Rankin's constant and blockwise lattice reduction

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 4117 LNCS, Issue , 2006, Pages 112-130

  Gama, Nicolas ^a   Howgrave Graham, Nick ^b   Koy, Henrik ^c   Nguyen, Phong Q ^a  

^a ECOLE NORMALE SUPÉRIEURE   (France)

^b NTRU Cryptosystems   (United States)

^c DEUTSCHE BANK AG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; MATHEMATICAL MODELS; SECURITY OF DATA; SECURITY SYSTEMS; STRATEGIC PLANNING;

BLOCKWISE LATTICE REDUCTION; CRYPTANALYSIS; RANKIN'S CONSTANT; SCHNORR'S ALGORITHM;

PUBLIC KEY CRYPTOGRAPHY;

EID: 33749542547     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/11818175_7     Document Type: Conference Paper

References (28)

1. M. Ajtai. The worst-case behavior of Schnorr's algorithm approximating the shortest nonzero vector in a lattice. In Proceedings of the Thirty-Fifth Annual ACM Symposium on Theory of Computing, pages 396-406 (electronic), New York, 2003. ACM.
2. M. Ajtai, R. Kumar, and D. Sivakumar. A sieve algorithm for the shortest lattice vector problem. In Proc. 33rd STOC, pages 601-610. ACM, 2001.
3. M. I. Boguslavsky. Radon transforms and packings. Discrete Appl. Math., 111(1-2):3-22, 2001.
4. D. Boneh. Twenty years of attacks on the RSA cryptosystem. Notices of the AMS, 46(2):203-213, 1999.
5. 0.292. In Proc. of Eurocrypt '99, volume 1592 of LNCS, pages 1-11. IACR, Springer-Verlag, 1999.
6. J. W. S. Cassels. Rational quadratic forms, volume 13 of London Mathematical Society Monographs. Academic Press Inc. [Harcourt Brace Jovanovich Publishers], London, 1978.
7. H. Cohen. A Course in Computational Algebraic Number Theory. Springer-Verlag, 1995. Second edition.
8. J. Conway and N. Sloane. Sphere Packings, Lattices and Groups. Springer-Verlag, 1998. Third edition.
9. D. Coppersmith. Small solutions to polynomial equations, and low exponent RSA vulnerabilities. J. of Cryptology, 10(4):233-260, 1997. Revised version of two articles from Eurocrypt '96.
10. M. Grötschel, L. Lovász, and A. Schrijver. Geometric algorithms and combinatorial optimization, volume 2 of Algorithms and Combinatorics: Study and Research Texts. Springer-Verlag, Berlin, 1988.
11. C. Hermite. Extraits de lettres de M. Hermite à M. Jacobi sur différents objets de la théorie des nombres, deuxième lettre. J. Reine Angew. Math., 40:279-290, 1850. Also available in the first volume of Hermite's complete works, published by Gauthier-Villars.
12. N. A. Howgrave-Graham and N. P. Smart. Lattice attacks on digital signature schemes. Des. Codes Cryptogr., 23(3):283-290, 2001.
13. J. L. Lagrange. Recherches d'arithmétique. Nouveaux Mémoires de l'Académie de Berlin, 1773.
14. A. K. Lenstra, H. W. Lenstra, Jr., and L. Lovász. Factoring polynomials with rational coefficients. Mathematische Ann., 261:513-534, 1982.
15. L. Lovász. An Algorithmic Theory of Numbers, Graphs and Convexity, volume 50. SIAM Publications, 1986. CBMS-NSF Regional Conference Series in Applied Mathematics.
16. J. Martinet. Les réseaux parfaits des espaces euclidiens. Masson, Paris, 1996.
17. D. Micciancio and S. Goldwasser. Complexity of lattice problems. The Kluwer International Series in Engineering and Computer Science, 671. Kluwer Academic Publishers, Boston, MA, 2002. A cryptographic perspective.
18. J. Milnor and D. Husemoller. Symmetric bilinear forms. Math. Z, 1973.
19. P. Q. Nguyen and I. E. Shparlinski. The insecurity of the digital signature algorithm with partially known nonces. J. Cryptology, 15(3):151-176, 2002.
20. P. Q. Nguyen and D. Stehle. Floating-point LLL revisited. In Proc. of Eurocrypt '05, volume 3494 of LNCS, pages 215-233. IACR, Springer-Verlag, 2005.
21. P. Q. Nguyen and J. Stern. The two faces of lattices in cryptology. In Proc. of CALC '01, volume 2146 of LNCS. Springer-Verlag, 2001.
22. A. M. Odlyzko. The rise and fall of knapsack cryptosystems. In Proc. of Cryptology and Computational Number Theory, volume 42 of Proc. of Symposia in Applied Mathematics, pages 75-88. AMA, 1989.
23. R. A. Rankin. On positive definite quadratic forms. J. London Math. Soc., 28:309-314, 1953.
24. C. P. Schnorr. A hierarchy of polynomial lattice basis reduction algorithms. Theoretical Computer Science, 53:201-224, 1987.
25. C. P. Schnorr. A more efficient algorithm for lattice basis reduction. J. of algorithms, 9(1):47-62, 1988.
26. C. P. Schnorr and M. Euchner. Lattice basis reduction: improved practical algorithms and solving subset sum problems. Math. Programming, 66:181-199, 1994.
27. C. P. Schnorr and H. H. Hörner. Attacking the Chor-Rivest cryptosystem by improved lattice reduction. In Proc. of Eurocrypt '95, volume 921 of LNCS, pages 1-12. IACR, Springer-Verlag, 1995.
28. J. L. Thunder. Higher-dimensional analogs of Hermite's constant. Michigan Math. J., 45(2):301-314, 1998.