Divisible Voting Scheme
Electronic voting is a prime application of cryptographic tools. Many researches are addressing election or confidence voting in this area. We address a new type of voting scheme ``Divisible Voting Scheme,'' in which each voter has multiple ballots where the number of ballots can be different among the voters. This type of voting is popular, however there is no secure protocol which achieves this type of voting. We first define the divisible voting scheme and show naive protocols based on existing voting schemes. Then we propose two efficient divisible voting schemes. The first scheme uses multisets, the second scheme uses $L$-adic representation of number of ballots. The total cost for a voter is $O(M^2 \log (N))$ in the first scheme and $O(M \log(N))$ in the second scheme where $M$ is the number of candidates to vote for and $N$ is the number of ballots for a voter.