@article{Cramer_Damgård_Nielsen_2000, title={Multiparty Computation from Threshold Homomorphic Encryption}, volume={7}, url={https://tidsskrift.dk/brics/article/view/20141}, DOI={10.7146/brics.v7i14.20141}, abstractNote={We introduce a new approach to multiparty computation (MPC) basing<br />it on homomorphic threshold crypto-systems. We show that given<br />keys for any sufficiently efficient system of this type, general MPC protocols<br />for n players can be devised which are secure against an active<br />adversary that corrupts any minority of the players. The total number of<br />bits sent is O(nk|C|), where k is the security parameter and |C| is the size<br />of a (Boolean) circuit computing the function to be securely evaluated.<br />An earlier proposal by Franklin and Haber with the same complexity was<br />only secure for passive adversaries, while all earlier protocols with active<br />security had complexity at least quadratic in n. We give two examples<br />of threshold cryptosystems that can support our construction and lead<br />to the claimed complexities.}, number={14}, journal={BRICS Report Series}, author={Cramer, Ronald and Damgård, Ivan B. and Nielsen, Jesper Buus}, year={2000}, month={Jan.} }