Proof of Graph converts the Byzantine General's problem into the Byzantine Soldier's problem. Each client is also a validator. More decentralized. Now transactions can be encrypted. Senders share keys directly with receivers.
During BackTrace, for Mike's client to validate Alice's past transactions chain, it must be able to decrypt ALL Alice's past transactions with everybody else. To facilitate this, each transaction contains the keys to the previous transaction allowing the "back trace".
Proof of Graph converts the Byzantine General's problem into the Byzantine Soldier's problem. Each client is also a validator. More decentralized. Now transactions can be encrypted. Senders share keys directly with receivers.
Each transaction is encrypted with a random symmetric key. Alice's client creates an encrypted transaction on chain and then shares the encryption key directly with Mike's client. Mike's client (validator) does validation BackTrace and then creates a receipt on chain.