Heuristics on lattice basis reduction in practice

ACM Journal of Experimental Algorithmics

Volumn 7, Issue , 2002, Pages

  Backes, Werner ^a   Wetzel, Susanne ^b  

^a MAX PLANCK INSTITUTE FOR INFORMATICS   (Germany)

^b Stevens Institute of Technology   (United States)

Author keywords

Dynamic approximation; General reduction heuristics; Lattice basis reduction; Modular and iterative heuristics

Indexed keywords

EID: 33746695240     PISSN: 10846654     EISSN: None     Source Type: Journal    
DOI: 10.1145/944618.944619     Document Type: Article

References (32)

1. th ACM Symposium on Theory of Computing, 99-108.
2. th ACM Symposium on Theory of Computing, 284-293.
3. BACKES, W. 1998. Berechnung kürzester Gittervektoren. Master's Thesis, Universität des Saarlandes, Saarbrücken, Germany
4. BACKES, W., AND WETZEL, S. 2000. New Results on Lattice Basis Reduction in Practice. Proceedings of Fourth Algorithmic Number Theory Symposium (ANTS IV), 135-152. Springer Lecture Notes in Computer Science LNCS 1838.
5. BACKES, W., AND WETZEL, S. 2000. Lattice Basis Reduction with Dynamic Approximation. Proceedings of Workshop on Algorithm Engineering (WAE), 63-73. Springer Lecture Notes in Computer Science LNCS 1982.
6. BACKES, W., AND WETZEL, S. 2000. http://www.mpi-sb.mpg.de/~backes/lattice-tests.
7. BIEHL, I., BUCHMANN, J., AND PAPANIKOLAOU, T. 1995. LiDIA: A Library for Computational Number Theory. Technical Report 03/95, SFB 124, Universität des Saarlandes, Saarbrücken, Germany
8. COHEN, H. 1993. A Course in Computational Algebraic Number Theory. Second Edition. Springer-Verlag, Heidelberg.
9. COPPERSMITH, D. 1996. Finding a Small Root of a Univariate Modular Equation. Proceedings of EUROCRYPT '96, 155-165. Springer Lecture Notes in Computer Science LNCS 1070.
10. COSTER, M.J., JOUX, A., LAMACCHIA, B.A., ODLYZKO, A.M., SCHNORR, C.P., AND STERN, J. 1992. Improved Low-Density Subset Sum Algorithms. Journal of Computational Complexity, Vol. 2, 111-128.
11. DOMICH, P.D., KANNAN, R., AND TROTTER, L.E. 1987. Hermite Normal Form Computation using Modulo Determinant Arithmetic. Mathematics Operations Research, Vol. 12, No. 1, 50-59.
12. GOLDREICH, O., GOLDWASSER, S., AND HALEVI, S. Public-Key-Cryptosystems from Lattice Reduction Problems. Proceedings of CRYPTO '97, 112-131. Springer Lecture Notes in Computer Science LNCS 1294.
13. GRÖTSCHEL, M., LOVÁSZ, L., AND SCHRIJVER, A. 1993. Geometric Algorithms and Combinatorial Optimization. Second Edition. Springer-Verlag, Heidelberg.
14. HAVAS, G., MAJEWSKI, B.S., AND MATTHEWS, K.R. 1994 Extended GCD Algorithms. Technical Report TR0302, The University of Queensland, Brisbane.
15. HECKER, C. 1994. Automatische Parallelisierung und parallele Gitterbasisreduktion. PhD Thesis, Universität des Saarlandes, Saarbrücken.
16. JOUX, A., AND STERN, J. 1998. Lattice Reduction: A Toolbox for the Cryptanalyst. Journal of Cryptology, Vol. 11, No. 3, 161-185.
17. KALTOFEN, E. 1983. On the Complexity of Finding Short Vectors in Integer Lattices. Proceedings of EUROCAL '83, 236-244. Springer Lecture Notes in Computer Science LNCS 162.
18. KNUTH, D.E. 1981. The Art of Computer Programming. Volume 2: Seminumerical algorithms. Second Edition. Addison-Wesley, Reading, Massachusetts.
19. LENSTRA, A.K., LENSTRA, H.W., AND LOVÁSZ, L. 1982. Factoring Polynomials with Rational Coefficients. Math. Ann. 261, 515-534.
20. LENSTRA, H.W. 1983. Integer Programming With a Fixed Number of Variables. Mathematics Operations Research, Vol. 9, 538-548.
21. LiDIA GROUP 1999. LiDIA Manual. Universität des Saarlandes/TU Darmstadt, Germany. http://www.informatik.tu-darmstadt.de/TI/LiDIA.
22. MAGMA 1999. http://www.maths.usyd.edu.au:8000/comp/magma/Overview.html.
23. NGUYEN, P. 1999. Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto '97. Proceedings of Crypto '99, 288-304. Springer Lecture Notes in Computer Science LNCS 1666.
24. NGUYEN, P., AND STERN, J. 1998. Cryptanalysis of a Fast Public Key Cryptosystem Presented at SAC '97. Proceedings of Selected Areas in Cryptography '98, 213-218. Springer Lecture Notes in Computer Science LNCS 1556.
25. NTL 1999. http://www.cs.wisc.edu/~shoup/ntl.
26. POHST, M.E., AND ZASSENHAUS, H.J. 1989. Algorithmic Algebraic Number Theory. Cambridge University Press.
27. 3 Algorithm. J. Combin. Math. Combin. Computation, Vol. 3, 49-63.
28. RICKERT, N.W. 1989. Efficient Reduction of Quadratic Forms. Proceedings of Computers and Mathematics '89, 135-139.
29. SCHNORR, C.P., AND EUCHNER, M. 1991. LATTICE Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems. Proceedings of Fundamentals of Computation Theory '91, 68-85. Springer Lecture Notes in Computer Science LNCS 529.
30. SZYDLO, M. 2001. Personal communication.
31. DE WEGER, B. 1988. Algorithms for Diophantine Equations. PhD Thesis, Centrum voor Wiskunde en Informatica, Amsterdam, Netherlands.
32. WETZEL, S. 1998. Lattice Basis Reduction Algorithms and their Applications. PhD Thesis, Universität des Saarlandes, Saarbrücken, Germany.