Skip to main content
SpringerLink
Log in

Formal and Precise Analysis of Soundness of Several Shuffling Schemes

  • Conference paper
Provable Security (ProvSec 2010)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6402))

Included in the following conference series:

  • 467 Accesses

Abstract

Some of the most efficient shuffling schemes employ the same main idea to prove validity of shuffling. However, the principle behind the idea has not been explained in a completely formal and precise way. So formal guarantee of soundness of the shuffling schemes is not complete. Especially, it is unknown exactly how large the probability of failure of soundness is and exactly how strong soundness is. In this paper, why the proof mechanism guarantees validity of shuffling is formally proved to provide a formal guarantee of soundness of those shuffling schemes. Especially, the exact upper bound of the probability of failure of soundness is given to convincingly ensure soundness. Although we do not doubt soundness of most of the shuffling schemes, a formal and precise proof of their soundness is still valuable as it strengthens security guarantee of the schemes and removes a potential obstacle for their application to critical environments requiring formally guaranteed and measurable soundness. Moreover, the formal and precise proof shows that some shuffling scheme has serious problem in soundness.

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

Access this chapter

Log in via an institution
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abe, M.: Mix-networks on permutation networks. In: Lam, K.-Y., Okamoto, E., Xing, C. (eds.) ASIACRYPT 1999. LNCS, vol. 1716, pp. 258–273. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  2. Abe, M., Hoshino, F.: Remarks on mix-network based on permutation networks. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 317–324. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  3. Chaum, D.: Untraceable electronic mail, return address and digital pseudonym. Communications of the ACM 24(2), 84–88 (1981)

    Article  Google Scholar 

  4. Chaum, D., Pedersen, T.: Wallet databases with observers. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 89–105. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  5. Fouque, P.-A., Poupard, G., Stern, J.: Sharing decryption in the context of voting or lotteries. In: Frankel, Y. (ed.) FC 2000. LNCS, vol. 1962, pp. 90–104. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  6. Furukawa, J., Sako, K.: An efficient scheme for proving a shuffle. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 368–387. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  7. Gabber, E., Gibbons, P.B., Matias, Y., Mayer, A.: How to make personalized web browsing simple, secure, and anonymous. In: Luby, M., Rolim, J.D.P., Serna, M. (eds.) FC 1997. LNCS, vol. 1318, pp. 17–31. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  8. Groth, J., Ishai, Y.: Sub-linear zero-knowledge argument for correctness of a shuffle. In: Smart, N.P. (ed.) EUROCRYPT 2008. LNCS, vol. 4965, pp. 379–396. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  9. Groth, J., Lu, S.: Verifiable shuffle of large size ciphertexts. In: Okamoto, T., Wang, X. (eds.) PKC 2007. LNCS, vol. 4450, pp. 377–392. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  10. Groth, J.: A verifiable secret shuffle of homomorphic encryptions. In: Desmedt, Y.G. (ed.) PKC 2003. LNCS, vol. 2567, pp. 145–160. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  11. Guillou, L.C., Quisquater, J.J.: A “paradoxical” identity-based signature scheme resulting from zero-knowledge. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 216–231. Springer, Heidelberg (1990)

    Chapter  Google Scholar 

  12. Furukawa, J.: Efficient and verifiable shuffling and shuffle-decryption. IEICE Transactions 88-A(1), 172–188 (2005)

    Article  Google Scholar 

  13. Andrew Neff, C.: A verifiable secret shuffle and its application to e-voting. In: ACM Conference on Computer and Communications Security 2001, pp. 116–125 (2001)

    Google Scholar 

  14. Andrew Neff, C.: Verifiable mixing (shuffling) of elgamal pairs (2004), http://theory.lcs.mit.edu/~rivest/voting/papers/Neff-2004-04-21-ElGamalShuffles.pdf

  15. Okamoto, T., Uchiyama, S.: A new public-key encyptosystem as secure as factoring. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 308–318. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  16. Paillier, P.: Public key cryptosystem based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  17. Peng, K.: A secure and efficient batched shuffling scheme. In: Qing, S., Imai, H., Wang, G. (eds.) ICICS 2007. LNCS, vol. 4861, Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  18. Peng, K., Bao, F.: An shuffling scheme with strict and strong security. To Appear at SecureWare 2010 (2010)

    Google Scholar 

  19. Peng, K., Boyd, C., Dawson, E.: Simple and efficient shuffling with provable correctness and ZK privacy. In: Shoup, V. (ed.) CRYPTO 2005. LNCS, vol. 3621, pp. 188–204. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  20. Peng, K., Boyd, C., Dawson, E., Viswanathan, K.: A correct, private and efficient mix network. In: Bao, F., Deng, R., Zhou, J. (eds.) PKC 2004. LNCS, vol. 2947, pp. 439–454. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  21. Wikstrom, D.: A sender verifiable mix-net and a new proof of a shuffle. In: Roy, B. (ed.) ASIACRYPT 2005. LNCS, vol. 3788, pp. 273–292. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Infocomm Research, Singapore

    Kun Peng & Feng Bao

Authors
  1. Kun Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Feng Bao
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Information Science and Technology, Jalan Ayer Keroh Lama, Multimedia University, 75450, Malacca, Malaysia

    Swee-Huay Heng

  2. Department of Computer and Information Sciences, Ibaraki University, 4-12-1 Nakanarusawa, 316-8511, Hitachi, Ibaraki, Japan

    Kaoru Kurosawa

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Peng, K., Bao, F. (2010). Formal and Precise Analysis of Soundness of Several Shuffling Schemes. In: Heng, SH., Kurosawa, K. (eds) Provable Security. ProvSec 2010. Lecture Notes in Computer Science, vol 6402. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16280-0_9

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-16280-0_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-16279-4

  • Online ISBN: 978-3-642-16280-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation