Abstract
In this paper, we propose an algebraic broadcast attack against NTRU, which recovers a single message encrypted multiple times using different NTRU public keys. Namely, when a message is broadcasted, under some reasonable assumptions, our attack can be completed in polynomial time and space. To the best of our knowledge, this is the first successful broadcast attack against NTRU.
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References
Arora, S., Ge, R.: New Algorithm for Learning in Presence of Errors, http://www.cs.princeton.edu/~rongge/LPSN.pdf
Buchmann, J., Cabarcas, D., Ding, J., Mohamed, M.S.E.: Flexible Partial Enlargement to Accelerate Gröbner Basis Computation over \(\mathbb{F}_2\). In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 69–81. Springer, Heidelberg (2010)
Coppersmith, D., Shamir, A.: Lattice Attacks on NTRU. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 52–61. Springer, Heidelberg (1997)
Courtois, N.T., Klimov, A.B., Patarin, J., Shamir, A.: Efficient Algorithms for Solving Overdefined Systems of Multivariate Polynomial Equations. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 392–407. Springer, Heidelberg (2000)
Ding, J.: Solving LWE problem with bounded errors in polynomial time. Cryptology ePrint Archive, Report 2010/558 (2010)
Ding, J.: Fast Algorithm to solve a family of SIS problem with l  ∞  norm. Cryptology ePrint Archive, Report 2010/581 (2010)
Ding, J.: Algebraic solvers for certain lattice-related problems. In: 2011 IEEE Information Theory Workshop (ITW), pp. 405–409. IEEE Conference Publications (2011)
Gama, N., Nguyên, P.Q.: New Chosen-Ciphertext Attacks on NTRU. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 89–106. Springer, Heidelberg (2007)
Hästad, J.: Solving simultaneous modular equations of low degree. SIAM J. Comput. 17, 336–341 (1988)
Hoffstein, J., Silverman, J.H.: Implementation Notes for NTRU PKCS Multiple Transmissions, Report #6, NTRU Technical Reports, http://www.securityinnovation.com/cryptolab/pdf/NTRUTech006.pdf
Hoffstein, J., Silverman, J.H.: Optimizations for NTRU. Technical report, NTRU Cryptosystems (June 2000), http://citeseer.ist.psu.edu/693057.html
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)
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., Nguyên, 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)
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
Howgrave-Graham, N., Silverman, J.H., Whyte, W.: Choosing Parameter Sets for NTRUEncrypt with NAEP and SVES-3. Technical Report, NTRU Cryptosystems (2005)
Hirschhorn, P.S., Hoffstein, J., Howgrave-Graham, N., Whyte, W.: Choosing NTRUEncrypt Parameters in Light of Combined Lattice Reduction and MITM Approaches. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 437–455. Springer, Heidelberg (2009)
IEEE. P1363.1 Public-Key Cryptographic Techniques Based on Hard Problems over Lattices. IEEE (June 2003), http://grouper.ieee.org/groups/1363/lattPK/index.html
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)
Mol, P., Yung, M.: Recovering NTRU Secret Key from Inversion Oracles. In: Cramer, R. (ed.) PKC 2008. LNCS, vol. 4939, pp. 18–36. Springer, Heidelberg (2008)
Nguyên, P.Q., Pointcheval, D.: Analysis and Improvements of NTRU Encryption Paddings. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 210–225. Springer, Heidelberg (2002)
Plantard, T., Susilo, W.: Broadcast Attacks against Lattice-Based Cryptosystems. In: Abdalla, M., Pointcheval, D., Fouque, P.-A., Vergnaud, D. (eds.) ACNS 2009. LNCS, vol. 5536, pp. 456–472. Springer, Heidelberg (2009)
Regev, O.: On lattices, learning with errors, random linear codes, and cryptography. In: Johnson, D.S., Feige, U. (eds.) Proc. of 37th STOC, pp. 84–93. ACM (2005)
Shoup, V.: NTL: A library for doing number theory, http://www.shoup.net/ntl/
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Ding, J., Pan, Y., Deng, Y. (2012). An Algebraic Broadcast Attack against NTRU. In: Susilo, W., Mu, Y., Seberry, J. (eds) Information Security and Privacy. ACISP 2012. Lecture Notes in Computer Science, vol 7372. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31448-3_10
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DOI: https://doi.org/10.1007/978-3-642-31448-3_10
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