Abstract
We present protocols for threshold decryption and threshold key generation in the GBD public-key cryptosystem in the “honest-but-curious” setting. These allow GBD computations to be performed in a distributed manner during both key generation and decryption, without revealing the private key to any party. GBD threshold decryption is similar to El-Gamal threshold decryption. GBD threshold key generation is based on adaptations of protocols for RSA key generation by Boneh and Franklin, and Catalano et al, and includes a new protocol for efficiently computing the inverse of a shared secret modulo another shared secret. We also show an application of GBD threshold cryptography to RSA key recovery, and point out two open problems in this application.
This work was partially funded by Australian Research Council Linkage Project Grant LP0347128.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
González-Nieto, J.M., Boyd, C., Dawson, E.: A public key cryptosystem based on a subgroup membership problem. In: Qing, S., Okamoto, T., Zhou, J. (eds.) ICICS 2001. LNCS, vol. 2229, pp. 352–363. Springer, Heidelberg (2001)
González-Nieto, J.M., Boyd, C., Dawson, E.: A public key cryptosystem based on a subgroup membership problem. Designs, Codes and Cryptography (2004) (accepted for publication)
Gemmell, P.: An introduction to threshold cryptography. CryptoBytes 2(3), 7–12 (1997)
Desmedt, Y., Frankel, Y.: Threshold cryptosystems. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 307–315. Springer, Heidelberg (1990)
De Santis, A., Desmedt, Y., Frankel, Y., Yung, M.: How to share a function securely. In: STOC 1994, pp. 522–533 (1994)
Pedersen, T.: A threshold cryptosystem without a trusted party. In: Davies, D.W. (ed.) EUROCRYPT 1991. LNCS, vol. 547, pp. 522–526. Springer, Heidelberg (1991)
Boneh, D., Franklin, M.: Efficient generation of shared RSA keys. J. ACM 48(4), 702–722 (2001)
Frankel, Y., MacKenzie, P., Yung, M.: Robust efficient distributed RSA-key generation. In: STOC 1998, pp. 663–672. ACM Press, New York (1998)
Brown, J., Dawson, E., González-Nieto, J.M.: Implementation of the GBD cryptosystem. In: Cryptographic Algorithms and their Uses, pp. 94–109. QUT Publications (2004)
Catalano, D., Gennaro, R., Halev, S.: Computing inverses over a shared secret modulus. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 190–206. Springer, Heidelberg (2000)
Algesheimer, J., Camenisch, J., Shoup, V.: Efficient computation modulo a shared secret with application to the generation of shared safe-prime products. In: Yung, M. (ed.) CRYPTO 2002. LNCS, vol. 2442, pp. 417–432. Springer, Heidelberg (2002)
Steketee, C., Brown, J., González Nieto, J., Montague, P.: GBD threshold cryptography with an application to RSA key recovery (2005), http://eprints.qut.edu.au/
Canetti, R.: Security and composition of multiparty cryptographic protocols. J. Cryptology 13(1), 143–202 (2000)
Malkin, M., Wu, T., Boneh, D.: Experimenting with shared generation of RSA keys. In: SNDSS 1999, pp. 43–56 (1999)
Paillier, P., Yung, M.: Self-escrowed public-key infrastructures. In: Song, J.S. (ed.) ICISC 1999. LNCS, vol. 1787, pp. 249–261. Springer, Heidelberg (2000)
Young, A., Yung, M.: Auto-recoverable and auto-certifiable cryptosystems. In: Nyberg, K. (ed.) EUROCRYPT 1998. LNCS, vol. 1403, pp. 17–31. Springer, Heidelberg (1998)
Micali, S.: Fair public-key cryptosystems. In: Brickell, E.F. (ed.) CRYPTO 1992. LNCS, vol. 740, pp. 113–138. Springer, Heidelberg (1993)
Paillier, P.: Public-key cryptosystems based on composite degree residuosity classes. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 223–238. Springer, Heidelberg (1999)
Fouque, P., 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)
Damgard, I., Jurik, M.: A generalisation, a simplification and some applications of paillier’s probabilistic public-key system. In: Kim, K.-c. (ed.) PKC 2001. LNCS, vol. 1992, pp. 119–136. Springer, Heidelberg (2001)
González-Nieto, J.M., Viswanathan, K., Boyd, C., Dawson, E.: A self-escrowed integer factorisation based public key infrastructure. In: VII Spanish Meeting on Cryptology and Information Security, Oviedo, Spain, pp. 315–328. Universidad de Oviedo (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Steketee, C., Brown, J., González Nieto, J.M., Montague, P. (2005). GBD Threshold Cryptography with an Application to RSA Key Recovery. In: Boyd, C., González Nieto, J.M. (eds) Information Security and Privacy. ACISP 2005. Lecture Notes in Computer Science, vol 3574. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11506157_33
Download citation
DOI: https://doi.org/10.1007/11506157_33
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26547-4
Online ISBN: 978-3-540-31684-8
eBook Packages: Computer ScienceComputer Science (R0)