Skip to main content

Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and ℓIC-Derivatives

  • Conference paper
Post-Quantum Cryptography (PQCrypto 2008)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 5299))

Included in the following conference series:

Abstract

We present instances of MPKCs (multivariate public key cryptosystems) with design, given the best attacks we know, and implement them on commodity PC hardware. We also show that they can hold their own compared to traditional alternatives. In fact, they can be up to an order of magnitude faster.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 49.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 64.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Akkar, M.-L., Courtois, N.T., Duteuil, R., Goubin, L.: A fast and secure implementation of SFLASH. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 267–278. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Bardet, M., Faugère, J.-C., Salvy, B.: On the complexity of Gröbner basis computation of semi-regular overdetermined algebraic equations. In: Proceedings of the International Conference on Polynomial System Solving, pp. 71–74, Previously INRIA report RR-5049 (2004)

    Google Scholar 

  3. Bardet, M., Faugère, J.-C., Salvy, B., Yang, B.-Y.: Asymptotic expansion of the degree of regularity for semi-regular systems of equations. In: Gianni, P. (ed.) MEGA 2005 Sardinia (Italy) (2005)

    Google Scholar 

  4. Berbain, C., Billet, O., Gilbert, H.: Efficient implementations of multivariate quadratic systems. In: Biham, E., Youssef, A.M. (eds.) SAC 2006. LNCS, vol. 4356, pp. 174–187. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  5. Bernstein, D.J., Birkner, P., Joye, M., Lange, T., Peters, C.: Twisted edwards curves. In: Vaudenay, S. (ed.) AFRICACRYPT 2008. LNCS, vol. 5023, pp. 389–405. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Bernstein, D.J., Lange, T.: Faster addition and doubling on elliptic curves. In: Kurosawa, K. (ed.) ASIACRYPT 2007. LNCS, vol. 4833, pp. 29–50. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  7. Bernstein, D.J., Lange, T.: Inverted edwards coordinates. In: Boztaş, S., Lu, H.-F. (eds.) AAECC 2007. LNCS, vol. 4851, pp. 20–27. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  8. Billet, O., Gilbert, H.: Cryptanalysis of rainbow. In: De Prisco, R., Yung, M. (eds.) SCN 2006. LNCS, vol. 4116, pp. 336–347. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Coppersmith, D., Stern, J., Vaudenay, S.: The security of the birational permutation signature schemes. Journal of Cryptology 10, 207–221 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  10. Courtois, N., Goubin, L., Patarin, J.: SFLASH: Primitive specification (second revised version), Submissions, Sflash, 11 pages (2002), https://www.cosic.esat.kuleuven.be/nessie

  11. Courtois, N.T., Klimov, A., 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), http://www.minrank.org/xlfull.pdf

    Chapter  Google Scholar 

  12. Ding, J.: A new variant of the Matsumoto-Imai cryptosystem through perturbation. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 305–318. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Ding, J., Gower, J.: Inoculating multivariate schemes against differential attacks. In: Yung, M., Dodis, Y., Kiayias, A., Malkin, T. (eds.) PKC 2006. LNCS, vol. 3958. Springer, Heidelberg (2006), http://eprint.iacr.org/2005/255

    Chapter  Google Scholar 

  14. Ding, J., Gower, J., Schmidt, D.: Multivariate Public-Key Cryptosystems. In: Advances in Information Security. Springer, Heidelberg (2006)

    Google Scholar 

  15. Ding, J., Schmidt, D.: Cryptanalysis of HFEv and internal perturbation of HFE. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 288–301. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Ding, J., Schmidt, D.: Rainbow, a new multivariable polynomial signature scheme. In: Ioannidis, J., Keromytis, A., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 164–175. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  17. Ding, J., Wolf, C., Yang, B.-Y.: ℓ-invertible cycles for multivariate quadratic public key cryptography. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 266–281. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Ding, J., Yang, B.-Y., Chen, C.-H.O., Chen, M.-S., Cheng, C.-M.: New differential-algebraic attacks and reparametrization of rainbow. In: Bellovin, S.M., Gennaro, R., Keromytis, A., Yung, M. (eds.) ACNS 2008. LNCS, vol. 5037, pp. 242–257. Springer, Heidelberg (2008), http://eprint.iacr.org/2008/108

    Chapter  Google Scholar 

  19. Ding, J., Yang, B.-Y., Dubois, V., Cheng, C.-M., Chen, O.C.-H.: Breaking the symmetry: a way to resist the new differential attack. In: ICALP 2008. LNCS. Springer, Heidelberg (2008), http://eprint.iacr.org/2007/366

    Google Scholar 

  20. Dubois, V., Fouque, P.-A., Shamir, A., Stern, J.: Practical cryptanalysis of SFLASH. In: Menezes, A. (ed.) CRYPTO 2007. LNCS, vol. 4622, pp. 1–12. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  21. Faugère, J.-C.: A new efficient algorithm for computing Gröbner bases (F 4). Journal of Pure and Applied Algebra 139, 61–88 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  22. Faugère, J.-C.: A new efficient algorithm for computing Gröbner bases without reduction to zero (F 5). In: International Symposium on Symbolic and Algebraic Computation — ISSAC 2002, pp. 75–83. ACM Press, New York (2002)

    Chapter  Google Scholar 

  23. Fouque, P.-A., Granboulan, L., Stern, J.: Differential cryptanalysis for multivariate schemes. In: Cramer, R. (ed.) EUROCRYPT 2005. LNCS, vol. 3494, pp. 341–353. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  24. Fouque, P.-A., Macario-Rat, G., Perret, L., Stern, J.: Total break of the ℓIC- signature scheme. In: Public Key Cryptography, pp. 1–17 (2008)

    Google Scholar 

  25. Goubin, L., Courtois, N.T.: Cryptanalysis of the TTM cryptosystem. In: Okamoto, T. (ed.) ASIACRYPT 2000. LNCS, vol. 1976, pp. 44–57. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  26. 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)

    Chapter  Google Scholar 

  27. Kipnis, A., Shamir, A.: Cryptanalysis of the oil and vinegar signature scheme. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 257–266. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  28. Matsumoto, T., Imai, H.: Public quadratic polynomial-tuples for efficient signature verification and message-encryption. In: Günther, C.G. (ed.) EUROCRYPT 1988. LNCS, vol. 330, pp. 419–545. Springer, Heidelberg (1988)

    Chapter  Google Scholar 

  29. Ogura, N., Uchiyama, S.: Remarks on the attack of fouque et al. against the ℓic scheme. Cryptology ePrint Archive, Report 2008/208 (2008), http://eprint.iacr.org/

  30. 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 

  31. Wolf, C., Preneel, B.: Taxonomy of public key schemes based on the problem of multivariate quadratic equations. Cryptology ePrint Archive, Report 2005/077, 64 pages, May 12 (2005), http://eprint.iacr.org/2005/077/

  32. Yang, B.-Y., Chen, J.-M.: 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 

  33. Yang, B.-Y., Chen, J.-M.: 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 

  34. Yang, B.-Y., Chen, J.-M., Chen, Y.-H.: TTS: High-speed signatures on a low-cost smart card. In: Joye, M., Quisquater, J.-J. (eds.) CHES 2004. LNCS, vol. 3156, pp. 371–385. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Chen, A.IT., Chen, CH.O., Chen, MS., Cheng, CM., Yang, BY. (2008). Practical-Sized Instances of Multivariate PKCs: Rainbow, TTS, and ℓIC-Derivatives. In: Buchmann, J., Ding, J. (eds) Post-Quantum Cryptography. PQCrypto 2008. Lecture Notes in Computer Science, vol 5299. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88403-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-88403-3_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88402-6

  • Online ISBN: 978-3-540-88403-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics