{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,10]],"date-time":"2026-04-10T04:19:32Z","timestamp":1775794772330,"version":"3.50.1"},"publisher-location":"Berlin, Heidelberg","reference-count":46,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"value":"9783662479889","type":"print"},{"value":"9783662479896","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":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2015]]},"DOI":"10.1007\/978-3-662-47989-6_1","type":"book-chapter","created":{"date-parts":[[2015,7,31]],"date-time":"2015-07-31T02:36:05Z","timestamp":1438310165000},"page":"3-22","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":81,"title":["Sieving for Shortest Vectors in Lattices Using Angular Locality-Sensitive Hashing"],"prefix":"10.1007","author":[{"given":"Thijs","family":"Laarhoven","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2015,8,1]]},"reference":[{"key":"1_CR1","doi-asserted-by":"crossref","unstructured":"Achlioptas, D.: Database-friendly random projections. In: PODS (2001)","DOI":"10.1145\/375551.375608"},{"key":"1_CR2","doi-asserted-by":"crossref","unstructured":"Aggarwal, D., Dadush, D., Regev, O., Stephens-Davidowitz, N.: Solving the shortest vector problem in $$2^n$$ 2 n time via discrete Gaussian sampling. In: STOC (2015)","DOI":"10.1145\/2746539.2746606"},{"key":"1_CR3","doi-asserted-by":"crossref","unstructured":"Ajtai, M.: Generating hard instances of lattice problems (extended abstract). In: STOC, pp. 99\u2013108 (1996)","DOI":"10.1145\/237814.237838"},{"key":"1_CR4","doi-asserted-by":"crossref","unstructured":"Ajtai, M.: The shortest vector problem in $$L_2$$ L 2 is NP-hard for randomized reductions (extended abstract). In: STOC, pp. 10\u201319 (1998)","DOI":"10.1145\/276698.276705"},{"key":"1_CR5","doi-asserted-by":"crossref","unstructured":"Ajtai, M., Kumar, R., Sivakumar, D.: A sieve algorithm for the shortest lattice vector problem. In: STOC, pp. 601\u2013610 (2001)","DOI":"10.1145\/380752.380857"},{"key":"1_CR6","doi-asserted-by":"crossref","unstructured":"Andoni, A., Indyk, P.: Near-optimal hashing algorithms for approximate nearest neighbor in high dimensions. In: FOCS, pp. 459\u2013468 (2006)","DOI":"10.1109\/FOCS.2006.49"},{"key":"1_CR7","doi-asserted-by":"crossref","unstructured":"Becker, A., Gama, N., Joux, A.: A sieve algorithm based on overlattices. In: ANTS, pp. 49\u201370 (2014)","DOI":"10.1112\/S1461157014000229"},{"key":"1_CR8","unstructured":"Becker, A., Gama, N., Joux, A.: Speeding-up lattice sieving without increasing the memory, using sub-quadratic nearest neighbor search. Preprint (2015)"},{"key":"1_CR9","doi-asserted-by":"crossref","unstructured":"Becker, A., Laarhoven, T.: Efficient sieving in (ideal) lattices using cross-polytopic LSH. Preprint (2015)","DOI":"10.1007\/978-3-319-31517-1_1"},{"key":"1_CR10","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-88702-7","volume-title":"Post-Quantum Cryptography","author":"DJ Bernstein","year":"2009","unstructured":"Bernstein, D.J., Buchmann, J., Dahmen, E.: Post-Quantum Cryptography. Springer, Heidelberg (2009)"},{"key":"1_CR11","unstructured":"Bos, J.W., Naehrig, M., van de Pol, J.: Sieving for shortest vectors in ideal lattices: a practical perspective. Cryptology ePrint Archive, Report 2014\/880 (2014)"},{"key":"1_CR12","doi-asserted-by":"crossref","unstructured":"Charikar, M.S.: Similarity estimation techniques from rounding algorithms. In: STOC, pp. 380\u2013388 (2002)","DOI":"10.1145\/509961.509965"},{"key":"1_CR13","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-6568-7","volume-title":"Sphere Packings, Lattices and Groups","author":"JH Conway","year":"1999","unstructured":"Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups. Springer, New York (1999)"},{"issue":"170","key":"1_CR14","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. Math. Comput. 44(170), 463\u2013471 (1985)","journal-title":"Math. Comput."},{"key":"1_CR15","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"288","DOI":"10.1007\/978-3-319-16295-9_16","volume-title":"Progress in Cryptology - LATINCRYPT 2014","author":"R Fitzpatrick","year":"2015","unstructured":"Fitzpatrick, R., Bischof, C., Buchmann, J., Dagdelen, \u00d6., G\u00f6pfert, F., Mariano, A., Yang, B.-Y.: Tuning GaussSieve for speed. In: Aranha, D.F., Menezes, A. (eds.) LATINCRYPT 2014. LNCS, vol. 8895, pp. 288\u2013305. Springer, Heidelberg (2015)"},{"key":"1_CR16","doi-asserted-by":"crossref","unstructured":"Gentry, C.: Fully homomorphic encryption using ideal lattices. In: STOC (2009)","DOI":"10.1145\/1536414.1536440"},{"key":"1_CR17","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. 1423, pp. 267\u2013288. Springer, Heidelberg (1998)"},{"key":"1_CR18","doi-asserted-by":"crossref","unstructured":"Indyk, P., Motwani, R.: Approximate nearest neighbors: towards removing the curse of dimensionality. In: STOC, pp. 604\u2013613 (1998)","DOI":"10.1145\/276698.276876"},{"key":"1_CR19","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"411","DOI":"10.1007\/978-3-642-54631-0_24","volume-title":"Public-Key Cryptography \u2013 PKC 2014","author":"T Ishiguro","year":"2014","unstructured":"Ishiguro, T., Kiyomoto, S., Miyake, Y., Takagi, T.: Parallel gauss sieve algorithm: solving the svp challenge over a 128-dimensional ideal lattice. In: Krawczyk, H. (ed.) PKC 2014. LNCS, vol. 8383, pp. 411\u2013428. Springer, Heidelberg (2014)"},{"key":"1_CR20","doi-asserted-by":"crossref","unstructured":"Kannan, R.: Improved algorithms for integer programming and related lattice problems. In: STOC, pp. 193\u2013206 (1983)","DOI":"10.1145\/800061.808749"},{"key":"1_CR21","doi-asserted-by":"crossref","unstructured":"Khot, S.: Hardness of approximating the shortest vector problem in lattices. In: FOCS, pp. 126\u2013135 (2004)","DOI":"10.1109\/FOCS.2004.31"},{"key":"1_CR22","unstructured":"Klein, P.: Finding the closest lattice vector when it\u2019s unusually close. In: SODA, pp. 937\u2013941 (2000)"},{"key":"1_CR23","unstructured":"Kleinjung, T.: Private Communication (2014)"},{"key":"1_CR24","unstructured":"Laarhoven, T.: Sieving for shortest vectors in lattices using angular locality-sensitive hashing (2015). Full version at http:\/\/eprint.iacr.org\/2014\/744"},{"key":"1_CR25","doi-asserted-by":"crossref","unstructured":"Laarhoven, T., de Weger, B.: Faster sieving for shortest lattice vectors using spherical locality-sensitive hashing. In: LATINCRYPT (2015)","DOI":"10.1007\/978-3-319-22174-8_6"},{"issue":"4","key":"1_CR26","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":"1_CR27","doi-asserted-by":"crossref","unstructured":"Li, P., Hastie, T.J., Church, K.W.: Very sparse random projections. In: KDD, pp. 287\u2013296 (2006)","DOI":"10.1145\/1150402.1150436"},{"key":"1_CR28","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1007\/978-3-642-19074-2_21","volume-title":"Topics in Cryptology \u2013 CT-RSA 2011","author":"R Lindner","year":"2011","unstructured":"Lindner, R., Peikert, C.: Better key sizes (and attacks) for LWE-based encryption. In: Kiayias, A. (ed.) CT-RSA 2011. LNCS, vol. 6558, pp. 319\u2013339. Springer, Heidelberg (2011)"},{"key":"1_CR29","doi-asserted-by":"crossref","unstructured":"Mariano, A., Timnat, S., Bischof, C.: Lock-free GaussSieve for linear speedups in parallel high performance SVP calculation. In: SBAC-PAD (2014)","DOI":"10.1109\/SBAC-PAD.2014.18"},{"key":"1_CR30","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"crossref","first-page":"48","DOI":"10.1007\/978-3-319-14325-5_5","volume-title":"Euro-Par 2014: Parallel Processing Workshops, Part I","author":"A Mariano","year":"2014","unstructured":"Mariano, A., Dagdelen, \u00d6., Bischof, C.: A comprehensive empirical comparison of parallel ListSieve and GaussSieve. In: Lopes, L., et al. (eds.) Euro-Par 2014: Parallel Processing Workshops, Part I. LNCS, vol. 8805, pp. 48\u201359. Springer, Switzerland (2014)"},{"key":"1_CR31","doi-asserted-by":"crossref","unstructured":"Mariano, A., Laarhoven, T., Bischof, C.: Parallel (probable) lock-free HashSieve: a practical sieving algorithm for the SVP. In: ICPP (2015)","DOI":"10.1109\/ICPP.2015.68"},{"key":"1_CR32","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Voulgaris, P.: A deterministic single exponential time algorithm for most lattice problems based on Voronoi cell computations. In: STOC (2010)","DOI":"10.1145\/1806689.1806739"},{"key":"1_CR33","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Voulgaris, P.: Faster exponential time algorithms for the shortest vector problem. In: SODA, pp. 1468\u20131480 (2010)","DOI":"10.1137\/1.9781611973075.119"},{"key":"1_CR34","doi-asserted-by":"crossref","unstructured":"Micciancio, D., Walter, M.: Fast lattice point enumeration with minimal overhead. In: SODA, pp. 276\u2013294 (2015)","DOI":"10.1137\/1.9781611973730.21"},{"issue":"2","key":"1_CR35","first-page":"181","volume":"2","author":"PQ Nguyen","year":"2008","unstructured":"Nguyen, P.Q., Vidick, T.: Sieve algorithms for the shortest vector problem are practical. J. Math. Crypt. 2(2), 181\u2013207 (2008)","journal-title":"J. Math. Crypt."},{"key":"1_CR36","doi-asserted-by":"crossref","unstructured":"Panigraphy, R.: Entropy based nearest neighbor search in high dimensions. In: SODA, pp. 1186\u20131195 (2006)","DOI":"10.1145\/1109557.1109688"},{"key":"1_CR37","unstructured":"Plantard, T., Schneider, M.: Ideal lattice challenge. http:\/\/latticechallenge.org\/ideallattice-challenge\/ (2014)"},{"issue":"1","key":"1_CR38","doi-asserted-by":"publisher","first-page":"37","DOI":"10.1145\/1089242.1089247","volume":"15","author":"ME Pohst","year":"1981","unstructured":"Pohst, M.E.: On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications. ACM Bull. 15(1), 37\u201344 (1981)","journal-title":"ACM Bull."},{"key":"1_CR39","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"290","DOI":"10.1007\/978-3-642-45239-0_17","volume-title":"Cryptography and Coding","author":"J Pol van de","year":"2013","unstructured":"van de Pol, J., Smart, N.P.: Estimating key sizes for high dimensional lattice-based systems. In: Stam, M. (ed.) IMACC 2013. LNCS, vol. 8308, pp. 290\u2013303. Springer, Heidelberg (2013)"},{"key":"1_CR40","unstructured":"Pujol, X., Stehl\u00e9, D.: Solving the shortest lattice vector problem in time $$2^{2.465n}$$ 2 2.465 n . Cryptology ePrint Archive, Report 2009\/605 (2009)"},{"key":"1_CR41","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"375","DOI":"10.1007\/978-3-642-38553-7_22","volume-title":"Progress in Cryptology \u2013 AFRICACRYPT 2013","author":"M Schneider","year":"2013","unstructured":"Schneider, M.: Sieving for shortest vectors in ideal lattices. In: Youssef, A., Nitaj, A., Hassanien, A.E. (eds.) AFRICACRYPT 2013. LNCS, vol. 7918, pp. 375\u2013391. Springer, Heidelberg (2013)"},{"key":"1_CR42","unstructured":"Schneider, M., Gama, N., Baumann, P., Nobach, L.: SVP challenge (2014). http:\/\/latticechallenge.org\/svp-challenge"},{"issue":"2","key":"1_CR43","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 time lattice basis reduction algorithms. Theoret. Comput. Sci. 53(2), 201\u2013224 (1987)","journal-title":"Theoret. Comput. Sci."},{"issue":"2","key":"1_CR44","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. Math. Programming 66(2), 181\u2013199 (1994)","journal-title":"Math. Programming"},{"key":"1_CR45","doi-asserted-by":"crossref","unstructured":"Wang, X., Liu, M., Tian, C., Bi, J.: Improved Nguyen-Vidick heuristic sieve algorithm for shortest vector problem. In: ASIACCS, pp. 1\u20139 (2011)","DOI":"10.1145\/1966913.1966915"},{"key":"1_CR46","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"29","DOI":"10.1007\/978-3-662-43414-7_2","volume-title":"Selected Areas in Cryptography \u2013 SAC 2013","author":"F Zhang","year":"2014","unstructured":"Zhang, F., Pan, Y., Hu, G.: A three-level sieve algorithm for the shortest vector problem. In: Lange, T., Lauter, K., Lison\u011bk, P. (eds.) SAC 2013. LNCS, vol. 8282, pp. 29\u201347. Springer, Heidelberg (2014)"}],"container-title":["Lecture Notes in Computer Science","Advances in Cryptology -- CRYPTO 2015"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-662-47989-6_1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,29]],"date-time":"2025-05-29T20:40:39Z","timestamp":1748551239000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-662-47989-6_1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"ISBN":["9783662479889","9783662479896"],"references-count":46,"URL":"https:\/\/doi.org\/10.1007\/978-3-662-47989-6_1","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":"1 August 2015","order":1,"name":"first_online","label":"First Online","group":{"name":"ChapterHistory","label":"Chapter History"}}]}}