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The hot, hot investment theme of changing how people pay for things is going to see even more dramatic changes in coming years than those imagined by upstarts such as Square.

A technology called blockchain, which has evolved as an open-source software program shared on the Internet, has the potential to remove multiple layers of processes and intermediaries in the sequence of steps that “settle” or “clear” payments from one party to another.

The immediate impact could be a big drop in the usefulness of credit-card networks such as Visa (ticker: V), MasterCard (MA), American Express (AXP), and Discover Financial Services (DFS).

As mentioned in this column last week, digital payment is the latest thing in technology, as evinced by the initial public offering two weeks ago of Square (SQ), the San Francisco start-up that provides merchants with an electronic reader for processing payments. Square’s shares recently were trading above $12, a third higher than the offering price.

But Square and other payment contenders, such as PayPal (PYPL), are just the start of a more profound revolution led by an open-source software program that creates a kind of financial ledger for transactions.

The technology came to prominence with the rise of Bitcoin. The virtual currency had a surge of popularity before a panic led to extreme skepticism about such fantasy money. But blockchain technology is a sound idea that’s separate from Bitcoin, and it could end up having a far greater impact than the currency.

Using a collection of computer codes, blockchain records credits and debits between parties. Whether the currency of those credits and debits is Bitcoin, dollars, or renminbi doesn’t matter. The system is kept honest by multiple computers comparing their versions of the ledger in order to come up with an authoritative single record.

THE APPEAL OF BLOCKCHAIN is that, by removing many of the layers of complexity for settlements and clearing, it reduces time and cost in payments and contracts. The fact that no one owns it creates a power vacuum that lots of parties are rushing to fill.

One company getting Wall Street’s attention is Digital Asset Holdings, the rather dull name of a New York start-up run by financial star Blythe Masters. The subject of a lengthy profile by Bloomberg this year, Masters is famous for developing the credit-default-swaps products business at JPMorgan before the 2008 financial crisis, with some even considering her a prime actor in the global meltdown.

Notoriety notwithstanding, Masters is in the odd role of promoting the greater transparency of blockchain. Her firm is making software that can create private blockchains for banking clients for loans and contracts and other transactions. Hers is just one of a gaggle of start-ups, including Chain of San Francisco and Blockchain Inc., that have received tens of millions in venture-capital funding.

The revolution may go deeper than what these start-ups promise. Blockchain is an Internet technology, not a financial-industry technology. Finance has seen lots of technology innovations, including the settlements network run by the Depository Trust and Clearing Corp., founded in the 1970s, and the Swift consortium for bank settlements. Those were creations of institutions, whereas blockchain emerged spontaneously from the open-source software world. Its coders design things following their own instincts, and the technology evolves organically rather than being dictated.

Blockchain may replace more than paperwork; it may reduce or remove the role played by numerous financial parties, including banks, the Federal Reserve, and similar institutions in other countries; private clearing entities such as Bank of New York Mellon (BK); and card networks like Visa and MasterCard.

In a blockchain world, all transactions are just a software program running on computers distributed across the Internet, rather than the private ledgers of banks. There’s already a model for this in the way that Websites operate. Every time you type a Web address into a browser, such as “barrons.com,” a set of computers called “registries” figure out the actual location on the Internet of Barron’s computers where those Web pages live. Doing so is accomplished by consulting a sort of global phone book, called DNS computers.

That phone book is maintained by a group of private entities called “registrars,” which are, in turn, authorized to do so by a nonprofit organization named Icann. The point is that the partnership of Icann and the registrars allows for loose organization that keeps the global Internet running without layers of bureaucracy, but instead with a set of compatible computer programs.

Even as blockchain computers come to be trusted by transacting parties, banks will probably maintain a role. The failure of Bitcoin as a currency suggests that we’ll be transacting in fiat currencies for years to come. Banks will benefit by acting as the underwriters of blockchain risk, guaranteeing deposits in local currencies around the world.

BUT VISA AND MASTERCARD, which are viewed as essential, are simply digital networks. It’s possible to see the emergence of a future in which the credit-card networks go away, and your bank-issued card or your smartphone is simply a way to plug into a blockchain that is maintained globally, reflecting all bank accounts.

Visa is not unaware of blockchain: In its annual report, the company warns of the threat of “rapid, significant technological changes” in the payments industry, including “mobile and other proximity payment and acceptance, eCommerce, tokenization, crypto-currency, and blockchain technologies.”

Start-ups such as Digital Asset Holdings and the rest will play an important but minor role, if the history of DNS is any indicator. The first private company that got the right to run the DNS computers, Network Solutions, was later sold to VeriSign (VRSN). Today, it’s a billion-dollar-a-year business for VeriSign, growing by single digits.

Companies such as PayPal and Square, if they play their cards right, may benefit if the card networks’ fees, which they pass along to their merchant customers, are eliminated. But they will be merely service providers in a larger ecosystem. As with much of the Internet, the greatest value will lie in a set of technologies that make amazing things possible, but that no one owns.

TIERNAN RAY can be reached at: tiernan.ray@barrons.com, blogs.barrons.com/techtraderdaily or www.twitter.com/barronstechblog