I'm recently trying to investigate whether we can deploy a private blockchain without using the functionality of the smart contract, or in that case can we deploy it on quorum without the functionality of smart contract
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1Your question is not clear , maybe you looking for something similar to plasma chains – Majd TL Dec 13 '19 at 8:39
A private blockchain is independent from a smart contract. You can run your own private Ethereum network (for example using ganache, geth or parity). To ensure (others) that you don't randomly rollback in a network based on Proof-of-Authority or a low computation power Proof-of-Work consensus mechanism (for example), you can send a transaction to a strong network like Ethereum every N blocks, including the latest block hash of your private chain in the transaction data.