Someren, N.: Factoring RSA keys from certified smart cards: Coppersmith in the wild. In: Sako, K., Sarkar, P. (eds.) ASIACRYPT 2013, Part II. LNCS, vol. 8270, pp. 341\u2013360. Springer, Heidelberg (2013)"},{"issue":"4","key":"5_CR4","doi-asserted-by":"publisher","first-page":"1339","DOI":"10.1109\/18.850673","volume":"46","author":"D Boneh","year":"2000","unstructured":"Boneh, D., Durfee, G.: Cryptanalysis of RSA with private key d less than N$${}^{\\text{0.292 }}$$. IEEE Trans. Inf. Theor. 46(4), 1339\u20131349 (2000)","journal-title":"IEEE Trans. Inf. Theor."},{"issue":"3\u20134","key":"5_CR5","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1006\/jsco.1996.0125","volume":"24","author":"W Bosma","year":"1997","unstructured":"Bosma, W., Cannon, J.J., Playoust, C.: The magma algebra system I: the user language. J. Symbolic Comput. 24(3\u20134), 235\u2013265 (1997)","journal-title":"J. Symbolic Comput."},{"issue":"4","key":"5_CR6","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s001459900030","volume":"10","author":"D Coppersmith","year":"1997","unstructured":"Coppersmith, D.: Small solutions to polynomial equations, and low exponent RSA vulnerabilities. J. Crypt. 10(4), 233\u2013260 (1997)","journal-title":"J. Crypt."},{"issue":"1","key":"5_CR7","doi-asserted-by":"publisher","first-page":"39","DOI":"10.1007\/s00145-006-0433-6","volume":"20","author":"J Coron","year":"2007","unstructured":"Coron, J., May, A.: Deterministic polynomial-time equivalence of computing the RSA secret key and factoring. J. Crypt. 20(1), 39\u201350 (2007)","journal-title":"J. Crypt."},{"key":"5_CR8","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"70","DOI":"10.1007\/978-3-642-13013-7_5","volume-title":"Public Key Cryptography \u2013 PKC 2010","author":"J-C Faug\u00e8re","year":"2010","unstructured":"Faug\u00e8re, J.-C., Marinier, R., Renault, G.: Implicit factoring with shared most significant and middle bits. In: Nguyen, P.Q., Pointcheval, D. (eds.) PKC 2010. LNCS, vol. 6056, pp. 70\u201387. Springer, Heidelberg (2010)"},{"key":"5_CR9","series-title":"LNCS","first-page":"131","volume-title":"Cryptography and Coding 1997","author":"N Howgrave-Graham","year":"1997","unstructured":"Howgrave-Graham, N.: Finding small roots of univariate modular equations revisited. In: Darnell, M.J. (ed.) Cryptography and Coding 1997. LNCS, vol. 1355, pp. 131\u2013142. Springer, Heidelberg (1997)"},{"key":"5_CR10","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/11935230_18","volume-title":"Advances in Cryptology \u2013 ASIACRYPT 2006","author":"E Jochemsz","year":"2006","unstructured":"Jochemsz, E., May, A.: A strategy for finding roots of multivariate polynomials with new applications in attacking RSA variants. In: Lai, X., Chen, K. (eds.) ASIACRYPT 2006. LNCS, vol. 4284, pp. 267\u2013282. Springer, Heidelberg (2006)"},{"key":"5_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"395","DOI":"10.1007\/978-3-540-74143-5_22","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"E Jochemsz","year":"2007","unstructured":"Jochemsz, E., May, A.: A polynomial time attack on RSA with private CRT-exponents smaller than $$N^0.073$$. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 395\u2013411. Springer, Heidelberg (2007)"},{"key":"5_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"217","DOI":"10.1007\/978-3-642-41383-4_14","volume-title":"Advances in Information and Computer Security","author":"K Kurosawa","year":"2013","unstructured":"Kurosawa, K., Ueda, T.: How to factor $$N_1$$ and $$N_2$$ when $$p_1=p_2\\;mod\\;2^t$$. In: Sakiyama, K., Terada, M. (eds.) IWSEC 2013. LNCS, vol. 8231, pp. 217\u2013225. Springer, Heidelberg (2013)"},{"key":"5_CR13","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":"AK 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. 7417, pp. 626\u2013642. Springer, Heidelberg (2012)"},{"issue":"4","key":"5_CR14","doi-asserted-by":"publisher","first-page":"515","DOI":"10.1007\/BF01457454","volume":"261","author":"AK Lenstra","year":"1982","unstructured":"Lenstra, A.K., Lenstra, H.W., Lov\u00e1sz, L.: Factoring polynomials with rational coefficients. Math. Ann. 261(4), 515\u2013534 (1982)","journal-title":"Math. Ann."},{"key":"5_CR15","first-page":"825","volume":"2014","author":"Y Lu","year":"2014","unstructured":"Lu, Y., Peng, L., Zhang, R., Lin, D.: Towards optimal bounds for implicit factorization problem. IACR Crypt. ePrint Arch. 2014, 825 (2014)","journal-title":"IACR Crypt. ePrint Arch."},{"key":"5_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/978-3-642-00468-1_1","volume-title":"Public Key Cryptography \u2013 PKC 2009","author":"A May","year":"2009","unstructured":"May, A., Ritzenhofen, M.: Implicit factoring: on polynomial time factoring given only an implicit hint. In: Jarecki, S., Tsudik, G. (eds.) PKC 2009. LNCS, vol. 5443, pp. 1\u201314. Springer, Heidelberg (2009)"},{"key":"5_CR17","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1007\/978-3-319-06734-6_11","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2014","author":"L Peng","year":"2014","unstructured":"Peng, L., Hu, L., Xu, J., Huang, Z., Xie, Y.: Further improvement of factoring RSA moduli with implicit hint. In: Pointcheval, D., Vergnaud, D. (eds.) AFRICACRYPT. LNCS, vol. 8469, pp. 165\u2013177. Springer, Heidelberg (2014)"},{"issue":"1","key":"5_CR18","doi-asserted-by":"publisher","first-page":"96","DOI":"10.1145\/357980.358017","volume":"26","author":"RL Rivest","year":"1983","unstructured":"Rivest, R.L., Shamir, A., Adleman, L.M.: A method for obtaining digital signatures and public-key cryptosystems (reprint). Commun. ACM 26(1), 96\u201399 (1983)","journal-title":"Commun. ACM"},{"issue":"6","key":"5_CR19","doi-asserted-by":"publisher","first-page":"4002","DOI":"10.1109\/TIT.2011.2137270","volume":"57","author":"S Sarkar","year":"2011","unstructured":"Sarkar, S., Maitra, S.: Approximate integer common divisor problem relates to implicit factorization. IEEE Trans. Inf. Theor. 57(6), 4002\u20134013 (2011)","journal-title":"IEEE Trans. Inf. Theor."},{"issue":"3","key":"5_CR20","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1109\/18.54902","volume":"36","author":"MJ Wiener","year":"1990","unstructured":"Wiener, M.J.: Cryptanalysis of short RSA secret exponents. IEEE Trans. Inf. Theor. 36(3), 553\u2013558 (1990)","journal-title":"IEEE Trans. Inf. Theor."}],"container-title":["Lecture Notes in Computer Science","Advances in Information and Computer Security"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-319-22425-1_5","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,1,24]],"date-time":"2023-01-24T13:41:51Z","timestamp":1674567711000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/978-3-319-22425-1_5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783319224244","9783319224251"],"references-count":20,"URL":"https:\/\/doi.org\/10.1007\/978-3-319-22425-1_5","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2015]]},"assertion":[{"value":"20 August 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}