A Practical Key Recovery Attack on Basic TCHo

  • Mathias Herrmann
  • Gregor Leander
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5443)


TCHo is a public key encryption scheme based on a stream cipher component, which is particular suitable for low cost devices like RFIDs. In its basic version, TCHo offers no IND-CCA2 security, but the authors suggest to use a generic hybrid construction to achieve this security level. The implementation of this method however, significantly increases the hardware complexity of TCHo and thus annihilates the advantage of being suitable for low cost devices. In this paper we show, that TCHo cannot be used without this construction. We present a chosen ciphertext attack on basic TCHo that recovers the secret key after approximately d 3/2 decryptions, where d is the number of bits of the secret key polynomial. The entropy of the secret key is \(\log_2\binom{d}{w}\), where w is the weight of the secret key polynomial, and w is usually small compared to d. In particular, we can break all of the parameters proposed for TCHo within hours on a standard PC.


TCHo chosen ciphertext attack stream cipher 


  1. 1.
    Abe, M., Gennaro, R., Kurosawa, K., Shoup, V.: Tag-KEM/DEM: A New Framework for Hybrid Encryption and A New Analysis of Kurosawa-Desmedt KEM. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 128–146. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  2. 2.
    El Aimani, L., von zur Gathen, J.: Finding low weight polynomial multiples using lattices. Cryptology ePrint Archive, Report 2007/423 (2007), http://eprint.iacr.org/
  3. 3.
    Aumasson, J.-P., Finiasz, M., Meier, W., Vaudenay, S.: TCHo: A hardware-oriented trapdoor cipher. In: Pieprzyk, J., Ghodosi, H., Dawson, E. (eds.) ACISP 2007. LNCS, vol. 4586, pp. 184–199. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Brent, R.P., Zimmermann, P.: Algorithms for finding almost irreducible and almost primitive trinomials. In: Primes and Misdemeanours: Lectures in Honour of the Sixtieth Birthday of Hugh Cowie Williams. The Fields Institute, Toronto, p. 212 (2003)Google Scholar
  5. 5.
    Canteaut, A., Chabaud, F.: A new algorithm for finding minimum-weight words in a linear code: Application to McEliece’s cryptosystem and to narrow-sense BCH codes of length 511. IEEE Transactions on Information Theory 44(1), 367–378 (1998)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Feldhofer, M., Rechberger, C.: A case against currently used hash functions in RFID protocols. In: Meersman, R., Tari, Z., Herrero, P. (eds.) OTM 2006 Workshops. LNCS, vol. 4277, pp. 372–381. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  7. 7.
    Finiasz, M., Vaudenay, S.: When stream cipher analysis meets public-key cryptography. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 266–284. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  8. 8.
    Fujisaki, E., Okamoto, T.: Secure integration of asymmetric and symmetric encryption schemes. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 537–554. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  9. 9.
    Shor, P.W.: Algorithms for quantum computation: Discrete logarithms and factoring. In: IEEE Symposium on Foundations of Computer Science, pp. 124–134 (1994)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mathias Herrmann
    • 1
  • Gregor Leander
    • 2
  1. 1.Horst Görtz Institute for IT-Security Faculty of MathematicsRuhr-University BochumGermany
  2. 2.Department of MathematicsTechnical University of DenmarkDenmark

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