J.P. Morgan Chase & Co. is working on a new twist on the technology behind bitcoin that would allow the bank to use a publicly available system for confidential transactions.

The move is a break with how some banks have approached the use of a bitcoin-style network, known generally as the blockchain, to try to replace creaking old systems with faster new technology. Instead of creating a completely new private blockchain, J.P. Morgan engineers say they have found a way to limit access to transactions shared via a network to...