Rainbow, a New Multivariable Polynomial Signature Scheme

  • Jintai Ding
  • Dieter Schmidt
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3531)

Abstract

Balanced Oil and Vinegar signature schemes and the unbalanced Oil and Vinegar signature schemes are public key signature schemes based on multivariable polynomials. In this paper, we suggest a new signature scheme, which is a generalization of the Oil-Vinegar construction to improve the efficiency of the unbalanced Oil and Vinegar signature scheme. The basic idea can be described as a construction of multi-layer Oil-Vinegar construction and its generalization. We call our system a Rainbow signature scheme. We propose and implement a practical scheme, which works better than Sflash\(^{v_2}\), in particular, in terms of signature generating time.

Keywords

public-key multivariable quadratic polynomials Oil and Vinegar 

References

  1. [ACDG03]
    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)CrossRefGoogle Scholar
  2. [Cou01]
    Courtois, N.T.: The security of hidden field equations (HFE). In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 266–281. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. [CSV97]
    Coppersmith, D., Stern, J., Vaudenay, S.: The security of the birational permutation signature schemes. J. Cryptology 10(3), 207–221 (1997)MATHCrossRefMathSciNetGoogle Scholar
  4. [D09]
    Dickson, L.E.: Definite forms in a finite field. Trans. Amer. Math. Soc. 10, 109–122 (1909)MATHMathSciNetCrossRefGoogle Scholar
  5. [DY04]
    Ding, J., Yin, Z.: Cryptanalysis of TTS and Tame–like signature schemes. In: Third International Workshop on Applied Public Key Infrastructures. Springer, Heidelberg (2004)Google Scholar
  6. [KPG99]
    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
  7. [KS99]
    Kipnis, A., Shamir, A.: Cryptanalysis of the HFE public key cryptosystem by relinearization. In: Wiener, M. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 19–30. Springer, Heidelberg (1999)Google Scholar
  8. [MI88]
    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. 419–453. Springer, Heidelberg (1988)Google Scholar
  9. [Pat95]
    Patarin, J.: Cryptanalysis of the Matsumoto and Imai public key scheme of Eurocrypt 1988. In: Coppersmith, D. (ed.) CRYPTO 1995. LNCS, vol. 963, pp. 248–261. Springer, Heidelberg (1995)Google Scholar
  10. [Pat96]
    Patarin, J.: Hidden field equations (HFE) and isomorphism of polynomials (IP): Two new families of asymmetric algorithms. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 33–48. Springer, Heidelberg (1996)Google Scholar
  11. [PCG01]
    Patarin, J., Courtois, N., Goubin, L.: Flash, a fast multivariate signature algorithm. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 298–307. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  12. [PGC98]
    Patarin, J., Goubin, L., Courtois, N.: C∗ − + and HM: variations around two schemes of T. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 35–50. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  13. [Sha98]
    Shamir, A.: Efficient signature schemes based on birational permutations. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 257–266. Springer, Heidelberg (1998)Google Scholar
  14. [WHLCY]
    Wang, L.-C., Hu, Y.-H., Lai, F., Chou, C.-Y., Yang, B.-Y.: Tractable rational map signature. In: Vaudenay, S. (ed.) PKC 2005. LNCS, vol. 3386, pp. 244–257. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  15. [WBP]
    Wolf, C., Braeken, A., Preneel, B.: Efficient cryptanalysis of RSE(2)PKC and RSSE(2)PKC, http://eprint.iacr.org/2004/237
  16. [YC03]
    Yang, B., Chen, J.: A more secure and efficacious TTS signature scheme. In: Lim, J.-I., Lee, D.-H. (eds.) ICISC 2003. B. Yang and J. Chen, vol. 2971. Springer, Heidelberg (2004), http://eprint.iacr.org/2003/160 Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Jintai Ding
    • 1
  • Dieter Schmidt
    • 2
  1. 1.Department of Mathematical SciencesUniversity of CincinnatiCincinnatiUSA
  2. 2.Department of Electrical & Computer Engineering and Computer ScienceUniversity of CincinnatiCincinnatiUSA

Personalised recommendations