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.
This work was supported in part by the NNSF of China (No. 11071285 and No. 60821002) and in part by 973 Project (No. 2011CB302401).
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References
Ajtai, M.: Gennerating hard instances of lattice problems. In: The 28th STOC, pp. 99–108. ACM, New York (1996)
Ajtai, M.: Representing hard lattices with O(nlogn) bits. In: The 37th STOC, pp. 94–103. ACM, New York (2005)
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)
Babai, L.: On Lovász lattice reduction and the nearest lattice point problem. Combinatorica 6, 1–13 (1986)
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)
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)
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)
Coppersmith, D., Shamir, A.: Lattice Attacks on NTRU. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 52–61. Springer, Heidelberg (1997)
Diffie, W., Hellman, M.: New Directions in Cryptography. IEEE Transactions on Information Theory 22, 644–654 (1976)
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)
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)
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)
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
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)
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
Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coeffcients. Math. Ann. 261, 515–534 (1982)
Malekian, E., Zakerolhosseini, A.: Ntru-like Public Key Cryptosystems beyond Dedekind Domain Up to Alternative Algebra, http://eprint.iacr.org/2009/446
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)
Merkle, R., Hellman, M.: Hiding Information and Signatures in Trapdoor Knapsacks. IEEE Transactions on Information Theory 24(5), 525–530 (1978)
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)
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)
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)
Peikert, C.: Public-Key Cryptosystems from the Worst-Case Shortest Vector Problem. In: The 41th STOC, pp. 333–342. ACM, New York (2009)
Regev, O.: New lattice-based cryptographic constructions. Journal of the ACM 51, 899–942 (2004)
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: The 37th STOC, pp. 84–93. ACM, New York (2005)
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)
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)
Shoup, V.: NTL: A library for doing number theory, http://www.shoup.net/ntl/
Vats, N.: NNRU, a noncommutative analogue of NTRU, http://arxiv.org/abs/0902.1891
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Pan, Y., Deng, Y. (2012). A General NTRU-Like Framework for Constructing Lattice-Based Public-Key Cryptosystems. In: Jung, S., Yung, M. (eds) Information Security Applications. WISA 2011. Lecture Notes in Computer Science, vol 7115. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27890-7_9
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DOI: https://doi.org/10.1007/978-3-642-27890-7_9
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