From a high level perspective, you can keep address balances private but it would be different than having encrypted ethereum balance. It would work more like this:
Alice, Bob and Charlie deposit 5 ETH to a deposit contract on Ethereum. Then the send private TXs to Enigma network to send each other TXs. Say Alice sends both Bob and Charlie 1 ETH. This is similar to how lightning network works. Enigma secret state updates balances - Alice 3 ETH, Bob 6 ETH, Charlie 6 ETH. This can happen multiple times and in a future time Alice, Bob and Charlie can settle on-chain. When they are settling on chain they can also use new (clean) addresses. (The addresses would too be private inputs a secret contract, for withdrawal). With a large set of users, the anonymity set would grow Hi @andreiIV, welcome to the forum.
From a high level perspective, you can keep address balances private but it would be different than having encrypted ethereum balance. It would work more like this:
Alice, Bob and Charlie deposit 5 ETH to a deposit contract on Ethereum. Then the send private TXs to Enigma network to send each other TXs. Say Alice sends both Bob and Charlie 1 ETH. This is similar to how lightning network works. Enigma secret state updates balances - Alice 3 ETH, Bob 6 ETH, Charlie 6 ETH. This can happen multiple times and in a future time Alice, Bob and Charlie can settle on-chain. When they are settling on chain they can also use new (clean) addresses. (The addresses would too be private inputs a secret contract, for withdrawal). With a large set of users, the anonymity set would grow