Secure Distributed Computation of the Square Root and Applications
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.
KeywordsSquare Root Fixed-Point Arithmetic Secure Computation QR-Decomposition
Unable to display preview. Download preview PDF.
- 10.Goldschmidt, R.E.: Applications of division by convergence. Master’s thesis, M.I.T. (1964)Google Scholar
- 11.Golub, G.H., van Loan, C.F.: Matrix Computations, 3rd edn. The Johns Hopkins University Press (1996)Google Scholar
- 13.Markstein, P.: Software division and square root using goldschmidt’s algorithms. In: 6th Conference on Real Numbers and Computers, pp. 146–157 (2004)Google Scholar