a590003

[5] A. Blum, A. Kalai, and H. Wasserman. Noise-tolerant learning, the parity problem, and the statistical
query model. J. ACM, 50(4):506–519, 2003.
[6] D. Boneh and D. M. Freeman. Linearly homomorphic signatures over binary fields and new tools for
lattice-based signatures. In Public Key Cryptography, pages 1–16, 2011.
[7] J.-Y. Cai and A. Nerurkar. An improved worst-case to average-case connection for lattice problems. In
FOCS, pages 468–477, 1997.
[8] Y. Chen and P. Q. Nguyen. BKZ 2.0: Better lattice security estimates. In ASIACRYPT, pages 1–20,
2011.
[9] D. Dadush, C. Peikert, and S. Vempala. Enumerative lattice algorithms in any norm via M-ellipsoid
coverings. In FOCS, pages 580–589, 2011.
[10] N. Döttling and J. Müller-Quade. Lossy codes and a new variant of the learning-with-errors problem.
Manuscript. To appear in Eurocrypt 2013, 2013.
[11] N. Gama and P. Q. Nguyen. Predicting lattice reduction. In EUROCRYPT, pages 31–51, 2008.
[12] C. Gentry, C. Peikert, and V. Vaikuntanathan. Trapdoors for hard lattices and new cryptographic
constructions. In STOC, pages 197–206, 2008.
[13] A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovász. Factoring polynomials with rational coefficients.
Mathematische Annalen, 261(4):515–534, December 1982.
[14] D. Micciancio. Almost perfect lattices, the covering radius problem, and applications to Ajtai’s
connection factor. SIAM J. Comput., 34(1):118–169, 2004.
[15] D. Micciancio. Duality in lattice cryptography. In Public Key Cryptography, 2010. Invited talk.
[16] D. Micciancio and S. Goldwasser. Complexity of Lattice Problems: a cryptographic perspective, volume
671 of The Kluwer International Series in Engineering and Computer Science. Kluwer Academic
Publishers, Boston, Massachusetts, 2002.
[17] D. Micciancio and P. Mol. Pseudorandom knapsacks and the sample complexity of LWE search-todecision
reductions. In CRYPTO, pages 465–484, 2011.
[18] D. Micciancio and C. Peikert. Trapdoors for lattices: Simpler, tighter, faster, smaller. In EUROCRYPT,
pages 700–718, 2012.
[19] D. Micciancio and O. Regev. Worst-case to average-case reductions based on Gaussian measures. SIAM
J. Comput., 37(1):267–302, 2007. Preliminary version in FOCS 2004.
[20] D. Micciancio and O. Regev. Lattice-based cryptography. In Post Quantum Cryptography, pages
147–191. Springer, February 2009.
[21] C. Peikert. Public-key cryptosystems from the worst-case shortest vector problem. In STOC, pages
333–342, 2009.
[22] C. Peikert. An efficient and parallel Gaussian sampler for lattices. In CRYPTO, pages 80–97, 2010.
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10. Hardness of SIS and LWE with Small Parameters