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A General NTRU-Like Framework for Constructing Lattice-Based Public-Key Cryptosystems

  • Yanbin Pan
  • Yingpu Deng
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7115)

Abstract

As we know, one of the most difficult points of constructing a new public-key cryptosystem is to hide its trapdoor. By studying how NTRU hides its trapdoor, we present a general NTRU-like framework. The framework reduces constructing new lattice-based public-key cryptosystems to finding some certain kinds of easy closest vector problems (CVPs). We also show how to use the framework to reobtain NTRU. What’s more, a new lattice-based public-key cryptosystem is proposed as an application of the framework.

Keywords

NTRU Lattice Public-Key Cryptosystem 

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References

  1. 1.
    Ajtai, M.: Gennerating hard instances of lattice problems. In: The 28th STOC, pp. 99–108. ACM, New York (1996)Google Scholar
  2. 2.
    Ajtai, M.: Representing hard lattices with O(nlogn) bits. In: The 37th STOC, pp. 94–103. ACM, New York (2005)Google Scholar
  3. 3.
    Ajtai, M., Dwork, C.: A public-key cryptosystem with worst-case/average-case equivalence. In: The 29th STOC, pp. 284–293. ACM, New York (1997)Google Scholar
  4. 4.
    Babai, L.: On Lovász lattice reduction and the nearest lattice point problem. Combinatorica 6, 1–13 (1986)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Banks, W.D., Shparlinski, I.E.: A Variant of NTRU with Non-Invertible Polynomials. In: Menezes, A., Sarkar, P. (eds.) INDOCRYPT 2002. LNCS, vol. 2551, pp. 62–70. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  6. 6.
    Cai, J.-Y., Cusick, T.W.: A Lattice-Based Public-Key Cryptosystem. In: Tavares, S., Meijer, H. (eds.) SAC 1998. LNCS, vol. 1556, pp. 219–233. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  7. 7.
    Coglianese, M., Goi, B.-M.: MaTRU: A New NTRU-Based Cryptosystem. In: Maitra, S., Veni Madhavan, C.E., Venkatesan, R. (eds.) INDOCRYPT 2005. LNCS, vol. 3797, pp. 232–243. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  8. 8.
    Coppersmith, D., Shamir, A.: Lattice Attacks on NTRU. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 52–61. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  9. 9.
    Diffie, W., Hellman, M.: New Directions in Cryptography. IEEE Transactions on Information Theory 22, 644–654 (1976)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Goldreich, O., Goldwasser, S., Halevi, S.: Public-Key Cryptosystems from Lattice Reduction Problems. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 112–131. Springer, Heidelberg (1997)CrossRefGoogle Scholar
  11. 11.
    Gentry, C., Peikert, C., Vaikuntanathan, V.: Trapdoors for hard lattices and new cryptographic constructions. In: The 40th STOC, pp. 197–206. ACM, New York (2008)Google Scholar
  12. 12.
    Howgrave-Graham, N.: A Hybrid Lattice-Reduction and Meet-in-the-Middle Attack Against NTRU. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 150–169. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  13. 13.
    Howgrave-Graham, N., Silverman, J.H., Whyte, W.: A Meet-In-The-Meddle Attack on an NTRU Private Key. Technical report, http://www.ntru.com/cryptolab/technotes.htm#004
  14. 14.
    Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A Ring-Based Public Key Cryptosystem. In: Buhler, J.P. (ed.) ANTS 1998. LNCS, vol. 1423, pp. 267–288. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  15. 15.
    Gaborit, P., Ohler, J., Sole, P.: CTRU, a polynomial analogue of NTRU. INRIA, Rapport de recherche 4621, INRIA (2002), ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4621.pdf
  16. 16.
    Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coeffcients. Math. Ann. 261, 515–534 (1982)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Malekian, E., Zakerolhosseini, A.: Ntru-like Public Key Cryptosystems beyond Dedekind Domain Up to Alternative Algebra, http://eprint.iacr.org/2009/446
  18. 18.
    May, A., Silverman, J.H.: Dimension Reduction Methods for Convolution Modular Lattices. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 110–125. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  19. 19.
    Merkle, R., Hellman, M.: Hiding Information and Signatures in Trapdoor Knapsacks. IEEE Transactions on Information Theory 24(5), 525–530 (1978)CrossRefGoogle Scholar
  20. 20.
    Nguyen, P., Stern, J.: Cryptanalysis of the Ajtai-Dwork Cryptosystem. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 223–242. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  21. 21.
    Nguyen, P.: Cryptanalysis of the Goldreich-Goldwasser-Halevi Cryptosystem from Crypto’97. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 288–304. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  22. 22.
    Pan, Y., Deng, Y.: A Ciphertext-Only Attack Against the Cai-Cusick Lattice-Based Public-Key Cryptosystem. IEEE Transactions on Information Theory 57, 1780–1785 (2011)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Peikert, C.: Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem. In: The 41th STOC, pp. 333–342. ACM, New York (2009)Google Scholar
  24. 24.
    Regev, O.: New lattice-based cryptographic constructions. Journal of the ACM 51, 899–942 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: The 37th STOC, pp. 84–93. ACM, New York (2005)Google Scholar
  26. 26.
    Rivest, R., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public-Key Cryptosystems. Communications of the ACM, Mach. 21, 120–126 (1978)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Shor, P.: Algorithms for Quantum Computation: Discrete Logarithms and Factoring. In: The 35th Annual Symposium on Foundations of Computer Science, pp. 124–134. IEEE Computer Science Press, Santa Fe (1994)CrossRefGoogle Scholar
  28. 28.
    Shoup, V.: NTL: A library for doing number theory, http://www.shoup.net/ntl/
  29. 29.
    Vats, N.: NNRU, a noncommutative analogue of NTRU, http://arxiv.org/abs/0902.1891

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Yanbin Pan
    • 1
  • Yingpu Deng
    • 1
  1. 1.Key Laboratory of Mathematics MechanizationAcademy of Mathematics and Systems Science, Chinese Academy of SciencesChina

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