Abstract
Catalano, Gennaro and Halevi (2000) present a protocol for the distributed computation of inverses over a shared secret modulus. The most important application of their protocol is the distributed computation of the private RSA key from the public key. The protocol is attractive, because it requires only two rounds of communication in the case of honest but curious players. The present paper gives a modification of this protocol, which reduces its complexity from O(n 3 (logn)2 + n 2 (logn) (logN) + (logN)2) to O(n 3 logn + n 2 logN + (logN)2) bit-operations per player, where n is the number of players and N is the RSA modulus. The number of communication rounds is the same as in the original protocol.
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
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the 20th Annual Symposium on Theory of Computing (STOC 1988), pp. 1–10. ACM Press, New York (1988)
Catalano, D.: Efficient distributed computation modulo a shared secret. In: Catalano, D., Cramer, R., Damgård, I., Di Crescenco, G., Pointcheval, D., Takagi, T. (eds.) Contemporary Cryptology, CRM Barcelona. Advanced Courses in Mathematics, pp. 1–39. Birkhäuser, Basel (2005)
Catalano, D., Gennaro, R., Halevi, S.: Computing inverses over a shared secret modulus. In: Preneel, B. (ed.) EUROCRYPT 2000. LNCS, vol. 1807, pp. 190–206. Springer, Heidelberg (2000)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: Proceedings of the 20th Annual Symposium on Theory of Computing (STOC 1988), pp. 11–19. ACM Press, New York (1988)
Cohen, H.: A Course in Computational Algebraic Number Theory. Springer, Berlin (2000)
Cramer, R., Shoup, V.: Signature schemes based on the Strong RSA Assumption. ACM Transactions on Information and System Security (ACM TISSEC) 3(3), 161–185 (2000)
Gennaro, R., Halevi, S., Rabin, T.: Secure hash-and-sign signatures without the random oracle. In: Stern, J. (ed.) EUROCRYPT 1999. LNCS, vol. 1592, pp. 123–139. Springer, Heidelberg (1999)
Gennaro, R., Rabin, M.O., Rabin, T.: Simplified VSS and fast-track multiparty computations with applications to threshold cryptography. In: Proceedings of the 17th ACM Symposium on Principles of Distributed Computing (PODC 1998), pp. 101–111. ACM Press, New York (1998)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of the 19th Annual Symposium on Theory of Computing (STOC 1987), pp. 218–229. ACM Press, New York (1987)
Hairer, E., Wanner, G.: Analysis by Its History. Springer, New York (1995)
Knuth, D.E.: The Art of Computer Programming. Seminumerical Algorithms, vol. 2. Addison-Wesley, Reading (1971)
Lory, P.: Reducing the complexity in the distributed multiplication protocol of two polynomially shared values. In: Proceedings of the 3rd IEEE International Symosium on Security in Networks and Distributed Systems (SSNDS 2007). AINA 2007, vol. 1, pp. 404–408. IEEE Computer Society Press, Los Alamitos (2007)
Mao, W.: Modern Cryptography: Theory and Practice. Prentice Hall, Upper Saddle River (2004)
Rivest, R., Shamir, A., Adleman, L.: A method for obtaining digital signatures and public key cryptosystems. Communications of the ACM 21(2), 120–126 (1978)
Shamir, A.: How to share a secret. Communications of the ACM 22(11), 612–613 (1979)
Stoer, J., Bulirsch, R.: Introduction to Numerical Analysis. Springer, Berlin (2002)
Yao, A.C.: How to generate and exchange secrets. In: Proceedings of the 27th IEEE Symposium on Foundations of Computer Science (FOCS 1986), pp. 162–167. IEEE Computer Society, Los Alamitos (1986)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2009 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lory, P. (2009). Reducing the Complexity in the Distributed Computation of Private RSA Keys. In: Boyd, C., González Nieto, J. (eds) Information Security and Privacy. ACISP 2009. Lecture Notes in Computer Science, vol 5594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02620-1_18
Download citation
DOI: https://doi.org/10.1007/978-3-642-02620-1_18
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-02619-5
Online ISBN: 978-3-642-02620-1
eBook Packages: Computer ScienceComputer Science (R0)