{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T04:20:57Z","timestamp":1775794857953,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":83,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783642209000","type":"print"},{"value":"9783642209017","type":"electronic"}],"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\/978-3-642-20901-7_10","type":"book-chapter","created":{"date-parts":[[2011,6,4]],"date-time":"2011-06-04T14:11:30Z","timestamp":1307196690000},"page":"159-190","source":"Crossref","is-referenced-by-count":58,"title":["Algorithms for the Shortest and Closest Lattice Vector Problems"],"prefix":"10.1007","author":[{"given":"Guillaume","family":"Hanrot","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xavier","family":"Pujol","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Damien","family":"Stehl\u00e9","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","reference":[{"issue":"8","key":"10_CR1","doi-asserted-by":"publisher","first-page":"2201","DOI":"10.1109\/TIT.2002.800499","volume":"48","author":"E. Agrell","year":"2002","unstructured":"Agrell, E., Eriksson, T., Vardy, A., Zeger, K.: Closest point search in lattices. IEEE Transactions on Information Theory\u00a048(8), 2201\u20132214 (2002)","journal-title":"IEEE Transactions on Information Theory"},{"key":"10_CR2","first-page":"99","volume-title":"Proc. of STOC","author":"M. Ajtai","year":"1996","unstructured":"Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: Proc. of STOC, pp. 99\u2013108. ACM, New York (1996)"},{"key":"10_CR3","doi-asserted-by":"crossref","first-page":"396","DOI":"10.1145\/780542.780602","volume-title":"Proc. of STOC","author":"M. Ajtai","year":"2003","unstructured":"Ajtai, M.: The worst-case behavior of Schnorr\u2019s algorithm approximating the shortest nonzero vector in a lattice. In: Proc. of STOC, pp. 396\u2013406. ACM, New York (2003)"},{"key":"10_CR4","first-page":"284","volume-title":"Proc. of STOC","author":"M. Ajtai","year":"1997","unstructured":"Ajtai, M., Dwork, C.: A public-key cryptosystem with worst-case\/average-case equivalence. In: Proc. of STOC, pp. 284\u2013293. ACM, New York (1997)"},{"key":"10_CR5","doi-asserted-by":"crossref","first-page":"601","DOI":"10.1145\/380752.380857","volume-title":"Proc. of STOC","author":"M. Ajtai","year":"2001","unstructured":"Ajtai, M., Kumar, R., Sivakumar, D.: A sieve algorithm for the shortest lattice vector problem. In: Proc. of STOC, pp. 601\u2013610. ACM, New York (2001)"},{"key":"10_CR6","doi-asserted-by":"crossref","unstructured":"Ajtai, M., Kumar, R., Sivakumar, D.: Sampling short lattice vectors and the closest lattice vector problem. In: Proc. of CCC, pp. 53\u201357 (2002)","DOI":"10.1109\/CCC.2002.1004339"},{"key":"10_CR7","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/BF02579403","volume":"6","author":"L. Babai","year":"1986","unstructured":"Babai, L.: On Lov\u00e1sz lattice reduction and the nearest lattice point problem. Combinatorica\u00a06, 1\u201313 (1986)","journal-title":"Combinatorica"},{"key":"10_CR8","doi-asserted-by":"publisher","first-page":"625","DOI":"10.1007\/BF01445125","volume":"296","author":"W. Banaszczyk","year":"1993","unstructured":"Banaszczyk, W.: New bounds in some transference theorems in the geometry of numbers. Math. Ann.\u00a0296, 625\u2013635 (1993)","journal-title":"Math. Ann."},{"issue":"18","key":"10_CR9","doi-asserted-by":"publisher","first-page":"1648","DOI":"10.1016\/j.tcs.2008.12.045","volume":"410","author":"J. Bl\u00f6mer","year":"2009","unstructured":"Bl\u00f6mer, J., Naewe, S.: Sampling methods for shortest vectors, closest vectors and successive minima. Theor. Comput. Science\u00a0410(18), 1648\u20131665 (2009)","journal-title":"Theor. Comput. Science"},{"issue":"3-4","key":"10_CR10","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., Playoust, C.: The Magma algebra system. I. The user language. Journal of Symbolic Computation\u00a024(3-4), 235\u2013265 (1997), http:\/\/magma.maths.usyd.edu.au\/magma\/","journal-title":"Journal of Symbolic Computation"},{"key":"10_CR11","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"160","DOI":"10.1007\/3-540-58691-1_54","volume-title":"Algorithmic Number Theory","author":"J. Buchmann","year":"1994","unstructured":"Buchmann, J.: Reducing Lattice Bases by Means of Approximations. In: Huang, M.-D.A., Adleman, L.M. (eds.) ANTS 1994. LNCS, vol.\u00a0877, pp. 160\u2013168. Springer, Heidelberg (1994)"},{"key":"10_CR12","unstructured":"Cad\u00e9, D., Pujol, X., Stehl\u00e9, D.: fplll-3.1, a floating-point LLL implementation, http:\/\/perso.ens-lyon.fr\/damien.stehle"},{"key":"10_CR13","volume-title":"An Introduction to the Geometry of Numbers","author":"J.W.S. Cassels","year":"1971","unstructured":"Cassels, J.W.S.: An Introduction to the Geometry of Numbers, 2nd edn. Springer, Heidelberg (1971)","edition":"2"},{"key":"10_CR14","volume-title":"Sphere Packings, Lattices and Groups","author":"J.H. Conway","year":"1998","unstructured":"Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups, 3rd edn. Springer, Heidelberg (1998)","edition":"3"},{"key":"10_CR15","doi-asserted-by":"crossref","unstructured":"Dadush, D., Peikert, C., Vempala, S.: Enumerative algorithms for the shortest and closest lattice vector problems in any norm via M-ellipsoid coverings (submitted 2011)","DOI":"10.1109\/FOCS.2011.31"},{"key":"10_CR16","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"124","DOI":"10.1007\/978-3-642-14712-8_8","volume-title":"Progress in Cryptology \u2013 LATINCRYPT 2010","author":"J. Detrey","year":"2010","unstructured":"Detrey, J., Hanrot, G., Pujol, X., Stehl\u00e9, D.: Accelerating lattice reduction with fPGAs. In: Abdalla, M., Barreto, P.S.L.M. (eds.) LATINCRYPT 2010. LNCS, vol.\u00a06212, pp. 124\u2013143. Springer, Heidelberg (2010)"},{"key":"10_CR17","volume-title":"50 Years of Integer Programming 1958-2008, From the Early Years to the State-of-the-Art","author":"F. Eisenbrand","year":"2009","unstructured":"Eisenbrand, F.: Integer Programming and Algorithmic Geometry of Numbers. In: 50 Years of Integer Programming 1958-2008, From the Early Years to the State-of-the-Art. Springer, Heidelberg (2009)"},{"key":"10_CR18","doi-asserted-by":"crossref","unstructured":"Eisenbrand, F., H\u00e4hnle, N., Niemeier, M.: Covering cubes and the closest vector problem. To appear in the Proceedings of SoCG (2011)","DOI":"10.1145\/1998196.1998264"},{"key":"10_CR19","unstructured":"van Emde\u00a0Boas, P.: Another NP-complete partition problem and the complexity of computing short vectors in a lattice. Technical report 81-04, Mathematisch Instituut, Universiteit van Amsterdam (1981)"},{"key":"10_CR20","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"194","DOI":"10.1007\/3-540-12868-9_103","volume-title":"Computer Algebra","author":"U. Fincke","year":"1983","unstructured":"Fincke, U., Pohst, M.: A procedure for determining algebraic integers of given norm. In: van Hulzen, J.A. (ed.) ISSAC 1983 and EUROCAL 1983. LNCS, vol.\u00a0162, pp. 194\u2013202. Springer, Heidelberg (1983)"},{"issue":"170","key":"10_CR21","doi-asserted-by":"publisher","first-page":"463","DOI":"10.1090\/S0025-5718-1985-0777278-8","volume":"44","author":"U. Fincke","year":"1985","unstructured":"Fincke, U., Pohst, M.: Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Math. Comp.\u00a044(170), 463\u2013471 (1985)","journal-title":"Math. Comp."},{"key":"10_CR22","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1007\/11818175_7","volume-title":"Advances in Cryptology - CRYPTO 2006","author":"N. Gama","year":"2006","unstructured":"Gama, N., Howgrave-Graham, N., Koy, H., Nguy\u00ean, P.Q.: Rankin\u2019s constant and blockwise lattice reduction. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol.\u00a04117, pp. 112\u2013130. Springer, Heidelberg (2006)"},{"key":"10_CR23","first-page":"207","volume-title":"Proc. of STOC","author":"N. Gama","year":"2008","unstructured":"Gama, N., Nguyen, P.Q.: Finding short lattice vectors within Mordell\u2019s inequality. In: Proc. of STOC, pp. 207\u2013216. ACM, New York (2008)"},{"key":"10_CR24","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"31","DOI":"10.1007\/978-3-540-78967-3_3","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2008","author":"N. Gama","year":"2008","unstructured":"Gama, N., Nguyen, P.Q.: Predicting lattice reduction. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol.\u00a04965, pp. 31\u201351. Springer, Heidelberg (2008)"},{"key":"10_CR25","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"257","DOI":"10.1007\/978-3-642-13190-5_13","volume-title":"Advances in Cryptology \u2013 EUROCRYPT 2010","author":"N. Gama","year":"2010","unstructured":"Gama, N., Nguyen, P.Q., Regev, O.: Lattice enumeration using extreme pruning. In: Gilbert, H. (ed.) EUROCRYPT 2010. LNCS, vol.\u00a06110, pp. 257\u2013278. Springer, Heidelberg (2010)"},{"key":"10_CR26","unstructured":"Gama, N., Schneider, M.: The SVP challenge homepage, http:\/\/www.latticechallenge.org\/svp-challenge\/"},{"key":"10_CR27","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"112","DOI":"10.1007\/BFb0052231","volume-title":"Advances in Cryptology - CRYPTO \u201997","author":"O. Goldreich","year":"1997","unstructured":"Goldreich, O., Goldwasser, S., Halevi, S.: Public-key cryptosystems from lattice reduction problems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol.\u00a01294, pp. 112\u2013131. Springer, Heidelberg (1997)"},{"issue":"2","key":"10_CR28","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. Inf. Process. Lett.\u00a071(2), 55\u201361 (1999)","journal-title":"Inf. Process. Lett."},{"key":"10_CR29","doi-asserted-by":"publisher","first-page":"165","DOI":"10.1515\/form.2003.009","volume":"15","author":"D. Goldstein","year":"2003","unstructured":"Goldstein, D., Mayer, A.: On the equidistribution of Hecke points. Forum Mathematicum\u00a015, 165\u2013189 (2003)","journal-title":"Forum Mathematicum"},{"key":"10_CR30","volume-title":"Geometry of Numbers","author":"M. Gruber","year":"1987","unstructured":"Gruber, M., Lekkerkerker, C.G.: Geometry of Numbers. North-Holland, Amsterdam (1987)"},{"issue":"2","key":"10_CR31","doi-asserted-by":"publisher","first-page":"90","DOI":"10.1007\/s00037-005-0193-y","volume":"14","author":"V. Guruswami","year":"2005","unstructured":"Guruswami, V., Micciancio, D., Regev, O.: The complexity of the covering radius problem. Computational Complexity\u00a014(2), 90\u2013121 (2005)","journal-title":"Computational Complexity"},{"key":"10_CR32","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"170","DOI":"10.1007\/978-3-540-74143-5_10","volume-title":"Advances in Cryptology - CRYPTO 2007","author":"G. Hanrot","year":"2007","unstructured":"Hanrot, G., Stehl\u00e9, D.: Improved analysis of kannan\u2019s shortest lattice vector algorithm (extended abstract). In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol.\u00a04622, pp. 170\u2013186. Springer, Heidelberg (2007)"},{"key":"10_CR33","unstructured":"Hanrot, G., Stehl\u00e9, D.: Worst-case Hermite-Korkine-Zolotarev reduced lattice bases. CoRR, abs\/0801.3331 (2008)"},{"issue":"11","key":"10_CR34","doi-asserted-by":"publisher","first-page":"2938","DOI":"10.1109\/78.726808","volume":"46","author":"A. Hassibi","year":"1998","unstructured":"Hassibi, A., Boyd, S.: Integer parameter estimation in linear models with applications to GPS. IEEE Transactions on Signal Process\u00a046(11), 2938\u20132952 (1998)","journal-title":"IEEE Transactions on Signal Process"},{"key":"10_CR35","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1145\/1250790.1250859","volume-title":"Proc. of STOC","author":"I. Haviv","year":"2007","unstructured":"Haviv, I., Regev, O.: Tensor-based hardness of the shortest vector problem to within almost polynomial factors. In: Proc. of STOC, pp. 469\u2013477. ACM, New York (2007)"},{"key":"10_CR36","doi-asserted-by":"publisher","first-page":"125","DOI":"10.1016\/0304-3975(85)90067-2","volume":"41","author":"B. Helfrich","year":"1985","unstructured":"Helfrich, B.: Algorithms to construct Minkowski reduced and Hermite reduced lattice bases. Theor. Comput. Science\u00a041, 125\u2013139 (1985)","journal-title":"Theor. Comput. Science"},{"key":"10_CR37","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"52","DOI":"10.1007\/978-3-642-12678-9_4","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2010","author":"J. Hermans","year":"2010","unstructured":"Hermans, J., Schneider, M., Buchmann, J., Vercauteren, F., Preneel, B.: Parallel shortest lattice vector enumeration on graphics cards. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol.\u00a06055, pp. 52\u201368. Springer, Heidelberg (2010)"},{"key":"10_CR38","unstructured":"Hermite, C.: \u0152uvres. Gauthiers-Villars (1905)"},{"key":"10_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"267","DOI":"10.1007\/BFb0054868","volume-title":"Algorithmic Number Theory","author":"J. Hoffstein","year":"1998","unstructured":"Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A ring-based public key cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol.\u00a01423, pp. 267\u2013288. Springer, Heidelberg (1998)"},{"key":"10_CR40","first-page":"183","volume":"63","author":"\u00c1.G. Horv\u00e1th","year":"1996","unstructured":"Horv\u00e1th, \u00c1.G.: On the Dirichlet-Voronoi cells of the unimodular lattices. Geometric\u00e6 Dedicata\u00a063, 183\u2013191 (1996)","journal-title":"Geometric\u00e6 Dedicata"},{"issue":"1","key":"10_CR41","first-page":"3","volume":"14","author":"G.A. Kabatyansky","year":"1978","unstructured":"Kabatyansky, G.A., Levenshtein, V.I.: Bounds for packings on a sphere and in space. Probl. Peredachi Inf.\u00a014(1), 3\u201325 (1978)","journal-title":"Probl. Peredachi Inf."},{"key":"10_CR42","first-page":"99","volume-title":"Proc. of STOC","author":"R. Kannan","year":"1983","unstructured":"Kannan, R.: Improved algorithms for integer programming and related lattice problems. In: Proc. of STOC, pp. 99\u2013108. ACM, New York (1983)"},{"issue":"3","key":"10_CR43","doi-asserted-by":"publisher","first-page":"415","DOI":"10.1287\/moor.12.3.415","volume":"12","author":"R. Kannan","year":"1987","unstructured":"Kannan, R.: Minkowski\u2019s convex body theorem and integer programming. Math. Oper. Res.\u00a012(3), 415\u2013440 (1987)","journal-title":"Math. Oper. Res."},{"key":"10_CR44","unstructured":"Khot, S.: Inapproximability results for computational problems on lattices. Chapter of [64]"},{"key":"10_CR45","first-page":"937","volume-title":"Proc. of SODA","author":"P.N. Klein","year":"2000","unstructured":"Klein, P.N.: Finding the closest lattice vector when it\u2019s unusually close. In: Proc. of SODA, pp. 937\u2013941. ACM, New York (2000)"},{"key":"10_CR46","doi-asserted-by":"publisher","first-page":"336","DOI":"10.1007\/BF01442795","volume":"6","author":"A. Korkine","year":"1873","unstructured":"Korkine, A., Zolotarev, G.: Sur les formes quadratiques. Math. Ann.\u00a06, 336\u2013389 (1873)","journal-title":"Math. Ann."},{"key":"10_CR47","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, 515\u2013534 (1982)","journal-title":"Math. Ann."},{"key":"10_CR48","first-page":"127","volume-title":"Algorithmic Number Theory","author":"H. Lenstra Jr.","year":"2008","unstructured":"Lenstra Jr., H.: Lattices. In: Buhler, J.P., Stevenhagen, P. (eds.) Algorithmic Number Theory, pp. 127\u2013181. MSRI Publications, Cambridge University Press (2008)"},{"key":"10_CR49","unstructured":"Lindner, R., R\u00fcckert, M.: The lattice challenge homepage, http:\/\/www.latticechallenge.org\/"},{"key":"10_CR50","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"450","DOI":"10.1007\/11830924_41","volume-title":"Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques","author":"Y.-K. Liu","year":"2006","unstructured":"Liu, Y.-K., Lyubashevsky, V., Micciancio, D.: On bounded distance decoding for general lattices. In: D\u00edaz, J., Jansen, K., Rolim, J.D.P., Zwick, U. (eds.) APPROX 2006 and RANDOM 2006. LNCS, vol.\u00a04110, pp. 450\u2013461. Springer, Heidelberg (2006)"},{"key":"10_CR51","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"577","DOI":"10.1007\/978-3-642-03356-8_34","volume-title":"Advances in Cryptology - CRYPTO 2009","author":"V. Lyubashevsky","year":"2009","unstructured":"Lyubashevsky, V., Micciancio, D.: On bounded distance decoding, unique shortest vectors, and the minimum distance problem. In: Halevi, S. (ed.) CRYPTO 2009. LNCS, vol.\u00a05677, pp. 577\u2013594. Springer, Heidelberg (2009)"},{"key":"10_CR52","volume-title":"Perfect Lattices in Euclidean Spaces","author":"J. Martinet","year":"2002","unstructured":"Martinet, J.: Perfect Lattices in Euclidean Spaces. Springer, Heidelberg (2002)"},{"key":"10_CR53","first-page":"84","volume-title":"Proc. of SODA","author":"D. Micciancio","year":"2008","unstructured":"Micciancio, D.: Efficient reductions among lattice problems. In: Proc. of SODA, pp. 84\u201393. SIAM, Philadelphia (2008)"},{"key":"10_CR54","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0897-7","volume-title":"Complexity of lattice problems : a cryptographic perspective","author":"D. Micciancio","year":"2002","unstructured":"Micciancio, D., Goldwasser, S.: Complexity of lattice problems : a cryptographic perspective. Kluwer Academic Press, Dordrecht (2002)"},{"key":"10_CR55","doi-asserted-by":"publisher","first-page":"147","DOI":"10.1007\/978-3-540-88702-7_5","volume-title":"Post-Quantum Cryptography","author":"D. Micciancio","year":"2009","unstructured":"Micciancio, D., Regev, O.: Lattice-based cryptography. In: Bernstein, D.J., Buchmann, J., Dahmen, E. (eds.) Post-Quantum Cryptography, pp. 147\u2013191. Springer, Heidelberg (2009)"},{"key":"10_CR56","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Voulgaris, P.: A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations, Draft of the full version of [57] (December 8, 2010), http:\/\/cseweb.ucsd.edu\/~pvoulgar\/pub.html","DOI":"10.1145\/1806689.1806739"},{"key":"10_CR57","first-page":"351","volume-title":"Proc. of STOC","author":"D. Micciancio","year":"2010","unstructured":"Micciancio, D., Voulgaris, P.: A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations. In: Proc. of STOC, pp. 351\u2013358. ACM, New York (2010)"},{"key":"10_CR58","volume-title":"Proc.\u00a0of SODA","author":"D. Micciancio","year":"2010","unstructured":"Micciancio, D., Voulgaris, P.: Faster exponential time algorithms for the shortest vector problem. In: Proc.\u00a0of SODA, ACM, New York (2010)"},{"key":"10_CR59","volume-title":"Geometrie der Zahlen","author":"H. Minkowski","year":"1896","unstructured":"Minkowski, H.: Geometrie der Zahlen. Teubner-Verlag, Stuttgart (1896)"},{"key":"10_CR60","doi-asserted-by":"publisher","first-page":"1591","DOI":"10.1109\/18.333872","volume":"40","author":"W.H. Mow","year":"1994","unstructured":"Mow, W.H.: Maximum likelihood sequence estimation from the lattice viewpoint. IEEE Transactions on Information Theory\u00a040, 1591\u20131600 (1994)","journal-title":"IEEE Transactions on Information Theory"},{"issue":"5","key":"10_CR61","doi-asserted-by":"publisher","first-page":"553","DOI":"10.1002\/wcm.140","volume":"3","author":"W.H. Mow","year":"2003","unstructured":"Mow, W.H.: Universal lattice decoding: Principle and recent advances. Wireless Communications and Mobile Computing, Special Issue on Coding and Its Applications in Wireless CDMA Systems\u00a03(5), 553\u2013569 (2003)","journal-title":"Wireless Communications and Mobile Computing, Special Issue on Coding and Its Applications in Wireless CDMA Systems"},{"key":"10_CR62","unstructured":"P.\u00a0Q. Nguyen. Hermite\u2019s constant and lattice algorithms. Chapter of [64]."},{"key":"10_CR63","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"238","DOI":"10.1007\/11792086_18","volume-title":"Algorithmic Number Theory","author":"P.Q. Nguy\u00ean","year":"2006","unstructured":"Nguy\u00ean, P.Q., Stehl\u00e9, D.: LLL on the average. In: Hess, F., Pauli, S., Pohst, M. (eds.) ANTS 2006. LNCS, vol.\u00a04076, pp. 238\u2013256. Springer, Heidelberg (2006)"},{"key":"10_CR64","series-title":"Information Security and Cryptography","volume-title":"The LLL Algorithm: Survey and Applications","year":"2009","unstructured":"Nguyen, P.Q., Vall\u00e9e, B. (eds.): The LLL Algorithm: Survey and Applications. Information Security and Cryptography. Springer, Heidelberg (2009)"},{"key":"10_CR65","doi-asserted-by":"crossref","unstructured":"Nguyen, P.Q., Vidick, T.: Sieve algorithms for the shortest vector problem are practical. Journal of Mathematical Cryptology\u00a02(2) (2008)","DOI":"10.1515\/JMC.2008.009"},{"key":"10_CR66","doi-asserted-by":"crossref","unstructured":"Odlyzko, A.M.: The rise and fall of knapsack cryptosystems. In: Cryptology and Computational Number Theory. Proc. of Symposia in Applied Mathematics, vol.\u00a042, pp. 75\u201388. A.M.S, Providence (1990)","DOI":"10.1090\/psapm\/042\/1095552"},{"key":"10_CR67","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"390","DOI":"10.1007\/978-3-540-89255-7_24","volume-title":"Advances in Cryptology - ASIACRYPT 2008","author":"X. Pujol","year":"2008","unstructured":"Pujol, X., Stehl\u00e9, D.: Rigorous and efficient short lattice vectors enumeration. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol.\u00a05350, pp. 390\u2013405. Springer, Heidelberg (2008)"},{"key":"10_CR68","unstructured":"Pujol, X., Stehl\u00e9, D.: Solving the shortest lattice vector problem in time 22.465n. Cryptology ePrint Archive (2009), http:\/\/eprint.iacr.org\/2009\/605"},{"key":"10_CR69","unstructured":"Regev, O.: Lecture notes of lattices in computer science, taught at the Computer Science Tel Aviv University, http:\/\/www.cs.tau.il\/~odedr"},{"key":"10_CR70","unstructured":"O.\u00a0Regev. On the complexity of lattice problems with polynomial approximation factors. Chapter of [64]."},{"key":"10_CR71","doi-asserted-by":"crossref","first-page":"84","DOI":"10.1145\/1060590.1060603","volume-title":"Proc. of STOC","author":"O. Regev","year":"2005","unstructured":"Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Proc. of STOC, pp. 84\u201393. ACM, New York (2005)"},{"key":"10_CR72","doi-asserted-by":"crossref","unstructured":"Regev, O.: The learning with errors problem, Invited survey in CCC 2010 (2010), http:\/\/www.cs.tau.ac.il\/~odedr\/","DOI":"10.1109\/CCC.2010.26"},{"key":"10_CR73","unstructured":"C.\u00a0P. Schnorr. Progress on LLL and lattice reduction. Chapter of [64]."},{"key":"10_CR74","doi-asserted-by":"publisher","first-page":"201","DOI":"10.1016\/0304-3975(87)90064-8","volume":"53","author":"C.P. Schnorr","year":"1987","unstructured":"Schnorr, C.P.: A hierarchy of polynomial lattice basis reduction algorithms. Theor. Comput. Science\u00a053, 201\u2013224 (1987)","journal-title":"Theor. Comput. Science"},{"key":"10_CR75","doi-asserted-by":"publisher","first-page":"181","DOI":"10.1007\/BF01581144","volume":"66","author":"C.P. Schnorr","year":"1994","unstructured":"Schnorr, C.P., Euchner, M.: Lattice basis reduction : improved practical algorithms and solving subset sum problems. Mathematics of Programming\u00a066, 181\u2013199 (1994)","journal-title":"Mathematics of Programming"},{"key":"10_CR76","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1007\/3-540-49264-X_1","volume-title":"Advances in Cryptology - EUROCRYPT \u201995","author":"C.-P. Schnorr","year":"1995","unstructured":"Schnorr, C.-P., H\u00f6rner, H.H.: Attacking the chor-rivest cryptosystem by improved lattice reduction. In: Guillou, L.C., Quisquater, J.-J. (eds.) EUROCRYPT 1995. LNCS, vol.\u00a0921, pp. 1\u201312. Springer, Heidelberg (1995)"},{"key":"10_CR77","unstructured":"Shoup, V.: NTL, Number Theory C++ Library, http:\/\/www.shoup.net\/ntl\/"},{"key":"10_CR78","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-662-08287-4","volume-title":"Lectures on the Geometry of Numbers","author":"C.L. Siegel","year":"1989","unstructured":"Siegel, C.L.: Lectures on the Geometry of Numbers. Springer, Heidelberg (1989)"},{"issue":"2","key":"10_CR79","doi-asserted-by":"publisher","first-page":"715","DOI":"10.1137\/060676362","volume":"23","author":"N. Sommer","year":"2009","unstructured":"Sommer, N., Feder, M., Shalvi, O.: Finding the closest lattice point by iterative slicing. SIAM J. Discrete Math.\u00a023(2), 715\u2013731 (2009)","journal-title":"SIAM J. Discrete Math."},{"key":"10_CR80","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"340","DOI":"10.1007\/978-3-642-14518-6_27","volume-title":"Algorithmic Number Theory","author":"D. Stehl\u00e9","year":"2010","unstructured":"Stehl\u00e9, D., Watkins, M.: On the extremality of an 80-dimensional lattice. In: Hanrot, G., Morain, F., Thom\u00e9, E. (eds.) ANTS-IX. LNCS, vol.\u00a06197, pp. 340\u2013356. Springer, Heidelberg (2010)"},{"key":"10_CR81","doi-asserted-by":"crossref","first-page":"198","DOI":"10.1515\/crll.1908.134.198","volume":"134","author":"G. Voronoi","year":"1908","unstructured":"Voronoi, G.: Nouvelles applications des param\u00e8tres continus \u00e0 la th\u00e9orie des formes quadratiques. Journal f\u00fcr die reine und angewandte Mathematik\u00a0134, 198\u2013287 (1908)","journal-title":"Journal f\u00fcr die reine und angewandte Mathematik"},{"key":"10_CR82","unstructured":"Voulgaris, P.: Personal communication"},{"key":"10_CR83","unstructured":"Wang, X., Liu, M., Tian, C., Bi, J.: Improved Nguyen-Vidick heuristic sieve algorithm for shortest vector problem. Cryptology ePrint Archive (2010), http:\/\/eprint.iacr.org\/2010\/647"}],"container-title":["Lecture Notes in Computer Science","Coding and Cryptology"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-20901-7_10","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,6,7]],"date-time":"2023-06-07T06:22:12Z","timestamp":1686118932000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-20901-7_10"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011]]},"ISBN":["9783642209000","9783642209017"],"references-count":83,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-20901-7_10","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"value":"0302-9743","type":"print"},{"value":"1611-3349","type":"electronic"}],"subject":[],"published":{"date-parts":[[2011]]}}}