Do you think Donald Trump is the world’s most divisive force? Are you impressed by the recent bull run of the stock market?

Think again. They may be bit players compared with the digital currency called bitcoin.

Bitcoin has been called a fraud and the most important advance since the internet. It has attracted money-launderers, data kidnappers, international drug dealers – and some of the world’s premier financial companies. China has tried to ban it. North Korea is starting to dabble in it.

Over the weekend, bitcoin hit a new high – a single bitcoin is worth more than $6,300 – a breathtaking runup of more than 500 percent in this year alone. The S&P 500, by comparison, has managed only 13 percent. The bitcoin price surge reflects partly some inherent scarcity in that currency's design, although finance experts also see a speculative bubble.

Clearly, something is going on with bitcoin and the 1,000 or so other cryptocurrencies now in circulation. The technological breakthrough behind these currencies has spawned at least three huge waves of innovation in the digital world that are beginning to wash over into the physical world. Dramatic changes may lie ahead.

First, there is the lure of purely digital currencies, which operate outside the control of any nation or central bank. There are now a dozen that exceed $1 billion in value.

Second, there’s the technology itself, called blockchain, a public record, stored on a decentralized network of computers, of every transaction in the cryptocurrency. The technology acts as a hacker-proof currency and a ledger rolled into one. It’s as if the dollar bill in your wallet or purse did its own bookkeeping, recording who gave it to you and where you spend it. Blockchain technology may cut billions of dollars out of business transaction costs and make everything from stock trades to insurance contracts cheaper and more secure.

The third wave, which is more speculative and perhaps more transformative in the long run, is the use of blockchain to tokenize things, from legal identification to human attention.

“You [take] the idea of the coin in a blockchain and you abstract it out to anything, literally anything that can be turned into a token,” says Lex Sokolin, global director of fin-tech strategy of Autonomous Research, an independent research provider based in London. “For example instead of having advertisers pay Facebook in order to reach you and me, advertisers can pay us directly, because we control tokens that can monetize our attention.”

Testing the possibilities

The experiments are coming fast and furious, much as they did in the heyday of the dot-com boom:

• Already, Swiss-based Viuly is creating a YouTube alternative using blockchain technology, where the creators of catchy video would get up to 65 percent of the ad revenue they generate and viewers would get 25 percent, just for watching the free video.

• To fight global warming, a UN official has proposed using blockchain to make companies’ trading of carbon credits more efficient.

• In Jordanian refugee camps, the UN’s World Food Program is experimenting with Ethereum, a blockchain rival to bitcoin, to distribute food vouchers to displaced Syrians.

• A consortium of UN agencies, nonprofits, companies, and governments is looking into using blockchain for creating secure and portable identity for the billion or so people in the world who are not officially recognized by a government.

Buffett’s rebuff

Is bitcoin caught up in a speculative frenzy? Almost certainly, according to savvy observers. A “real bubble,” superinvestor Warren Buffett told a group of business students in mid-October.

“If you’re stupid enough to buy it, you’ll pay the price someday,” Jamie Dimon, chief executive of J.P. Morgan Chase, warned an audience in Washington earlier this month. The banker has previously called bitcoin a fraud and threatened to fire traders in his company who buy it.

Yet for now, the value of bitcoin and other cryptocurrencies keeps going up. Bitcoin started the year trading at just over $1,000 apiece; it topped $6,000 on Oct. 21. Speculators, hoping to ride the next bitcoin-like wave, scoop up new currencies as soon as they come out in initial coin offerings or ICOs (similar to companies selling stock in initial public offerings, or IPOs). Novum Insights, a research group tracking financial technology, estimates that through September blockchain ICOs had raised $2.2 billion this year.

That level of activity suggests bitcoin may be acting more like a store of value, like gold or even stocks, rather than a medium of exchange.

“I think bitcoin is more of an investment security than a currency,” David Yermack, a finance professor at New York University’s Stern School of Business, writes in an e-mail. Some 90 percent of the transactions appear to be between investors rather than as payments for goods and services, he says.

After the bubble bursts, which many old-school investors say is inevitable, bitcoin or some other cryptocurrencies could emerge as a more stable, less volatile digital money.

“Cryptocurrencies are in a position to be more valuable than gold, dollar, euro, or yen, as long as there is a clear [case for their] use,” Asheesh Birla, vice president of product at blockchain firm Ripple, writes in an email. At the moment, for example, when a big bank pulls out of an emerging market, their clients can use a cryptocurrency instead to continue transacting business in that market, he adds. [Editor's note: This paragraph was changed to clarify Ripple's business.]

In the meantime, financial companies from the Royal Bank of Canada to Goldman Sachs to even Mr. Dimon’s J.P. Morgan are experimenting with the technology behind bitcoin – blockchain – to cut the costs of financial transactions.

No forgery

This recording of each transaction is also what makes blockchain secure. To forge a cryptocurrency “coin,” you would have to correctly alter the entire chain of transactions since the coin was created – an almost impossible feat mathematically. By one estimate, top banks could save 30 percent (some $8 billion to $12 billion apiece) in their operational costs by switching to blockchain.

The third wave – the use of blockchain to turn just about anything into a tradable token – is the least developed and the most volatile. One maker of hardware for bitcoin “mining” (the process of creating new bitcoins) has turned itself into a social network where people join to get paid in special tokens for answering emails and completing tasks. Epazz Inc., a software maker whose products include a cryptocurrency to make it easier to buy legalized marijuana, lost half its market value on a single trading day this week.

Privacy ... and nefarious uses

The technology’s lure for many users – no government control and anonymity – also makes it a useful tool for criminals.

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A month ago, when data thieves hijacked the data of Montgomery County, Ala., and threatened to erase it, they demanded – and county officials paid them – in bitcoin worth between $40,000 and $50,000. In Benton County, Ark., the sheriff’s office has just announced a pilot program to use bitcoin in undercover sting operations against child pornographers and other online criminals.

“We’re just in a place where the hackers and the artists are building things that are cool and they’re interesting,” says Mr. Sokolin of Autonomous Research. “The incumbents are a little scared, so they’re playing around with the same Lego pieces. But we’re just in the beginning of what will be a fairly different world.”