Skip to main content
SpringerLink
Log in
Book cover

IMA International Conference on Cryptography and Coding

IMACC 2011: Cryptography and Coding pp 97–111Cite as

A Secure and Efficient Proof of Integer in an Interval Range

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 7089))

Abstract

A new range proof scheme is proposed in this paper. We study a related technique, range test, and show how its idea can be used to design a more advanced range proof technique. The main advantage of the new range proof technique over the existing solutions is that it achieves the best trade-off between soundness, privacy and efficiency. Is achieves information-theoretic and absolutely precise soundness and thus is more secure than those range proof schemes with conditional soundness. It achieves formally provable zero knowledge in privacy and thus is more secure than those range proof schemes without formally proven zero knowledge. It only needs a small constant number of computations and employs normal-length parameters and thus is more efficient than those range proof schemes needing super-linear cost or extra large integers.

This is a preview of subscription content, 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bellare, M., Garay, J.A., Rabin, T.: Fast Batch Verification for Modular Exponentiation and Digital Signatures. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 236–250. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  2. Boudot, F., Traore, J.: Efficient Publicly Verifiable Secret Sharing Schemes with Fast or Delayed Recovery. In: Varadharajan, V., Mu, Y. (eds.) ICICS 1999. LNCS, vol. 1726, pp. 87–102. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  3. Boudot, F.: Efficient Proofs that a Committed Number Lies in an Interval. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 431–444. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  4. Camenisch, J.L., Chaabouni, R., Shelat, A.: Efficient Protocols for Set Membership and Range Proofs. In: Pieprzyk, J. (ed.) ASIACRYPT 2008. LNCS, vol. 5350, pp. 234–252. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  5. Camenisch, J.L., Michels, M.: A Group Signature Scheme with Improved Efficiency. In: Ohta, K., Pei, D. (eds.) ASIACRYPT 1998. LNCS, vol. 1514, pp. 160–174. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  6. Chaabouni, R., Lipmaa, H., Shelat, A.: Additive Combinatorics and Discrete Logarithm Based Range Protocols. In: Steinfeld, R., Hawkes, P. (eds.) ACISP 2010. LNCS, vol. 6168, pp. 336–351. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

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

    Chapter  Google Scholar 

  8. Chida, K., Yamamoto, G.: Batch processing for proofs of partial knowledge and its applications. IEICE Trans. Fundamentals E91CA(1), 150–159 (2008)

    Article  Google Scholar 

  9. Cramer, R., Damgård, I.B., Schoenmakers, B.: Proofs of Partial Knowledge and Simplified Design of Witness Hiding Protocols. In: Desmedt, Y.G. (ed.) CRYPTO 1994. LNCS, vol. 839, pp. 174–187. Springer, Heidelberg (1994)

    Google Scholar 

  10. Damgård, I., Cramer, R.: On ∑-protocols. Cryptologic Protocol Theory (2002), http://www.daimi.au.dk/~ivan/Sigma.ps

  11. Fujisaki, E., Okamoto, T.: A Practical and Provably Secure Scheme for Publicly Verifiable Secret Sharing and its Applications. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 32–46. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  12. Groth, J.: Non-Interactive Zero-Knowledge Arguments for Voting. In: Ioannidis, J., Keromytis, A.D., Yung, M. (eds.) ACNS 2005. LNCS, vol. 3531, pp. 467–482. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  13. Lee, B., Kim, K.: Receipt-free electronic voting through collaboration of voter and honest verifier. In: JW-ISC 2000, pp. 101–108 (2000)

    Google Scholar 

  14. Lee, B., Kim, K.: Receipt-Free Electronic Voting Scheme with a Tamper-Resistant Randomizer. In: Lee, P.J., Lim, C.H. (eds.) ICISC 2002. LNCS, vol. 2587, pp. 389–406. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  15. Lipmaa, H.: On Diophantine Complexity and Statistical Zero-Knowledge Arguments. In: Laih, C.-S. (ed.) ASIACRYPT 2003. LNCS, vol. 2894, pp. 398–415. Springer, Heidelberg (2003)

    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., Bao, F.: Batch ZK Proof and Verification of or Logic. In: Yung, M., Liu, P., Lin, D. (eds.) Inscrypt 2008. LNCS, vol. 5487, pp. 141–156. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  18. Peng, K., Bao, F.: Batch Range Proof for Practical Small Ranges. In: Bernstein, D.J., Lange, T. (eds.) AFRICACRYPT 2010. LNCS, vol. 6055, pp. 114–130. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  19. Peng, K., Bao, F., Dawson, E.: Correct, private, flexible and efficient range test. Journal of Researchand Practice in Information Technology 40(4), 275–291 (2008)

    Google Scholar 

  20. Poupard, G., Stern, J.: Fair Encryption of RSA Keys. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 172–189. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  21. Schnorr, C.: Efficient signature generation by smart cards. Journal of Cryptology 4, 161–174 (1991)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute For Inforcomm Research, Singapore

    Kun Peng

Authors
  1. Kun Peng
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Hewlett-Packard Laboratories, UK

    Liqun Chen

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Peng, K. (2011). A Secure and Efficient Proof of Integer in an Interval Range. In: Chen, L. (eds) Cryptography and Coding. IMACC 2011. Lecture Notes in Computer Science, vol 7089. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25516-8_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-25516-8_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-25515-1

  • Online ISBN: 978-3-642-25516-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation