Abstract
The square root is an important mathematical primitive whose secure, efficient, distributed computation has so far not been possible. We present a solution to this problem based on Goldschmidt’s algorithm. The starting point is computed by linear approximation of the normalized input using carefully chosen coefficients. The whole algorithm is presented in the fixed-point arithmetic framework of Catrina/Saxena for secure computation. Experimental results demonstrate the feasibility of our algorithm and we show applicability by using our protocol as a building block for a secure QR-Decomposition of a rational-valued matrix.
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.
References
Beaver, D., Micali, S., Rogaway, P.: The round complexity of secure protocols. In: Proceedings of the Twenty-second Annual ACM Symposium on Theory of Computing, STOC 1990, pp. 503–513. ACM, New York (1990)
Ben-Or, M., Goldwasser, S., Wigderson, A.: Completeness theorems for non-cryptographic fault-tolerant distributed computation. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 1–10. ACM, New York (1988)
Catrina, O., de Hoogh, S.: Improved Primitives for Secure Multiparty Integer Computation. In: Garay, J.A., De Prisco, R. (eds.) SCN 2010. LNCS, vol. 6280, pp. 182–199. Springer, Heidelberg (2010)
Catrina, O., de Hoogh, S.: Secure Multiparty Linear Programming Using Fixed-Point Arithmetic. In: Gritzalis, D., Preneel, B., Theoharidou, M. (eds.) ESORICS 2010. LNCS, vol. 6345, pp. 134–150. Springer, Heidelberg (2010)
Catrina, O., Saxena, A.: Secure Computation with Fixed-Point Numbers. In: Sion, R. (ed.) FC 2010. LNCS, vol. 6052, pp. 35–50. Springer, Heidelberg (2010)
Chaum, D., Crépeau, C., Damgård, I.: Multiparty unconditionally secure protocols. In: Proceedings of the Twentieth Annual ACM Symposium on Theory of Computing, STOC 1988, pp. 11–19. ACM, New York (1988)
Cramer, R., Damgård, I.: Secure Distributed Linear Algebra in a Constant Number of Rounds. In: Kilian, J. (ed.) CRYPTO 2001. LNCS, vol. 2139, pp. 119–136. Springer, Heidelberg (2001)
Cramer, R., Damgård, I., Ishai, Y.: Share Conversion, Pseudorandom Secret-Sharing and Applications to Secure Computation. In: Kilian, J. (ed.) TCC 2005. LNCS, vol. 3378, pp. 342–362. Springer, Heidelberg (2005)
Goldreich, O., Micali, S., Wigderson, A.: How to play any mental game. In: Proceedings of the Nineteenth Annual ACM Symposium on Theory of Computing, STOC 1987, pp. 218–229. ACM, New York (1987)
Goldschmidt, R.E.: Applications of division by convergence. Master’s thesis, M.I.T. (1964)
Golub, G.H., van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press (1996)
Ito, M., Takagi, N., Yajima, S.: Efficient initial approximation for multiplicative division and square root by a multiplication with operand modification. IEEE Transactions on Computers 46, 495–498 (1997)
Markstein, P.: Software division and square root using goldschmidt’s algorithms. In: 6th Conference on Real Numbers and Computers, pp. 146–157 (2004)
Shamir, A.: How to share a secret. Commun. ACM 22, 612–613 (1979)
Stoer, J., Bulirsch, R.: Introduction to numerical analysis. Texts in applied mathematics. Springer, Heidelberg (2002)
Yao, A.C.: Protocols for secure computations. In: Proceedings of the 23rd Annual Symposium on Foundations of Computer Science, SFCS 1982, pp. 160–164. IEEE Computer Society, Washington, DC, USA (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Liedel, M. (2012). Secure Distributed Computation of the Square Root and Applications. In: Ryan, M.D., Smyth, B., Wang, G. (eds) Information Security Practice and Experience. ISPEC 2012. Lecture Notes in Computer Science, vol 7232. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29101-2_19
Download citation
DOI: https://doi.org/10.1007/978-3-642-29101-2_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29100-5
Online ISBN: 978-3-642-29101-2
eBook Packages: Computer ScienceComputer Science (R0)