Dimension Reduction Methods for Convolution Modular Lattices

M. Ajtai, The shortest vector problem in l ₂ is NP-hard for randomized reductions, Proc. 30th ACM Symposium on the Theory of Computing, pages 10–19, 1998Google Scholar

M. Ajtai, R. Kumar, D. Sivakumar, A sieve algorithm for the shortest lattice vector problem, Proc. 33rd ACM Symposium on Theory of Computing, 2001 (to appear)Google Scholar

J.W.S. Cassels, An Introduction to the Geometry of Numbers, Die Grundlehren Der Mathematischen Wissenschaften, Springer-Verlag, 1959.Google Scholar

O. Goldreich, S. Goldwasser, S. Halevi, Public-key cryptography from lattice reduction problems, CRYPTO’97, Lect. Notes in Computer Science 1294, Springer-Verlag, 1997, 112–131.Google Scholar

O. Goldreich, D. Micciancio, S. Safra and J.P. Seifert, Approximating shortest lattice vectors is not harder than approximating closest vectors, Information Processing Letters, vol. 71, pp. 55–61, 1999.zbMATHMathSciNetCrossRefGoogle Scholar

J. Hoffstein, J. Pipher, J.H. Silverman, NTRU: A new high speed public key cryptosystem, in Algorithmic Number Theory (ANTS III), Portland, OR, June 1998, Lecture Notes in Computer Science 1423 (J.P. Buhler, ed.), Springer-Verlag, Berlin, 1998, 267–288.CrossRefGoogle Scholar

J. Hoffstein, J. Pipher, J.H. Silverman, NSS: An NTRU Lattice-Based Signature Scheme, Advances in Cryptology—Eurocrypt 2001, Lecture Notes in Computer Science, Springer-Verlag, 2001.Google Scholar

J. Hoffstein, J. Pipher, J.H. Silverman, The NTRU Signature Scheme: Theory and Practice, preprint, June 2001.Google Scholar

IEEE P1363.1, Standard Specification for Public-Key Cryptographic Techniques Based on Hard Problems over Lattices, Draft 2, 2001.Google Scholar

Number Theory Library, Victor Shoup, http://www.cs.wisc.edu/~shoup/ntl

H. Koy, C.-P. Schnorr, Segment LLL-Reduction of Lattice Bases, Cryptography and Lattice Conference (CaLC 2001), Lecture Notes in Computer Science, Springer-Verlag, this volume.Google Scholar

H. Koy, C.-P. Schnorr, Segment LLL-Reduction with Floating Point Orthogonalization, Cryptography and Lattice Conference (CaLC 2001), Lecture Notes in Computer Science, Springer-Verlag, this volume.Google Scholar

A.K. Lenstra, H.W. Lenstra Jr., L. Lovász, Factoring polynomials with rational coefficients, Mathematische Ann. 261 (1982), 513–534.Google Scholar

A. May, Auf Polynomgleichungen basierende Public-Key-Kryptosysteme, Johann Wolfgange Goethe-Universitat, Frankfurt am Main, Fachbereich Informatik. (Masters Thesis in Computer Science, 4 June, 1999; Thesis advisor C.P. Schnorr).Google Scholar

A. May, Cryptanalysis of NTRU-107, preprint, April 1999 (unpublished).Google Scholar

D. Micciancio, The Shortest Vector in a Lattice is Hard to Approximate within Some Constant, Proc. 39th IEEE Symposium on Foundations of Computer Science, pages 92–98, 1998Google Scholar

P. Nguyen, Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem, Advances in Cryptology-Proceedings of CRYPTO’ 99, M. Wiener (ed.), Lecture Notes in Computer Science, Springer-Verlag, 1999.Google Scholar

C.P. Schnorr, M. Euchner, Lattice basis reduction: improved practical algorithms and solving subset sum problems, Math. Programming 66 (1994), no. 2, Ser. A, 181–199.MathSciNetCrossRefGoogle Scholar

C.P. Schnorr, A hierarchy of polynomial time lattice basis reduction algorithms, Theoretical Computer Science 53, pages 201–224, 1987zbMATHMathSciNetCrossRefGoogle Scholar