Abstract
CTRU, a public key cryptosystem was proposed by Gaborit, Ohler and Sole. It is analogue of NTRU, the ring of integers replaced by the ring of polynomials \(\mathbb{F}_2[T]\). It attracted attention as the attacks based on either LLL algorithm or the Chinese Remainder Theorem are avoided on it, which is most common on NTRU. In this paper we presents a polynomial-time algorithm that breaks CTRU for all recommended parameter choices that were derived to make CTRU secure against popov normal form attack. The paper shows if we ascertain the constraints for perfect decryption then either plaintext or private key can be achieved by polynomial time linear algebra attack.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
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.: Finding a Small Root of a Bivariate Integer Equation; Factoring with High Bits Known. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 178–189. Springer, Heidelberg (1996)
Coppersmith, D.: Small Solution to Polynomial Equations, and Low Exponent RSA Vulner-Abilities. Journal of Cryptology 10, 223–260 (1997)
Coppersmith, D., Shamir, A.: Lattice Attacks on NTRU. In: Fumy, W. (ed.) EUROCRYPT 1997. LNCS, vol. 1233, pp. 52–61. Springer, Heidelberg (1997)
Coppersmith, D.: Finding Small Solution to Small Degree Polynomials. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 20–31. Springer, Heidelberg (2001)
Gaborit, P., Ohler, J., Sole, P.: CTRU, a Polynomial Analogue of NTRU, INRIA. Rapport de recherche, N.4621 (November 2002), (ISSN 0249-6399), ftp://ftp.inria.fr/INRIA/publication/publi-pdf/RR/RR-4621.pdf
Hoffstein, J., Howgrave-Graham, N., Pipher, J., Silverman, J.H., Whyte, W.: NTRUSign: Digital Signatures Using the NTRU Lattice. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 122–140. Springer, Heidelberg (2003)
Hoffestein, 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)
Hoffestein, J., Pipher, J., Silverman, J.H.: NSS: An NTRU Lattice-Based Signature Scheme. In: Pfitzmann, B. (ed.) EUROCRYPT 2001. LNCS, vol. 2045, pp. 211–228. Springer, Heidelberg (2001)
Hoffstein, J., Silverman, J.H.: Optimizations for NTRU. In: Public-Key Cryptography and computational Number Theory (2000)
Hoffistein, J., Silverman, J.H.: Random Small Hamming Weight Products with Applications to Cryptography. Discrete Applied Mathematics 130, 37–49 (2000)
Howgrave-Graham, N., Nguyen, P.Q., Pointcheval, D., Proos, J.: The Impact of Decrption Failures on the Security of NTRU Encryption. In: Boneh, D. (ed.) CRYPTO 2003. LNCS, vol. 2729, pp. 226–246. Springer, Heidelberg (2003)
Jaulmes, E., Joux, A.: A Chosen Ciphertext Attack on NTRU. In: Bellare, M. (ed.) CRYPTO 2000. LNCS, vol. 1880, pp. 20–35. Springer, Heidelberg (2000)
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)
McEliece, R.J.: A Public-Key Cryptosystem Based on Alzebraic Coding Theory. JPL DSN Progress report 42-44, 114–116 (1978)
Nguyen, 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)
Nguyen, P.Q., Stern, J.: The Two Faces of Lattice in Cryptology. In: Silverman, J.H. (ed.) CaLC 2001. LNCS, vol. 2146, pp. 148–180. Springer, Heidelberg (2001)
Rivest, R.L., Shamir, A., Adleman, L.: A Method for Obtaining Digital Signatures and Public Key Cryptosystem. Communications of the ACM 21, 120–126 (1978)
Schnorr, C.P.: A Hierarchy of Polynomial Time Lattice Basis Reduction Algorithms. Theoretical Computer Science 53, 201–224 (1987)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vats, N. (2008). Algebraic Cryptanalysis of CTRU Cryptosystem. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_24
Download citation
DOI: https://doi.org/10.1007/978-3-540-69733-6_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69732-9
Online ISBN: 978-3-540-69733-6
eBook Packages: Computer ScienceComputer Science (R0)