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International Conference on Pairing-Based Cryptography

Pairing 2010: Pairing-Based Cryptography - Pairing 2010 pp 116–135Cite as

Increased Resilience in Threshold Cryptography: Sharing a Secret with Devices That Cannot Store Shares

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Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 6487))

Abstract

Threshold cryptography increases security and resilience by sharing a private cryptographic key over different devices. Many personal devices, however, are not suited for threshold schemes, because they do not offer secure storage, which is needed to store shares of the private key. We present a solution that allows to include devices without them having to store their share. Shares are stored in protected form, possibly externally, which makes our solution suitable for low-cost devices with a factory-embedded key, e.g., car keys and access cards. By using pairings we achieve public verifiability in a wide range of protocols, which removes the need for private channels. We demonstrate how to modify existing discrete-log based threshold schemes to work in this setting. Our core result is a new publicly verifiable distributed key generation protocol that is provably secure against static adversaries and does not require all devices to be present.

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References

  1. Abe, M., Fehr, S.: Adaptively secure Feldman VSS and applications to universally-composable threshold cryptography. In: Franklin, M.K. (ed.) CRYPTO 2004. LNCS, vol. 3152, pp. 317–334. Springer, Heidelberg (2004)

    Google Scholar 

  2. Bao, F., Deng, R.H., Zhu, H.: Variations of Diffie-Hellman problem. In: Qing, S., Gollmann, D., Zhou, J. (eds.) ICICS 2003. LNCS, vol. 2836, pp. 301–312. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  3. Beaver, D., Haber, S.: Cryptographic protocols provably secure against dynamic adversaries. In: Rueppel, R.A. (ed.) EUROCRYPT 1992. LNCS, vol. 658, pp. 307–323. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  4. Brown, D.R.L.: Generic groups, collision resistance, and ECDSA. Designs, Codes and Cryptography 35(1), 119–152 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  5. Canetti, R.: Universally composable security: A new paradigm for cryptographic protocols. In: FOCS 2001, pp. 136–145. IEEE Computer Society, Los Alamitos (2001)

    Google Scholar 

  6. Canetti, R., Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Adaptive security for threshold cryptosystems. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 98–115. Springer, Heidelberg (1999)

    Google Scholar 

  7. Cramer, R., Shoup, V.: A practical public key cryptosystem provably secure against adaptive chosen ciphertext attack. In: Krawczyk, H. (ed.) CRYPTO 1998. LNCS, vol. 1462, pp. 13–25. Springer, Heidelberg (1998)

    Google Scholar 

  8. Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: FOCS 1987, pp. 427–437. IEEE Computer Society, Los Alamitos (1987)

    Google Scholar 

  9. Fouque, P.A., Stern, J.: One round threshold discrete-log key generation without private channels. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 300–316. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  10. Frankel, Y., MacKenzie, P.D., Yung, M.: Adaptively-secure distributed public-key systems. In: Nešetřil, J. (ed.) ESA 1999. LNCS, vol. 1643, pp. 4–27. Springer, Heidelberg (1999)

    Google Scholar 

  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. Galbraith, S., Hess, F., Vercauteren, F.: Aspects of pairing inversion. IEEE Transactions on Information Theory 54(12), 5719–5728 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  13. Galbraith, S., Paterson, K., Smart, N.: Pairings for cryptographers. Cryptology ePrint Archive, Report 2006/165 (2006), http://eprint.iacr.org/

  14. Gamal, T.E.: A public key cryptosystem and a signature scheme based on discrete logarithms. In: Blakely, G.R., Chaum, D. (eds.) CRYPTO 1984. LNCS, vol. 196, pp. 10–18. Springer, Heidelberg (1985)

    Google Scholar 

  15. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 295–310. Springer, Heidelberg (1999)

    Google Scholar 

  16. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure applications of Pedersen’s distributed key generation protocol. In: Joye, M. (ed.) CT-RSA 2003. LNCS, vol. 2612, pp. 373–390. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  17. Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Secure distributed key generation for discrete-log based cryptosystems. J. of Cryptology 20(1), 51–83 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  18. Heidarvand, S., Villar, J.L.: Public verifiability from pairings in secret sharing schemes. In: Avanzi, R., Keliher, L., Sica, F. (eds.) SAC 2008. LNCS, vol. 5381, pp. 294–308. Springer, Heidelberg (2009)

    Google Scholar 

  19. Jarecki, S., Lysyanskaya, A.: Adaptively secure threshold cryptography: Introducing concurrency, removing erasures. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 221–242. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  20. Malone-Lee, J., Smart, N.P.: Modifications of ECDSA. In: Nyberg, K., Heys, H.M. (eds.) SAC 2002. LNCS, vol. 2595, pp. 1–12. Springer, Heidelberg (2002)

    Google Scholar 

  21. Mao, W.: Modern Cryptography: Theory and Practice. Prentice Hall, Englewood Cliffs (2003)

    Google Scholar 

  22. Pedersen, T.P.: A threshold cryptosystem without a trusted party (extended abstract). In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991)

    Google Scholar 

  23. Pedersen, T.P.: Non-interactive and information-theoretic secure verifiable secret sharing. In: Feigenbaum, J. (ed.) CRYPTO 1991. LNCS, vol. 576, pp. 129–140. Springer, Heidelberg (1992)

    Google Scholar 

  24. Pointcheval, D., Stern, J.: Security arguments for digital signatures and blind signatures. J. of Cryptology 13(3), 361–396 (2000)

    Article  MATH  Google Scholar 

  25. Schnorr, C.P.: Efficient identification and signatures for smart cards. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 239–252. Springer, Heidelberg (1989)

    Google Scholar 

  26. Schoenmakers, B.: A simple publicly verifiable secret sharing scheme and its application to electronic voting. In: Wiener, M.J. (ed.) CRYPTO 1999. LNCS, vol. 1666, pp. 148–164. Springer, Heidelberg (1999)

    Google Scholar 

  27. Shamir, A.: How to share a secret. Comm. of the ACM 22(11), 612–613 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  28. Smart, N.P., Vercauteren, F.: On computable isomorphisms in efficient asymmetric pairing-based systems. Discrete Applied Mathematics 155(4), 538–547 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  29. Stadler, M.: Publicly verifiable secret sharing. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 190–199. Springer, Heidelberg (1996)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Electrical Engineering, COSIC Katholieke Universiteit Leuven and IBBT, Belgium

    Koen Simoens, Roel Peeters & Bart Preneel

Authors
  1. Koen Simoens
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  2. Roel Peeters
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  3. Bart Preneel
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Editor information

Editors and Affiliations

  1. Technicolor, Security and Content Protection Labs, 1 avenue de Belle Fontaine, 35576, Cesson-Sévigné Cedex, France

    Marc Joye

  2. Japan Advanced Institute of Science and Technology (JAIST), 923-1292, Nomi, Ishikawa, Japan

    Atsuko Miyaji

  3. National Institute of Advanced Industrial Science and Technoloy (AIST), 101-0021, Tokyo, Japan

    Akira Otsuka

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Simoens, K., Peeters, R., Preneel, B. (2010). Increased Resilience in Threshold Cryptography: Sharing a Secret with Devices That Cannot Store Shares. In: Joye, M., Miyaji, A., Otsuka, A. (eds) Pairing-Based Cryptography - Pairing 2010. Pairing 2010. Lecture Notes in Computer Science, vol 6487. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17455-1_8

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  • DOI: https://doi.org/10.1007/978-3-642-17455-1_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-17454-4

  • Online ISBN: 978-3-642-17455-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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