Representing hard lattices with O(n log n) bits

Proceedings of the Annual ACM Symposium on Theory of Computing

Volumn , Issue , 2005, Pages 94-103

  Ajtai, Miklós ^a  

^a IBM ALMADEN RESEARCH CENTER   (United States)

Author keywords

Algorithm; Lattice; Public key cryptosystem

Indexed keywords

APPROXIMATION PROBLEMS; LATTICE; RANDOM BITS; TEXT/CLEAR TEXT RATIO;

ALGORITHMS; APPROXIMATION THEORY; COMPUTER SOFTWARE; EQUIVALENCE CLASSES; PROBLEM SOLVING; SECURITY SYSTEMS; TEXT PROCESSING; THEOREM PROVING; VECTORS;

PUBLIC KEY CRYPTOGRAPHY;

EID: 34848855804     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1060590.1060604     Document Type: Conference Paper

References (13)

1. M. Ajtai and C. Dwork In A Public-Key Cryptosystem with Worst-Case/Average-Case Equivalence, In Proc. of 29th ACM STOC 1997 or Electronic Colloquium on Computational Complexity, 1996, http://www.eccc.uni-trier.de/eccc/
2. M. Ajtai, R. Kumar, and D. Sivakumar.A Sieve Algorithm for the Shortest Lattice Vector Problem, Proc. of 33rd ACM Symposium On the Theory of Computing, 2001.
3. W. Banaszczyk, New bounds in some transference theorems in the geometry of numbers. Matematische Annalen 296(4):625-635, 1993.
4. O. Goldreich, S. Goldwasser, S. Halevi, Eliminating decryption errors in the Ajtai-Dwork cryptosystem. In Advances in cryptology, volume 1294, Lecture Notes in Computer Science pages 112-131. Springer, 1997.
5. P. M. Gruber and C. G. Lekkerkerker. Geometry of Numbers, Chapters. North Holland 1987.
6. P. R. Halmos Measure Theory D. Van Nostrand Company, 1950.
7. J. Hoffstein, J. Piper, J. H. Silverman. NTRU: a ring based public key cryptosystem. In J. Buhler, editor, Algorithmic number theory (ANTS 111), volume 1423 of Lecture Notes in Computer Science, pages 267-288, Springer 1988
8. A. K. Lenstra, H. W. Lenstra, L. Lovász Factoring polynomials with rational coefficients, Math. Ann. 261, 515-534 (1982).
9. D. Micciancio, Generalized compact knapsacks, cyclic lattices, and efficient one-way functions from worst-case assumptions., Proc. of 43rd IEEE Annual symposium on foundations of computer science- FOCS 2002, pp 356-365.
10. D. Micciancio, Improving lattice based cryptosystems using the Hermite normal form, In Cryptography and Lattices Conference (CaLC), volume 2146 of Lecture Notes in Computer Science, pp 126-145, Springer 2001
11. O. Regev, New Lattice Based Cryptographic Constructions Proceedings of the 35th ACM STOC 2003, pp 407-416.
12. C. P. Schnorr, A hierarchy of polynomial time lattice basis reduction algorithms Theoretical Computer Science 53, (1987) 201-224.
13. Wolfgang M. Schmidt Diophantine approximation, Springer Lecture Notes, Springer 1970.