A hybrid lattice-reduction and meet-in-the-middle attack against NTRU

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

Volumn 4622 LNCS, Issue , 2007, Pages 150-169

  Howgrave Graham, Nick ^a  

^a NTRU Cryptosystems

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTATIONAL COMPLEXITY; CRYPTOGRAPHY; EXTRAPOLATION; HYBRID COMPUTERS; PARAMETER ESTIMATION;

LATTICE REDUCTION; NTRUENCRYPT PARAMETERS; SECURITY PARAMETER;

SECURITY OF DATA;

EID: 38049125101     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-540-74143-5_9     Document Type: Conference Paper

References (24)

1. Ajtai, M., Kumar, R., Sivakumar, D.: A sieve algorithm for the shortest lattice vector problem. In: Proc. of 29th STOC, pp. 284-293. ACM Press, New York (1997)
2. Babai, L.: On Lovász lattice reduction and the nearest lattice point problem. Combinatorica 6, 1-13 (1986)
3. Casseis, J.W.S.: An introduction to the geometry of numbers, Springer-Verlag, Reprint of the 1st ed. Berlin Heidelberg New York, Corr. 2nd printing 1971, 1997, VIII (1959)
4. Conway, J.H., Sloane, N.J.A.: Sphere Packings, Lattices and Groups. Grundlehren der mathematischen Wissenschaften, 290 (1993)
5. Coppersmith, D., Shamir, A.: Lattice Attacks on NTRU. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 52-61. Springer, Heidelberg (1997)
6. Fincke, U., Pohst, M.: Improved methods for calculating vectors of short length in a lattice, including a complexity analysis. Math. Comp. 44, 463-471 (1985)
7. Fürst, M.L., Kannan, R.: Succinct certificates for almost all subset sum problems. SIAM Journal on Computing 1989, 550-558
8. Gama, N., Howgrave-Graham, N., Nguyen, P.Q.: Rankin's Constant and Blockwise Lattice Reduction. In: Dwork, C. (ed.) CRYPTO 2006. LNCS, vol. 4117, pp. 112-130. Springer, Heidelberg (2006)
9. Gama, N., Howgrave-Graham, N., Nguyen, P.Q.: Symplectic Lattice Reduction and NTRU. In: Vaudenay, S. (ed.) EUROCRYPT 2006. LNCS, vol. 4004, pp. 233-253. Springer, Heidelberg (2006)
10. Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A Ring-Based Public Key Cryptosystem. In: Buhler, J.P. (ed.) Algorithmic Number Theory. LNCS, vol. 1423, pp. 267-288. Springer, Heidelberg (1998)
11. Howgrave-Graham, N., Nguyen, P.Q., Pointcheval, D., Proos, J., Silverman, J.H., Singer, A., Whyte, W.: The Impact of Decryption Failures on the Security of NTRU Encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 226-246. Springer, Heidelberg (2003)
12. Howgrave-Graham, N.: Computational Mathematics Inspired by RSA, PhD. Thesis, University of Bath (1998)
13. Howgrave-Graham, N.: Finding Small Roots of Univariate Modular Equations Revisited. IMA Int. Conf. pp. 131-142 (1997)
14. Howgrave-Graham, N., Silverman, J.H., Whyte, W.: Choosing Parameter Sets for NTRUEncrypt with NAEP and SVES-3. In: Menezes, A.J. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 118-135. Springer, Heidelberg (2005), http://www.ntru.com/ cryptolab/articles.htm#2005_l
15. Howgrave-Graham, N., Silverman, J.H., Whyte, W.: A Meet-In-The-Middle Attack on an NTRU Private Key, http://www. ntru. com/cryptolab/tech_notes. htm#004
16. W. Whyte, (ed.) IEEE P1363, 1/D9 Draft Standard for Public-Key Cryptographic Techniques Based on Hard Problems over Lattices
17. Kannan, R.: Improved algorithms for integer programming and related lattice problems. In: Proc. of the 15th Symposium on the Theory of Computing (STOC 1983), pp. 99-108. ACM Press, New York (1983)
18. Philip, N.: Finding the closest lattice vector when it's unusually close. In: Proceedings, ACM-SIAM Symposium on Discrete Algorithms, pp. 937-941. ACM, New York (2000)
19. Lenstra, A., Verheul, E.: Selecting Cryptographic Key Sizes. Journal of Cryptology 14(4), 255-293 (2001)
20. Pohst, M.: On the computation of lattice vectors of minimal length, successive minima and reduced bases with applications. ACM SIGSAM Bull. 15, 37-44 (1981)
21. Schnorr, C.P.: Lattice Reduction by Random Sampling and Birthday Methods. In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 145-156. Springer, Heidelberg (2003)
22. Schnorr, C.P., Euchner, M.: Lattice Basis Reduction: Improved Practical Algorithms and Solving Subset Sum Problems. Mathematical Programming 66, 181-191 (1994)
23. Shoup, V.: NTL: A Library for doing Number Theory, Version 5.4, http ://www.shoup.net/ntl
24. Wagner, D.: A Generalized Birthday Problem. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 288-303. Springer, Heidelberg (2002), http://www.cs.berkeley.edu/daw/papers