binary constrain merkle tree paths

[barryWhiteHat]

We need to binary constain the merkle tree path as binary. This is because we use multiplicaions and additions to do merkle tree lookups https://github.com/barryWhiteHat/RollupNC/blob/master/tokens_transfer/tokens_transfer.circom#L47

and we don't want an attacker to be able to pass non binary values to mess with the path in the tree.

[vaibhavchellani]

We can totally add a constraint like a*(a-1) === 0; to check the binary check. But do we really need it? The constraint here probably wont match if the inputs are non-binary I think.

[barryWhiteHat]

I think there are some attacks where we can play with the merkle path. It seems like pretty difficult to exploit but from a defence in depth argument i think we shoudl include the chcek.

[therealyingtong]

or a*a == a. should we add this in now?