Skip to main content

A Practical Multivariate Blind Signature Scheme

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 10322))

Abstract

Multivariate Cryptography is one of the main candidates for creating post-quantum cryptosystems. Especially in the area of digital signatures, there exist many practical and secure multivariate schemes. However, there is a lack of multivariate signature schemes with special properties such as blind, ring and group signatures. In this paper, we propose a generic technique to transform the Rainbow multivariate signature scheme into a blind signature schemes. The resulting scheme satisfies the usual blindness criterion and a one-more-unforgeability criterion adapted to MQ signatures, produces short blind signatures and is very efficient.

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 EPUB and 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

References

  1. Boneh, D., Dagdelen, Ö., Fischlin, M., Lehmann, A., Schaffner, C., Zhandry, M.: Random oracles in a quantum world. In: Lee, D.H., Wang, X. (eds.) ASIACRYPT 2011. LNCS, vol. 7073, pp. 41–69. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-25385-0_3

    Chapter  MATH  Google Scholar 

  2. Chaum, D.: Blind signatures for untraceable payment. In: Proceedings of CRYPTO 1982, pp. 199–203. Plenum Press (1983)

    Google Scholar 

  3. Bogdanov, A., Eisenbarth, T., Rupp, A., Wolf, C.: Time-area optimized public-key engines: \(\cal{MQ}\)-cryptosystems as replacement for elliptic curves? In: Oswald, E., Rohatgi, P. (eds.) CHES 2008. LNCS, vol. 5154, pp. 45–61. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85053-3_4

    Chapter  Google Scholar 

  4. Chen, A.I.-T., Chen, M.-S., Chen, T.-R., Cheng, C.-M., Ding, J., Kuo, E.L.-H., Lee, F.Y.-S., Yang, B.-Y.: SSE implementation of multivariate PKCs on modern x86 CPUs. In: Clavier, C., Gaj, K. (eds.) CHES 2009. LNCS, vol. 5747, pp. 33–48. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04138-9_3

    Chapter  Google Scholar 

  5. Ding, J., Dubois, V., Yang, B.-Y., Chen, O.C.-H., Cheng, C.-M.: Could SFLASH be repaired? In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 691–701. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70583-3_56

    Chapter  Google Scholar 

  6. 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). https://doi.org/10.1007/11496137_12

    Chapter  Google Scholar 

  7. Faugère, J.C.: A new efficient algorithm for computing Gröbner bases (F4). J. Pure Appl. Algebra 139, 61–88 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman and Company, New York (1979)

    MATH  Google Scholar 

  9. Hülsing, A., Rijneveld, J., Samardjiska, S., Schwabe, P.: From 5-pass MQ-based identification to MQ-based signatures. Cryptology ePrint Archive: Report 2016/708

    Google Scholar 

  10. Juels, A., Luby, M., Ostrovsky, R.: Security of blind digital signatures. In: Kaliski, B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 150–164. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0052233

    Chapter  Google Scholar 

  11. Kravitz, D.: Digital Signature Algorithm. US patent 5,231,668, July 1991

    Google Scholar 

  12. 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). https://doi.org/10.1007/3-540-48910-X_15

    Chapter  Google Scholar 

  13. Goodin, D.: NSA preps quantum-resistant algorithms to head off crypto-apocalypse. http://arstechnica.com/security/2015/08/nsa-preps-quantum-resistant-algorithms-to-head-off-crypto-apocolypse/

  14. National Institute of Standards and Technology: Report on post-quantum Cryptography. NISTIR draft 8105. http://csrc.nist.gov/publications/drafts/nistir-8105/nistir_8105_draft.pdf

  15. Patarin, J., Courtois, N., Goubin, L.: QUARTZ, 128-bit long digital signatures. In: Naccache, D. (ed.) CT-RSA 2001. LNCS, vol. 2020, pp. 282–297. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45353-9_21

    Chapter  Google Scholar 

  16. Petzoldt, A., Bulygin, S., Buchmann, J.: Selecting parameters for the rainbow signature scheme. In: Sendrier, N. (ed.) PQCrypto 2010. LNCS, vol. 6061, pp. 218–240. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-12929-2_16

    Chapter  Google Scholar 

  17. Petzoldt, A., Bulygin, S., Buchmann, J.: CyclicRainbow – a multivariate signature scheme with a partially cyclic public key. In: Gong, G., Gupta, K.C. (eds.) INDOCRYPT 2010. LNCS, vol. 6498, pp. 33–48. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17401-8_4

    Chapter  Google Scholar 

  18. Petzoldt, A., Chen, M.-S., Yang, B.-Y., Tao, C., Ding, J.: Design principles for HFEv- based multivariate signature schemes. In: Iwata, T., Cheon, J.H. (eds.) ASIACRYPT 2015. LNCS, vol. 9452, pp. 311–334. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-48797-6_14

    Chapter  Google Scholar 

  19. Rivest, R.L., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)

    Article  MathSciNet  MATH  Google Scholar 

  20. Rückert, M.: Lattice-based blind signatures. In: Abe, M. (ed.) ASIACRYPT 2010. LNCS, vol. 6477, pp. 413–430. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-17373-8_24

    Chapter  Google Scholar 

  21. SageMath, the Sage Mathematics Software System (Version 7.1), The Sage Developers (2016). http://www.sagemath.org

  22. Sakumoto, K., Shirai, T., Hiwatari, H.: Public-key identification schemes based on multivariate quadratic polynomials. In: Rogaway, P. (ed.) CRYPTO 2011. LNCS, vol. 6841, pp. 706–723. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22792-9_40

    Chapter  Google Scholar 

  23. Shor, P.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM J. Comput. 26(5), 1484–1509 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  24. Thomae, E., Wolf, C.: Solving underdetermined systems of multivariate quadratic equations revisited. In: Fischlin, M., Buchmann, J., Manulis, M. (eds.) PKC 2012. LNCS, vol. 7293, pp. 156–171. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-30057-8_10

    Chapter  Google Scholar 

  25. Yasuda, T., Dahan, X., Huang, Y.-J., Takagi, T., Sakurai, K.: MQ challenge: hardness evaluation of solving multivariate quadratic problems. IACR Cryptology ePrint Archive 2015/275 (2015)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the reviewers and the shepherd in particular for their helpful comments. This work was supported in part by the Research Council KU Leuven: C16/15/058. In addition, this work was supported by the European Commission through the Horizon 2020research and innovation programme under grant agreement No H2020-ICT-2014-644371 WITDOM, H2020-ICT-2014-645622 PQCRYPTO and H2020-DS-2014-653497 PANORAMIX, and through the SECURITY programme under FP7-SEC-2013-1-607049 EKSISTENZ. Alan Szepieniec is being supported by a doctoral grant of the Flemish Agency for Innovation and Entrepreneurship (VLAIO, formerly IWT).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alan Szepieniec .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2017 International Financial Cryptography Association

About this paper

Cite this paper

Petzoldt, A., Szepieniec, A., Mohamed, M.S.E. (2017). A Practical Multivariate Blind Signature Scheme. In: Kiayias, A. (eds) Financial Cryptography and Data Security. FC 2017. Lecture Notes in Computer Science(), vol 10322. Springer, Cham. https://doi.org/10.1007/978-3-319-70972-7_25

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-70972-7_25

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-70971-0

  • Online ISBN: 978-3-319-70972-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics