{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,9,6]],"date-time":"2024-09-06T03:35:32Z","timestamp":1725593732700},"publisher-location":"Berlin, Heidelberg","reference-count":32,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642219689"},{"type":"electronic","value":"9783642219696"}],"license":[{"start":{"date-parts":[[2011,1,1]],"date-time":"2011-01-01T00:00:00Z","timestamp":1293840000000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2011]]},"DOI":"10.1007\/978-3-642-21969-6_15","type":"book-chapter","created":{"date-parts":[[2011,6,28]],"date-time":"2011-06-28T19:41:28Z","timestamp":1309290088000},"page":"242-259","source":"Crossref","is-referenced-by-count":0,"title":["Using the Inhomogeneous Simultaneous Approximation Problem for Cryptographic Design"],"prefix":"10.1007","author":[{"given":"Frederik","family":"Armknecht","sequence":"first","affiliation":[]},{"given":"Carsten","family":"Elsner","sequence":"additional","affiliation":[]},{"given":"Martin","family":"Schmidt","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"5\/6","key":"15_CR1","doi-asserted-by":"publisher","first-page":"1507","DOI":"10.1007\/BF01054431","volume":"66","author":"P.R. Baldwin","year":"1992","unstructured":"Baldwin, P.R.: A convergence exponent for multidimensional continued-fraction algorithms. Journal of Statistical Physics\u00a066(5\/6), 1507\u20131526 (1992)","journal-title":"Journal of Statistical Physics"},{"key":"15_CR2","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0069405","volume-title":"The Jacobi-Perron algorithm, it\u2019s theory and application","author":"L. Bernstein","year":"1971","unstructured":"Bernstein, L.: The Jacobi-Perron algorithm, it\u2019s theory and application. Lecture Notes in Mathematics, vol.\u00a0207. Springer, Heidelberg (1971)"},{"key":"15_CR3","unstructured":"Brentjes, A.J.: Multi-dimensional continued fraction algorithms. Mathematical Centre Tracts\u00a0145 (1981)"},{"key":"15_CR4","unstructured":"Elsner, C., Schmidt, M.: KronCrypt - a new symmetric cryptosystem based on Kronecker\u2019s approximation theorem. Cryptology ePrint Archive, Report 2009\/416 (2009), http:\/\/eprint.iacr.org\/"},{"issue":"2","key":"15_CR5","doi-asserted-by":"publisher","first-page":"13","DOI":"10.1145\/1236463.1236468","volume":"33","author":"L. Fousse","year":"2007","unstructured":"Fousse, L., Hanrot, G., Lef\u00e8vre, V., P\u00e9lissier, P., Zimmermann, P.: MPFR: A multiple-precision binary floating-point library with correct rounding. ACM Trans. Math. Softw.\u00a033(2), 13 (2007)","journal-title":"ACM Trans. Math. Softw."},{"key":"15_CR6","doi-asserted-by":"publisher","first-page":"134","DOI":"10.1007\/BF01899194","volume":"39","author":"R. G\u00e4rtner","year":"1982","unstructured":"G\u00e4rtner, R.: Zur Geometrie des Jacobi-Perron Algorithmus. Arch. Math.\u00a039, 134\u2013146 (1982)","journal-title":"Arch. Math."},{"issue":"2","key":"15_CR7","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1016\/S0020-0190(99)00083-6","volume":"71","author":"O. Goldreich","year":"1999","unstructured":"Goldreich, O., Micciancio, D., Safra, S., Seifert, J.-P.: Approximating shortest lattice vectors is not harder than approximating closest lattice vectors. Information Processing Letters\u00a071(2), 55\u201361 (1999)","journal-title":"Information Processing Letters"},{"key":"15_CR8","volume-title":"An introduction to the theory of numbers","author":"G.H. Hardy","year":"1954","unstructured":"Hardy, G.H., Wright, E.M.: An introduction to the theory of numbers, 3rd edn. Clarendon Press, Oxford (1954)","edition":"3"},{"key":"15_CR9","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"47","DOI":"10.1007\/3-540-46885-4_7","volume-title":"Advances in Cryptology - EUROCRYPT \u201989","author":"H. Isselhorst","year":"1990","unstructured":"Isselhorst, H.: The use of fractions in public-key cryptosystems. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol.\u00a0434, pp. 47\u201355. Springer, Heidelberg (1990)"},{"key":"15_CR10","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1515\/crll.1868.69.29","volume":"69","author":"C.G.J. Jacobi","year":"1868","unstructured":"Jacobi, C.G.J.: Allgemeine Theorie der kettenbruch\u00e4hnlichen Algorithmen, in welchen jede Zahl aus drei vorhergehenden gebildet wird. Journal F\u00fcr Die Reine und Angewandte Mathematik (Crelle\u2019s Journal)\u00a069, 29\u201364 (1868)","journal-title":"Journal F\u00fcr Die Reine und Angewandte Mathematik (Crelle\u2019s Journal)"},{"key":"15_CR11","doi-asserted-by":"publisher","first-page":"909","DOI":"10.1137\/0221054","volume":"21","author":"B. Just","year":"1992","unstructured":"Just, B.: Generalizing the continued fraction algorithm to arbitrary dimensions. SIAM Journal on Computing\u00a021, 909\u2013926 (1992)","journal-title":"SIAM Journal on Computing"},{"key":"15_CR12","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/3-540-39799-X_1","volume-title":"Advances in Cryptology","author":"D. Estes","year":"1986","unstructured":"Estes, D., Adleman, L.M., Kompella, K., McCurley, K.S., Miller, G.L.: Breaking the Ong-Schnorr-Shamir signature scheme for quadratic number fields. In: Williams, H.C. (ed.) CRYPTO 1985. LNCS, vol.\u00a0218, pp. 3\u201313. Springer, Heidelberg (1986)"},{"issue":"1","key":"15_CR13","doi-asserted-by":"publisher","first-page":"196","DOI":"10.1137\/0214016","volume":"14","author":"J.C. Lagarias","year":"1985","unstructured":"Lagarias, J.C.: The computational complexity of simultaneous diophantine approximation problems. SIAM J. Comput.\u00a014(1), 196\u2013209 (1985)","journal-title":"SIAM J. Comput."},{"key":"15_CR14","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., Lovasz, L.: Factoring polynomials with rational coefficients. Mathematische Annalen\u00a0261, 515\u2013534 (1982)","journal-title":"Mathematische Annalen"},{"issue":"4","key":"15_CR15","doi-asserted-by":"publisher","first-page":"538","DOI":"10.1287\/moor.8.4.538","volume":"8","author":"H.W. Lenstra Jr.","year":"1983","unstructured":"Lenstra Jr., H.W.: Integer programming with a fixed number of variables. Mathematics of Operations Research\u00a08(4), 538\u2013548 (1983)","journal-title":"Mathematics of Operations Research"},{"key":"15_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-68130-1","volume-title":"Introduction to number theory","author":"H.L. Keng","year":"1982","unstructured":"Keng, H.L.: Introduction to number theory, 5th edn. Springer, Heidelberg (1982)","edition":"5"},{"key":"15_CR17","volume-title":"Information Security and Cryptography","author":"P.Q. Nguyen","year":"2010","unstructured":"Nguyen, P.Q., Valle, B.: The LLL Algorithm. Survey and Applications. In: Information Security and Cryptography, Springer, Heidelberg (2010)"},{"key":"15_CR18","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF01449880","volume":"64","author":"O. Perron","year":"1907","unstructured":"Perron, O.: Grundlagen f\u00fcr eine Theorie des Jacobischen Kettenbruchalgorithmus. Math. Ann.\u00a064, 1\u201376 (1907)","journal-title":"Math. Ann."},{"issue":"6","key":"15_CR19","doi-asserted-by":"publisher","first-page":"899","DOI":"10.1145\/1039488.1039490","volume":"51","author":"O. Regev","year":"2004","unstructured":"Regev, O.: New lattice-based cryptographic constructions. J. ACM\u00a051(6), 899\u2013942 (2004)","journal-title":"J. ACM"},{"key":"15_CR20","volume-title":"Zahlentheorie","author":"G.J. Rieger","year":"1976","unstructured":"Rieger, G.J.: Zahlentheorie. Vandenhoeck & Ruprecht, G\u00f6ttingen (1976)"},{"key":"15_CR21","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"494","DOI":"10.1007\/3-540-61550-4_173","volume-title":"Mathematical Foundations of Computer Science 1996","author":"C. R\u00f6ssner","year":"1996","unstructured":"R\u00f6ssner, C., Seifert, J.-P.: Approximating good simultaneous diophantine approximations is almost NP-hard. In: Penczek, W., Sza\u0142as, A. (eds.) MFCS 1996. LNCS, vol.\u00a01113, pp. 494\u2013505. Springer, Heidelberg (1996)"},{"key":"15_CR22","volume-title":"Diophantine approximations","author":"W. Schmidt","year":"1980","unstructured":"Schmidt, W.: Diophantine approximations. Springer, Berlin (1980)"},{"key":"15_CR23","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"281","DOI":"10.1007\/3-540-46416-6_24","volume-title":"Advances in Cryptology - EUROCRYPT \u201991","author":"C.-P. Schnorr","year":"1991","unstructured":"Schnorr, C.-P.: Factoring integers and computing discrete logarithms via diophantine approximation. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol.\u00a0547, pp. 281\u2013293. Springer, Heidelberg (1991)"},{"key":"15_CR24","series-title":"Lecture Notes in Mathematics","doi-asserted-by":"crossref","DOI":"10.1007\/BFb0059845","volume-title":"The metrical theory of Jacobi-Perron algorithm","author":"F. Schweiger","year":"1973","unstructured":"Schweiger, F.: The metrical theory of Jacobi-Perron algorithm. Lecture Notes in Mathematics, vol.\u00a0334. Springer, Heidelberg (1973)"},{"key":"15_CR25","doi-asserted-by":"crossref","DOI":"10.1093\/oso\/9780198506867.001.0001","volume-title":"Multidimensional continued fractions","author":"F. Schweiger","year":"2000","unstructured":"Schweiger, F.: Multidimensional continued fractions. Oxford University Press, Oxford (2000)"},{"key":"15_CR26","doi-asserted-by":"publisher","first-page":"231","DOI":"10.1007\/s00591-006-0003-x","volume":"53","author":"F. Schweiger","year":"2006","unstructured":"Schweiger, F.: Was leisten mehrdimensionale Kettenbr\u00fcche? Mathematische Semesterberichte\u00a053, 231\u2013244 (2006)","journal-title":"Mathematische Semesterberichte"},{"key":"15_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/3-540-45353-9_24","volume-title":"Topics in Cryptology - CT-RSA 2001","author":"J.-P. Seifert","year":"2001","unstructured":"Seifert, J.-P.: Using fewer qubits in Shor\u2019s factorization algorithm via simultaneous diophantine approximation. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol.\u00a02020, pp. 319\u2013327. Springer, Heidelberg (2001)"},{"key":"15_CR28","first-page":"145","volume-title":"SFCS 1982: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science","author":"A. Shamir","year":"1982","unstructured":"Shamir, A.: A polynomial time algorithm for breaking the basic Merkle-Hellman cryptosystem. In: SFCS 1982: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, pp. 145\u2013152. IEEE Computer Society, Washington, DC, USA (1982)"},{"key":"15_CR29","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"313","DOI":"10.1007\/3-540-46877-3_28","volume-title":"Advances in Cryptology - EUROCRYPT \u201990","author":"J. Stern","year":"1991","unstructured":"Stern, J., Toffin, P.: Cryptanalysis of a public-key cryptosystem based on approximations by rational numbers. In: Damg\u00e5rd, I.B. (ed.) EUROCRYPT 1990. LNCS, vol.\u00a0473, pp. 313\u2013317. Springer, Heidelberg (1991)"},{"key":"15_CR30","first-page":"113","volume":"13","author":"C. Szekeres","year":"1980","unstructured":"Szekeres, C.: Multidimensional continued fractions. Ann. Univ. Sci. Budap. E\u00f6t\u00f6s, Sect. Math.\u00a013, 113\u2013140 (1980)","journal-title":"Ann. Univ. Sci. Budap. E\u00f6t\u00f6s, Sect. Math."},{"key":"15_CR31","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"24","DOI":"10.1007\/978-3-642-13190-5_2","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"M. Dijk van","year":"2010","unstructured":"van Dijk, M., Gentry, C., Halevi, S., Vaikuntanathan, V.: Fully homomorphic encryption over the integers. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol.\u00a06110, pp. 24\u201343. Springer, Heidelberg (2010)"},{"key":"15_CR32","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1109\/18.54902","volume":"36","author":"M.J. Wiener","year":"1990","unstructured":"Wiener, M.J.: Cryptanalysis of short RSA secret exponents. IEEE Transactions on Information Theory\u00a036, 553\u2013558 (1990)","journal-title":"IEEE Transactions on Information Theory"}],"container-title":["Lecture Notes in Computer Science","Progress in Cryptology \u2013 AFRICACRYPT 2011"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-21969-6_15","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,4,8]],"date-time":"2024-04-08T07:23:32Z","timestamp":1712561012000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-21969-6_15"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642219689","9783642219696"],"references-count":32,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-21969-6_15","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2011]]}}}