Zcash uses special proof to provide a network called zk-snark - or proof of construction. This allows the network to maintain a balance sheet without disclosing parties or amounts involved in the transactions. This is done by using zero evidence of knowledge - or basically when the person who performs the transaction has the ability to spend an EEK and the values are balanced and not spent before. InBitcoin each full node keeps the balance of what is kept from each address in the UXTO output database or unused transactions - for each transaction being checked to unlock this output