How to check and enforce valid vote? Since vivi=(pix1,ix2,i)(pix1,ix2,i)=pipipix1,ipix2,ipix1,i+x1,ix1,i+ x1,ix2,ipix2,i+x1,ix2,i+x2,ix2,i Since two of the terms, x1,1x2,i and x1,ix2,i, require secrets from both collectors, STPM needs to be used twice. One application yields s1+s2=x1,ix2,i(modn), and another application yields s1+s2=x1,ix2,i(modn). Next, each collector creates a sum of secret terms. They include the results from the two applications of STPM. So, collector 1 computes S1=pix1,ipix1,i+x1,ix1,i+s1+s1(modn) and collector 2 computes S2=pix2,ipix2,i+x2,ix2,i+s2+s2(modn). Each collector commits to Sj. Finally, each collector gives its sum (only after receiving the other's commitment) to the other and verifies that pipi+S1+S2=2L1(modn). Question: if collector 1 and collector 2 exchange s1+s1 and s2+s2 instead of S1 and S2, (assume that they also exchange pix1,ipix1,i+x1,ix1,i and pix2,ipix2,i+x2,ix2,i ) any collector will be able to figure out the voter's vote. Can you prove why? Furthermore, why does exchanging S1 and S2 work well without disclosure of voter's vote