Abstract
This paper studies the NTRU public key cryptosystem to identify the most influential parameters for decryption failure confirming that decryption failure is key-dependent. The study uses binary polynomials and analyzes the correlation between the parameter sets recommended in the EESS 1v2 (2003) and Jeffrey Hoffstein et al. (2003). The observed relationships are then used to recommend an extended parameter selection criteria which ensures invertibility and reduced probability of decryption failure. We then recommend a condition for selecting an appropriately large size of q which is the least size required for ensuring successful message decryption. The study focuses on binary polynomials as it allows for a smaller public key size and for the purpose of providing better insights leading to further study into other variants of NTRU.
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References
Qingjun, C., Yuli, Z.: Subliminal channels in the ntru and the subliminal-free methods. Wuhan Univ. J. Nat. Sci. 11(6), 1541–1544 (2006). http://dx.doi.org/10.1007/BF02831816
Whyte, W., Hoffstein, J.: NTRU. In: Whyte, W., Hoffstein, J. (eds.) Encyclopedia of Cryptography and Security, pp. 858–861. Springer, Boston (2011). http://dx.doi.org/10.1007/978-1-4419-5906-5_464
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). http://dx.doi.org/10.1007/BFb0054868
Hoffstein, J., Pipher, J., Schanck, J.M., Silverman, J.H., Whyte, W., Zhang, Z.: Choosing parameters for ntruencrypt. Report, Cryptology ePrint Archive, Report 2015/708 (2015)
onsortium for Efficient Embedded Security: Efficient embedded security standard (EESS) EESS 1, version 3.0, 31 March 2015. https://github.com/NTRUOpenSourceProject/ntru-crypto
Silverman, J.H.: Wraps, gaps, and lattice constants. NTRU Report 11 (2001)
Hoffstein, J., Silverman, J.H., Whyte, W.: Estimated breaking times for NTRU lattices. In: version 2, NTRU Cryptosystems (2003). Citeseer (1999). http://www.ntru.com/cryptolab/tech_notes.htm#012
IEEE: Efficient embedded security standards (EESS), EESS 1: implementation aspects of ntruencrypt and ntrusign, version 2.0, 20 June 2003
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). doi:10.1007/978-3-642-01957-9_27
Ieee draft standard specification for public- key cryptographic techniques based on hard problems over lattices. IEEE Unapproved Draft Std P1363.1/D12, p. 1, October 2008
Hoffstein, J., Jill Pipher, W.W.: More efficient parameters keys and encoding for hybrid resistant ntruencrypt and ntrusign. Report, NTRU Cryptosystems Inc., Security Innovation (2009)
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). http://dx.doi.org/10.1007/978-3-540-45146-4_14
Pipher, J.: Lectures on the ntru encryption algorithm and digital signaturescheme: Grenoble, June 2002. Report, Brown University, Providence, RI 02912, June 2002. http://www.math.brown.edu/~jpipher/grenoble.pdf
Howgrave-Graham, N., Silverman, J.H., Singer, A., Whyte, W., Cryptosystems, N.: Naep: Provable security in the presence of decryption failures. IACR Cryptology ePrint Archive 2003, 172 (2003)
Howgrave-Graham, N., Silverman, J.H., Whyte, W.: Choosing parameter sets for NTRUEncrypt with NAEP and SVES-3. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 118–135. Springer, Heidelberg (2005). http://dx.doi.org/10.1007/978-3-540-30574-3_10
Athreya, K.B., Lahiri, S.N.: Central limit theorems. In: Athreya, K.B., Lahiri, S.N. (eds.) Measure Theory and Probability Theory, pp. 343–382. Springer, New York (2006). http://dx.doi.org/10.1007/978-0-387-35434-7_12
Lincoln University: Sample size (2006). http://library.lincoln.ac.nz/global/library/learning/mathsandstats/qmet103/sample-size.pdf
Levy, P.S., Lemeshow, S.: Sampling of Populations: Methods and Applications. Wiley, Hoboken (2013)
Magma Group: Magma computational algebra system, version 2.21-2, Sydney (2015)
Hermans, J., Vercauteren, F., Preneel, B.: Speed records for NTRU. In: Pieprzyk, J. (ed.) CT-RSA 2010. LNCS, vol. 5985, pp. 73–88. Springer, Heidelberg (2010). doi:10.1007/978-3-642-11925-5_6
Xu, J., Hu, L., Sun, S., Xie, Y.: Cryptanalysis of countermeasures against multiple transmission attacks on NTRU. IET Commun. 8(12), 2142–2146 (2014)
Bourgeois, G., Faugère, J.C.: Algebraic attack on ntru using witt vectors and Gröbner bases. J. Math. Crypt. 3(3), 205–214 (2009)
Hornik, K., Buchta, C., Zeileis, A.: Open-source machine learning: R meets Weka. Comput. Stat. 24(2), 225–232 (2009)
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Gaithuru, J.N., Salleh, M., Mohamad, I., Adeyemi, I.R. (2017). NTRU Binary Polynomials Parameters Selection for Reduction of Decryption Failure. In: Phon-Amnuaisuk, S., Au, TW., Omar, S. (eds) Computational Intelligence in Information Systems. CIIS 2016. Advances in Intelligent Systems and Computing, vol 532. Springer, Cham. https://doi.org/10.1007/978-3-319-48517-1_16
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