nspired by proof$-$of$-$stake, Amir would like to create an Ethereum smart contract in which

people can lock up their funds $($in ether$)$ and then vote on a very important matter. The matter

can be resolved in one of $$ ways, thus each person$$s vote is an integer $\{1,2,...,\}.$ Amir is

asking for your help. Specifically, he would like to have a protocol $($explained in English in a

pdf file$)$ and a smart contract $($implemented in solidity$)$ that provides as many of the following

functionality$/$desired properties as possible:

a$.$ Anyone on the Ethereum network can sign up in the protocol by depositing $1$ ether. One

may sign up several times and thus pay a larger overall deposit.

b$.$ At the end of the protocol, everyone can get their deposits back. The returned value may

be a bit smaller than the original deposit, e$.$g$.0\mathrm{.}9$ ether, if you need to pay for something in

your protocol.

c$.$ Each deposit of $1$ ether entitles the depositor to one vote.

d$.$ After a particular deadline $1,$ the contract stops accepting deposits and instead only accepts

votes by those who have already deposited money.

e$.$ No one can vote twice for the same deposit.

f$.$ After a later deadline $2,$ the contract stops accepting votes.

g$.$ After an even later deadline $3,$ everyone with access to the blockchain should be able to

figure out which option from the set $\{1,2,...,\}$ received the maximum number of votes. If

there is a tie, you can break it arbitrarily as you wish.

h$.$ No one should be able to know another person$$s vote.

i$.$ If Alice has voted for $$ in $\{1,2,...,\}$ and she wants to prove this to Bob, she should be able

to do so$.$ You can assume that Bob has access to the blockchain.

j$.$ Your contract should not have any of the security vulnerabilities discussed in the lectures.

k$.$ Your contract should use as little gas as possible and be affordable. You should find out

exactly how much gas each one of your functions uses in the worst case and report it in

your pdf file.

Finally, you are allowed to have participants in the contract who take roles other than voting,

but any such participation should be well$-$incentivized, i$.$e$.$ you should argue why they can

make money by helping you run your contract if your protocol depends on their participation.

$2$