The problem ZeroWei solves

A dollar note cash has two properties

1. It is private: It doesn't carry a tx trace with it. It doesn't have an owner. The holder of the note is the owner. No one else know I gave a dollar note to you other than you and me.
2. It is instantaneous: As soon as I give the dollar note to you, you can spend it. There is no waiting.
3. It is costless: When I give it to you, I don't have to pay anyone else for that tx.

We are enabling instant, private near zero cost transactions for Ethereum. You can send someone 1wei(or single unit of any ERC20 token), instantaneously with near 0 tx cost.

How we do it?
We implement Ecash implementation on top of Ethereum where you can mint or redeem Ecash tokens against depositing/withdrawing ETH to a third party. Once you have Ecash tokens, you can transfer those to anyone instantaneously without revealing any information about yourself, with near 0 cost. When someone wants to convert their Ecash tokens back to ETH they send back the Ecash tokens to the minter (third party) and get ETH back on Ethereum which cost the ETH gas fee.

Current Trust assumptions:
It relies on a custodial party to create/mint ECash against ETH deposited. So technically somepne can mint millions of Ecash and make it fractionalised like a dollar bank. We don't know yet, if some kind of ZK or other techniques can make the minting of Ecash for Ethereum trustless.

Challenges we ran into

The core challenge was to enable two paties to share private keys on a public channel. idea in implementing it was ability
The inspiration came from a Bitcoin project which implemented Ecash implementation on top of Bitcoin.
We needed to understand how lightening, atomic swap, Blinded Diffie-Hellman key exchange work.

We needed to come up with a way where we can implement a lightening invoice kind of setup on Ethereum.