Abstract
In a threshold RSA signature scheme, dishonest participants can disrupt signature generation by submitting junk instead of their partial signatures. A threshold signature system is robust if it allows generation of correct signatures for a group of t honest participants, and in the presence of malicious participants. The purpose of this paper is two-fold. First we show that a robust (t, n) threshold RSA signature scheme, proposed by Rabin in Crypto’98, lacks an essential property of (t, n) threshold schemes and allows an adversary to forge signatures. Then we propose a new approach to the construction of t-robust (t, n) threshold RSA signature scheme which can be seen as the dual to Rabin’s approach. We discuss the efficiency of our system and show that when t is small (compared to n) our scheme is much more efficient than other existing schemes.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Alon, N., Naor, M.: Derandomization. witnesses for Boolean matrix multiplication and construction of perfect hash functions (1996)
Atici, M., Magliveras, S.S., Stinson, D.R., Wei, W.D.: Some Recursive Constructions for Perfect Hash Families. Journal of Combinatorial l Designs 4, 353–363 (1996)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness Theorems for Non cryptographic Fault-Tolerant Distributed Computations. In: Proc. 20th Annual Symp. on the Theory of Computing, pp. 1–10. ACM, New York (1988)
Blackburn, S.R.: Combinatorics and Threshold Cryptology, in Combinatorial Designs and their Applications(Pitman Research Notes in Mathematics) (to appear)
Blackburn, S.R., Blake-Wilson, S., Burmester, M., Galbraith, S.: Shared generation of shared RSA keys. Tech. Report CORR98-19, University of Waterloo
Blackburn, S.R., Burmester, M., Desmedt, Y., Wild, P.R.: Efficient multiplicative sharing schemes. In: Maurer, U.M. (ed.) EUROCRYPT 1996. LNCS, vol. 1070, pp. 107–118. Springer, Heidelberg (1996)
Blum, M., Kannan, S.: Program correctness checking and the design of programs that check their work. In: Proc. of the 21st ACM Symposium on Theory of Computing (1989)
Boneh, D., Franklin, M.: Efficient generation of shared RSA keys. In: Kaliski Jr., B.S. (ed.) CRYPTO 1997. LNCS, vol. 1294, pp. 425–439. Springer, Heidelberg (1997)
Boyd, C.: Digital multisignatures. In: Beker, Piper (eds.) Cryptography and coding, pp. 241–246. Clarendon Press (1989)
Brickell, E., Stinson, D.: The Detection of Cheaters in Threshold Schemes. In: Goldwasser, S. (ed.) CRYPTO 1988. LNCS, vol. 403, pp. 564–577. Springer, Heidelberg (1990)
Czech, Z.J., Havas, G., Majewski, B.S.: Perfect Hasing. Theoretical Computer Science 182, 1–143 (1997)
Croft, R.A., Harris, S.P.: Public-key cryptography and re-usable shared secrets. In: Beker, Piper (eds.) Cryptography and coding, pp. 241–246. Clarendon Press (1989)
Desmedt, Y.: Society and group oriented cryptology: a new concept. In: Pomerance, C. (ed.) CRYPTO 1987. LNCS, vol. 293, pp. 120–127. Springer, Heidelberg (1988)
Desmedt, Y.: Threshold cryptography. European Trans. on Telecommunications 5(4), 449–457 (1994)
Desmedt, Y.: Some recent research aspects of threshold cryptography. In: Okamoto, E. (ed.) ISW 1997. LNCS, vol. 1396, pp. 99–114. Springer, Heidelberg (1998)
Desmedt, Y., Di Crescenzo, G., Burmester, M.: Multiplicative non-abelian sharing schemes and their application to threshold cryptography. In: Brassard, G. (ed.) CRYPTO 1989. LNCS, vol. 435, pp. 21–32. Springer, Heidelberg (1990)
De Santis, A., Desmedt, Y., Frankel, Y., Yung, M.: How to share a function securely. In: Proc. 26th Annual Symp. on the Theory of Computing, pp. 522–533. ACM, New York (1994)
Desmedt, Y., Frankel, Y.: Homomorphic zero-knowledge threshold schemes over any finite group. SIAM J. Disc. Math. 7(4), 667–679 (1994)
Desmedt, Y., King, B., Kishimoto, W., Kurosawa, K.: A comment on the efficiency of secret sharing scheme over any finite abelian group. In: Boyd, C., Dawson, E. (eds.) ACISP 1998. LNCS, vol. 1438, pp. 391–402. Springer, Heidelberg (1998)
Feldman, P.: A practical scheme for non-interactive verifiable secret sharing. In: Proc. 28th Annual FOCS, pp. 437–437. IEEE Computer Society Press, Los Alamitos (1987)
Frankel, Y.: A practical protocol for large group oriented networks. In: Quisquater, J.-J., Vandewalle, J. (eds.) EUROCRYPT 1989. LNCS, vol. 434, pp. 56–61. Springer, Heidelberg (1990)
Frankel, Y., Gemmell, P., MacKenzie, P., Yung, M.: Optimal resilience proactive public-key cryptosystems. In: Proc. 38th FOCS, pp. 384–393. IEEE Computer Society Press, Los Alamitos (1997)
Frankel, Y., Gemmell, P., Yung, M.: Witness-based Cryptographic Program Checking and Robust Function Sharing. In: Proc. 28th STOC, pp. 499–508. ACM Press, New York (1996)
Frankel, Y., MacKenzie, P., Yung, M.: Robust efficient distributed RSA-key generation. In: Proc. 30th STOC, pp. 663–672. ACM Press, New York (1998)
Gennaro, R., Jarecki, S., Krawczyk, H., Rabin, T.: Robust and efficient sharing of RSA functions. In: Koblitz, N. (ed.) CRYPTO 1996. LNCS, vol. 1109, pp. 157–172. Springer, Heidelberg (1996)
Goldreich, O., Micali, S., Wigderson, A.: Proofs that yield Nothing but the validity of the assertion, and a methodology of cryptographic protocol design. In: Proceeding 27th Annual Symposium on the Foundations of Computer Science, pp. 174–187. ACM Press, New York (1986)
Karnin, E., Greene, J., Hellman, M.: On Secret Sharing Systems. IEEE Transactions on Information Theory IT-29, 35–41 (1983)
Mehlhorn, K.: Data Structures and Algorithms. Springer, Heidelberg (1984)
Miyazaki, S., Sakurai, K., Yung, M.: On threshold RSA-signing with no dealer. In: Song, J.S. (ed.) ICISC 1999. LNCS, vol. 1787, pp. 187–197. Springer, Heidelberg (1999) (see also this proceedings)
Rabin, T.: A simplified Approach to Threshold and Proactive RSA. In: CRYPTO 1996. LNCS, vol. 1109, pp. 89–104. Springer, Heidelberg (1998)
Shamir, A.: How to Share a Secret. Communications of the ACM 22, 612–613 (1979)
Simmons, G., Jackson, W.-A., Martin, K.: The Geometry of Shared Secret Schemes. Bulletin of the Institute of Combinatorics and its Applications (ICA) 1, 71–88 (1991)
Tompa, M., Woll, H.: How To Share a Secret with Cheaters. Journal of Cryptology 1(2), 133–138 (1988)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Safavi-Naini, R., Wang, H., Lam, KY. (2000). A New Approach to Robust Threshold RSA Signature Schemes. In: Song, J. (eds) Information Security and Cryptology - ICISC’99. ICISC 1999. Lecture Notes in Computer Science, vol 1787. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10719994_15
Download citation
DOI: https://doi.org/10.1007/10719994_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67380-4
Online ISBN: 978-3-540-45568-4
eBook Packages: Springer Book Archive