Skip to main content

Cryptanalysis of Variants of UOV

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 4176))

Abstract

The Unbalanced Oil and Vinegar scheme (UOV) is a signature scheme based on multivariate quadratic equations. It has o oil variables and v vinegar variables. UOV has m equations and n variables, where m = o and n = v+o. In this paper, we define the weak key of UOV and study how to find the weak key from the public key. Second, we study the security when m > o. And our result shows that the security strengths of the current version of TTS, TRMS, Rainbow and MFE are 259 ~267.6 3DES operations.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ars, G., Faugère, J.-C., Imai, H., Kawazoe, M., Sugita, M.: Comparison Between XL and Gröbner Basis Algorithms. In: Lee, P.J. (ed.) ASIACRYPT 2004. LNCS, vol. 3329, pp. 338–353. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  2. Braeken, A., Wolf, C., Preneel, B.: A Study of the Security of Unbalanced Oil and Vinegar Signature Schemes. In: Menezes, A. (ed.) CT-RSA 2005. LNCS, vol. 3376, pp. 29–43. Springer, Heidelberg (2005), extended version: http://eprint.iacr.org/2004/222/

    Chapter  Google Scholar 

  3. Courtois, N., Daum, M., Felke, P.: On the security of HFE, hFEv- and quartz. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 337–350. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  4. 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)

    Chapter  Google Scholar 

  5. Ding, J., Schmidt, D.: Rainbow, a New Multivariable Polynomial Signature Scheme. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  6. Garay, M.R., Johnson, D.S.: Computers and Intractability, A Guide to the Theory of NP-completeness, p. 251. W.H. Freeman and Company, New York (1979)

    Google Scholar 

  7. Yuh-Hua, H., Lih-Chung, W., Chun-Yen, C., Feipei, L.: Similar Keys of Multivariate Quadratic Public Key Cryptosystems. In: Desmedt, Y.G., Wang, H., Mu, Y., Li, Y. (eds.) CANS 2005. LNCS, vol. 3810, pp. 211–222. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  8. Kipnis, A., Shamir, A.: Cryptanalysis of the Oil & Vinegar Signature Scheme. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 257–267. Springer, Heidelberg (1998)

    Google Scholar 

  9. Kipnis, A., Patarin, J., Goubin, L.: Unbalanced Oil and Vinegar Signature Schemes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 206–222. Springer, Heidelberg (1999)

    Google Scholar 

  10. Patarin, J.: The Oil and Vinegar Algorithm for Signatures. In: Dagstuhl Workshop on Cryptography (September 1997)

    Google Scholar 

  11. Wolf, C., Braeken, A., Preneel, B.: Efficient Cryptanalysis of RSE(2)PKC and RSSE(2)PKC. In: Blundo, C., Cimato, S. (eds.) SCN 2004. LNCS, vol. 3352, pp. 294–309. Springer, Heidelberg (2005), http://eprint.iacr.org/2004/237/

    Chapter  Google Scholar 

  12. Wolf, C., Preneel, B.: Large Superfluous Keys in \(\mathcal{M}\)ultivariate \(\mathcal{Q}\)uadratic Asymmetric Systems. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 275–287. Springer, Heidelberg (2005),(extended version): http://eprint.iacr.org/2004/361/

    Chapter  Google Scholar 

  13. Lih-Chung, W., Yuh-Hua, H., Feipei, L., Chun-Yen, C., Bo-Yin, Y.: Tractable Rational Map Signature. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 244–257. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Lih-Chung, W., Bo-Yin, Y., Yuh-Hua, H., Feipei, L.: A “Medium-Field” Multivariate Public-Key Encryption Scheme. In: Pointcheval, D. (ed.) CT-RSA 2006. LNCS, vol. 3860, pp. 132–149. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  15. Bo-Yin, Y., Jiun-Ming, C.: All in the XL family: Theory and practice. In: Park, C.-s., Chee, S. (eds.) ICISC 2004. LNCS, vol. 3506, pp. 67–86. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Bo-Yin, Y., Jiun-Ming, C.: Building Secure Tame-like Multivariate Public-Key Cryptosystems: The New TTS. In: Boyd, C., González Nieto, J.M. (eds.) ACISP 2005. LNCS, vol. 3574, pp. 518–531. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2006 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Hu, YH., Chou, CY., Wang, LC., Lai, F. (2006). Cryptanalysis of Variants of UOV. In: Katsikas, S.K., López, J., Backes, M., Gritzalis, S., Preneel, B. (eds) Information Security. ISC 2006. Lecture Notes in Computer Science, vol 4176. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11836810_12

Download citation

  • DOI: https://doi.org/10.1007/11836810_12

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38341-3

  • Online ISBN: 978-3-540-38343-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics