Abstract
In this correspondence, we show that partial information of plaintext can be used to simplify the decryption problem in the case of the GGH cryptosystem. Combined with Nguyen’s previous attack, we solve the numerical GGH challenge of the highest dimension 400, proposed on the Internet by the authors of the cryptosystem. We also discuss how to avoid this attack.
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References
Ajtai, M.: The shortest vector problem in L2 is NP-hard for randomized reductions (extended abstract). In: Proceedings of STOC’98, pp. 10–19 (1998)
Babai L.: On Lovász lattice reduction and the nearest lattice point problem. Combinatorica 6, 1–13 (1986)
Goldreich, O., Goldwasser, S., Halevi, S.: Public-key cryptosystems from lattice reduction problems. In: Proceedings of Crypto’97, LNCS, vol. 1294, pp. 112–131 (1997)
Goldreich, O., Goldwasser, S., Halevi, S.: The GGH Cryptosystem. Available at http://groups.csail.mit.edu/cis/lattice/challenge.html
Hoffstein, J., Pipher, J., Silverman, J.H.: NTRU: A Ring-Based Public Key Cryptosystem. In:ANTS III, LNCS, vol. 1423, pp. 267–288 (1998)
Hoffstein, J., Silverman, J.H.: Protecting NTRU Against Chosen Ciphertext and Reaction Attacks. NTRU Cryptosystems Technical Report, Available at http://www.ntru.com/cryptolab/tech_notes.htm#016, Report #016
Ludwig, C.: The Security and Efficiency of Micciancio’s Cryptosystem. Technical Report. Available at http://www.cdc.informatik.tu-darmstadt.de/reports/TR/TI-02-07.MiccPaper.pdf
May, A.: Cryptanalysis of NTRU, preprint
May, A., Silverman, J.H.: Dimension Reduction Methods for Convolution Modular Lattices. In: CaLC 2001, LNCS, vol. 2146, pp. 110–125 (2001)
Micciancio, D.: Improving lattice based cryptosystems using the hermite normal form. In: CaLC 2001, LNCS, vol. 2146, pp. 126–145 (2001)
Nguyen, P.: Cryptanalysis of the Goldreich–Goldwasser–Halevi cryptosystem from Crypto’97. In: Proceedings of Crypto’99, LNCS, vol. 1666, pp. 288–304 (1999)
Kannan R.: Minkowski’s convex body theorem and integer programming. Math. Oper. Res. 12(3), 415–440 (1987)
Shoup, V.: Number Theory C++ Library (NTL) version 5.4.1. Available at http://www.shoup.net/ntl/
Silverman, J.H.: Dimension-reduced lattices, zero-forced lattices, and the NTRU public key cryptosystem. NTRU Cryptosystems Technical Report #013, Version 1 (1999)
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This work was partially supported by the Korea Science and Engineering Foundation (KOSEF) grant funded by the Korea government (MOST) (No. R11-2007-035-01000-0).
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Lee, M.S., Hahn, S.G. Cryptanalysis of the GGH Cryptosystem. Math.Comput.Sci. 3, 201–208 (2010). https://doi.org/10.1007/s11786-009-0018-5
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DOI: https://doi.org/10.1007/s11786-009-0018-5