Abstract
The cryptanalysis of Gentry and Szydlo of the revised NTRU signature scheme requires the computation of the integer matrix decomposition M = UU t. We propose a heuristic algorithm to compute this decomposition and investigate its properties. Our test implementation of this algorithm in Magma is able to deal with matrices up to 158 rows and columns.
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References
Bosma, W., Cannon, J., Playoust, C.: The Magma algebra system I: The user language. J. Symbolic Comput. 24, 235–265 (1997)
Cohen, H.: A Course in Computational Algebraic Number Theory. Springer, Heidelberg (1996)
Computational algebra group, Uni. Sydney. Magma (2002) see, http://www.maths.usyd.edu.au:8000/u/magma/
Consortium for Efficient Embedded Security. Efficient Embedded Security Standard (EESS), see http://www.ceesstandards.org/
Gentry, C., Szydlo, M.: Cryptanalysis of the Revised NTRU Signature Scheme. In: Knudsen, L.R. (ed.) EUROCRYPT 2002. LNCS, vol. 2332, pp. 299–320. Springer, Heidelberg (2002)
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)
Hoffstein, J., Howgrave-Graham, N., Pipher, J., Silverman, J.H., Whyte, W.: NTRUSign: Digital Signatures Using the NTRU Lattice (2002), see http://www.ntru.com/
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)
Hoffstein, J., Pipher, J., Silverman, J.H.: NSS: The NTRU Signature Scheme. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 211–228. Springer, Heidelberg (2001)
Lenstra, A.K., Lenstra, H.W., Lovász, L.: Factoring polynomials with rational coefficients. Math. Ann. 261, 515–534 (1982)
Stern, J., Nguyen, P.: Lattice reduction in cryptology: an update. In: Bosma, W. (ed.) ANTS 2000. LNCS, vol. 1838, pp. 85–112. Springer, Heidelberg (2000)
Szydlo, M.: Hypercubic Lattice Reduction and Analysis of GGH and NTRU Signatures. In: Biham, E. (ed.) EUROCRYPT 2003. LNCS, vol. 2656, pp. 433–448. Springer, Heidelberg (2003)
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Geißler, K., Smart, N.P. (2003). Computing the M = UU t Integer Matrix Decomposition. In: Paterson, K.G. (eds) Cryptography and Coding. Cryptography and Coding 2003. Lecture Notes in Computer Science, vol 2898. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-40974-8_18
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DOI: https://doi.org/10.1007/978-3-540-40974-8_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-20663-7
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