Ballot Aggregation

At the conclusion of voting, all of the ballot encryptions are published in the election record together with the proofs that the ballots are well-formed. Additionally, all of the encryptions of each option are homomorphically combined to form an encryption of the total number of times that option was selected. The encryptions $\mathbf{(}{\alpha }_i,{\beta }_i)$ of each individual option are combined by forming the product $(A,B)=({\mathrm{\Pi }}_i{\alpha }_{i}modp,{\mathrm{\Pi }}_i{\beta }_{i}modp)$. This aggregate encryption $(A,B)$, which represents an encryption of the tally of that option, is published in the election record for each option.