Advertisement

Forward-Secure Signatures with Fast Key Update

  • Anton Kozlov
  • Leonid Reyzin
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2576)

Abstract

In regular digital signatures, once the secret key is compromised, all signatures, even those that were issued by the honest signer before the compromise, will not be trustworthy any more. Forward-secure signatures have been proposed to address this major shortcoming. We present a new forward-secure signature scheme, called KREUS, with several advantages. It has the most efficient Key Update of all known schemes, requiring just a single modular squaring. Our scheme thus enables more frequent Key Update and hence allows shorter time periods, enhancing security: fewer signatures might become invalid as a result of key compromise. In addition, the on-line component of Signing is also very efficient, consisting of a single multiplication. We precisely analyze the total signer costs and show that they are lower when the number of signatures per time period is small; the advantage of our scheme increases considerably as the number of time periods grows.

Our scheme’s security relies on the Strong-RSA assumption and the random-oracle-based Fiat-Shamir transform.

Keywords

Signature Scheme Random Oracle Discrete Logarithm Security Parameter Modular Multiplication 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AABN02.
    Jee Hea An, Michel Abdalla, Mihir Bellare, and Chanathip Namprempre. From identification to signatures via the Fiat-Samir transform: Minimizing assumptions for security and forward-security. In Knudsen [Knu02].Google Scholar
  2. ACJT00.
    Giuseppe Ateniese, Jan Camenisch, Marc Joye, and Gene Tsudik. A practical and provably secure coalition-resistant group signature scheme. In Mihir Bellare, editor, Advances in Cryptology-CRYPTO 2000, volume 1880 of Lecture Notes in Computer Science, pages 255–270. Springer-Verlag, 2000.Google Scholar
  3. And97.
    Ross Anderson. Invited lecture. In Fourth Annual Conference on Computer and Communications Security. ACM, 1997. Summary appears in [And01].Google Scholar
  4. And01.
    Ross Anderson. Two remarks on public key cryptology. http://www.cl.cam.ac.uk/users/rja14/, 2001.
  5. AR00.
    Michel Abdalla and Leonid Reyzin. A new forward-secure digital signature scheme. In Tatsuaki Okamoto, editor, Advances in Cryptology-ASIACRYPT 2000, volume 1976 of Lecture Notes in Computer Science.Google Scholar
  6. BG92.
    Mihir Bellare and Oded Goldreich. On defining proofs of knowledge. In Ernest F. Brickell, editor, Advances in Cryptology-CRYPTO’ 92, volume 740 of Lecture Notes in Computer Science, pages 390–420. Springer-Verlag, 1993, 16–20 August 1992.Google Scholar
  7. BM99.
    Mihir Bellare and Sara Miner. A forward-secure digital signature scheme. In Michael Wiener, editor, Advances in Cryptology-CRYPTO’ 99, volume 1666 of Lecture Notes in Computer Science, pages 431–448. Springer-Verlag, 15–19 August 1999.Google Scholar
  8. BP97.
    Niko Barić and Birgit Pfitzmann. Collision-free accumulators and failstop signature schemes without trees. In Walter Fumy, editor, Advances in Cryptology-EUROCRYPT 97, volume 1233 of Lecture Notes in Computer Science, pages 480–494. Springer-Verlag, 11–15 May 1997.Google Scholar
  9. BR93.
    Mihir Bellare and Phillip Rogaway. Random oracles are practical: A paradigm for designing efficient protocols. In Proceedings of the 1st ACM Conference on Computer and Communication Security, pages 62–73, November 1993.Google Scholar
  10. CJ02.
    Don Coppersmith and Markus Jakobsson. Almost optimal hash sequence traversal. In 6th International Financial Cryptography Conference, 2002.Google Scholar
  11. CM98.
    Jan Camenisch and Markus Michels. A group signature scheme based on an RSA-variant. Technical Report RS-98-27, BRICS, University of Aarhus, November 1998.Google Scholar
  12. CS00.
    Ronald Cramer and Victor Shoup. Signature schemes based on the strong RSA assumption. ACM Transactions on Information and System Security, 3(3):161–185, 2000.CrossRefGoogle Scholar
  13. Dam90.
    I. B. Damgård, editor. Advances in Cryptology-EUROCRYPT 90, volume 473 of Lecture Notes in Computer Science. Springer-Verlag, 1991.zbMATHGoogle Scholar
  14. FO97.
    Eiichiro Fujisaki and Tatsuaki Okamoto. Statistical zero knowledge protocols to prove modular polynomial relations. In Burton S. Kaliski Jr., editor, Advances in Cryptology-CRYPTO’ 97, volume 1294 of Lecture Notes in Computer Science, pages 16–30. Springer-Verlag, 17–21 August 1997.CrossRefGoogle Scholar
  15. FS86.
    Amos Fiat and Adi Shamir. How to prove yourself: Practical solutions to identification and signature problems. In Andrew M. Odlyzko, editor, Advances in Cryptology-CRYPTO’ 86, volume 263 of Lecture Notes in Computer Science, pages 186–194. Springer-Verlag, 1987, 11–15 August 1986.Google Scholar
  16. Gir90.
    Marc Girault. An identity-based identification scheme based on discrete logarithms modulo a composite number. In [Dam90], pages 481–486.Google Scholar
  17. Gir91.
    Marc Girault. Self-certified public keys. In D. W. Davies, editor, Advances in Cryptology-EUROCRYPT 91, volume 547 of Lecture Notes in Computer Science, pages 490–497. Springer-Verlag, 8–11 April 1991.Google Scholar
  18. GMR88.
    Shafi Goldwasser, Silvio Micali, and Ronald L. Rivest. A digital signature scheme secure against adaptive chosen-message attacks. SIAM Journal on Computing, 17(2):281–308, April 1988.zbMATHCrossRefMathSciNetGoogle Scholar
  19. GQ88.
    Louis Claude Guillou and Jean-Jacques Quisquater. A “paradoxical” indentity-based signature scheme resulting from zero-knowledge. In Shafi Goldwasser, editor, Advances in Cryptology-CRYPTO’ 88, volume 403 of Lecture Notes in Computer Science, pages 216–231. Springer-Verlag, 1990.Google Scholar
  20. IR01.
    Gene Itkis and Leonid Reyzin. Forward-secure signatures with optimal signing and verifying. In Joe Kilian, editor, Advances in Cryptology-CRYPTO 2001, volume 2139 of Lecture Notes in Computer Science, 2001.CrossRefGoogle Scholar
  21. IR02.
    Gene Itkis and Leonid Reyzin. Forward-secure signatures with optimal signing and verifying. Cryptobytes, 5(2), 2002.Google Scholar
  22. Jak02.
    Markus Jakobsson. Fractal hash sequence representation and traversal. In 2002 IEEE International Symposium on Information Theory, 2002.Google Scholar
  23. Knu02.
    Lars Knudsen, editor. Advances in Cryptology-EUROCRYPT 2002, volume 2332 of Lecture Notes in Computer Science. Springer-Verlag, 2002.zbMATHGoogle Scholar
  24. Kra00.
    Hugo Krawczyk. Simple forward-secure signatures from any signature scheme. In Seventh ACM Conference on Computer and Communication Security. ACM, November 1–4 2000.Google Scholar
  25. Mau96.
    Ueli Maurer, editor. Advances in Cryptology-EUROCRYPT 96, volume 1070 of Lecture Notes in Computer Science. Springer-Verlag, 1996.zbMATHGoogle Scholar
  26. MMM02.
    Tal Malkin, Daniele Micciancio, and Sara Miner. Efficient generic forwardsecure signatures with an unbounded number of time periods. In [Knu02].Google Scholar
  27. OS90.
    Heidroon Ong and Claus P. Schnorr. Fast signature generation with a Fiat Shamir-like scheme. In Damgård [Dam90], pages 432–440.Google Scholar
  28. PS96.
    David Pointcheval and Jacques Stern. Security proofs for signature schemes. In Maurer [Mau96], pages 387–398.Google Scholar
  29. PS98.
    Guillaume Poupard and Jacques Stern. Security analysis of a practical “on the fly” authentication and signature generation. In Nyberg, editor, Advances in Cryptology-EUROCRYPT 98, volume 1403 of LNCS.Google Scholar
  30. Sch91.
    Claus-Peter Schnorr. Efficient signature generation by smart cards. Journal of Cryptology, 4(3):161–174, 1991.Google Scholar
  31. Sha83.
    Adi Shamir. On the generation of cryptographically strong pseudorandom sequences. ACM Transactions on Computer Systems, 1(1):38–44, 1983.CrossRefMathSciNetGoogle Scholar
  32. Sho96.
    Victor Shoup. On the security of a practical identification scheme. In Maurer [Mau96], pages 344–353.Google Scholar
  33. Son01.
    Dawn Xiaodong Song. Practical forward secure group signature schemes. In Eighth ACM Conference on Computer and Communication Security, 2001.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Anton Kozlov
    • 1
  • Leonid Reyzin
    • 1
  1. 1.Boston University Computer ScienceBostonUSA

Personalised recommendations