【正文】
(Paillier) ? Round table protocol with constant rounds ? Same approach as above, but several technical issues to overe (interpolating over encrypted values, handling errors, proofs of knowledge…) Thank you! Preprocessing Verification ? Correct putation of new variables ? Correct degree of input sharing polynomials ? HEPKPV Protocol Party 1: x1,…,xn Common: c1,…, L (x1,…,xn) in L ci = ENC(xi) input proof output Party 2: Accept/Reject enc(r1) enc(r2) enc(rn) c1 * enc(r1) c2 * enc(r2) … * enc(rn) x1+r1,…,xn+rn in L r1,…,rn in L open 0 1 Client Simulator ? Extract Client’s input in HEPKPV ? Submit to TP and receives output ? Shares output and mits as output shares ? Simulates Server in interaction with Client mitting to random input ? Makes sure can open correctly and verify putation of k output shares ? Rewinds cointossing for cutandchoose to select the above k shares Server Simulator ? Simulates the Client in the interaction with the Server using random encryption of 0 ? Extracts Server’s inputs in HEPKPV ? Rewinds coin tossing to open all Server’s shares ? Makes sure that most output shares are consistent with extracted input ? If the above holds, submit extracted input to TP Communication Complexity ? Improved Communication Complexity – O(mk2log2(n)+nk) – circuit evaluation – size of circuit – mn ZKN proofs – Important in realistic scenarios with large input sets m,n k