The country’s voting machines are susceptible to hacking, which could be done in a way so that it leaves no fingerprints, making it impossible to know whether the outcome was changed, computer experts told President Trump’s voter integrity commission Tuesday.

The testimony marked a departure for the commission, which was formed to look into fraud and barriers to voting, but which heard that a potentially greater threat to confidence in American elections is the chance for enemy actors to meddle.

“There’s no perfect security; there’s only degrees of insecurity,” said Ronald Rivest, a professor at the Massachusetts Institute of Technology.

He said hackers have myriad ways of attacking voting machines. “You don’t want to rest the election of the president on, ‘Maybe the Wi-Fi was turned on when it shouldn’t have been.’”

He and two other computer security experts said bar codes on ballots and smartphones in voting locations could give hackers a chance to rewrite results in ways that couldn’t be traceable, short of sampling of ballots or hand recounts — and those work only in cases where there’s a paper trail.

Andrew Appel, a professor at Princeton University, said it would be easy to write a program that cheats on election results and deletes evidence of the hack as soon as the results are reported.

The analysts didn’t point to any specific election that they knew had been compromised, but they said hackers likely would leave fingerprints only if they wanted to be spotted and hurt confidence in the U.S. electoral system.

“To ignore the fact that the computers are completely hackable and to try to run elections, as some states do, where they entirely rely on the word of a computer program on who won is entirely irresponsible,” Mr. Appel said.

The revelations stunned members of the Presidential Advisory Commission on Election Integrity, which was in New Hampshire on Tuesday for its second meeting.

“I’m sufficiently shaken,” said Ken Blackwell, a commissioner and former secretary of state in Ohio.

The computer security panel was the final business of a daylong hearing that also looked at prevalence of voter fraud and what can be done to combat it.

Testimony included an estimate that tens of thousands of people double-voted in last year’s elections by casting ballots in two states.

Ken Block, president of Simpatico Software Systems, said his firm checked records from states that released names and birthdates of voters, ran those through a couple of more screens and came up with an estimate for the whole nation.

Another 15,000 people who voted last year listed UPS delivery stores as their residences.

“There’s a high likelihood of voter fraud,” Mr. Block said. “There’s likely a lot more to be found.”

Democrats in Washington have resisted those claims, saying reports of fraud are rare and barriers to voting are bigger issues.

The 2016 Democratic presidential nominee, Hillary Clinton, was touring the country to promote her new book, which says she lost Wisconsin in the election because of the state’s voter ID law. She said it stopped 200,000 people from voting.

“I think this commission, what it’s trying to do, flies in the face of what this country is all about,” said Senate Minority Leader Charles E. Schumer, New York Democrat. “The real threat to election integrity comes not from voter fraud, but from foreign meddling and cyberattacks.”

Democrats also pushed back against implications of a report last week that found thousands of people who registered to vote on Election Day in New Hampshire never went back to get driver’s licenses or register vehicles.

Commission Vice Chairman Kris Kobach, Kansas secretary of state, wrote a column for Breitbart suggesting those were illegal out-of-state voters.

That drew a rebuke from two fellow secretaries of state serving on the voter commission.

Matthew Dunlap, Maine’s secretary of state, called it “a reckless statement to make,” and New Hampshire Secretary of State Bill Gardner said that while the numbers Mr. Kobach cited may be correct, the conclusions he draws about ineligible voters were wrong.

He said there are other reasons someone may have been eligible for same-day registration and to vote but didn’t need to change their address, get a license or register a car.

“Those facts don’t create the proof,” Mr. Gardner said.

As the commission searches for solutions, John Lott, president of the Crime Prevention Research Center, suggested that the federal government’s gun background check program, the Justice Department’s National Instant Criminal Background Check System, could be harnessed to try to weed out ineligible voters.

He said the system has most of the information registrars are interested in — chiefly citizenship status and criminal history — when they sign up voters.

Since liberal-leaning politicians generally support the background check system, Mr. Lott said, there is already a political consensus that could help tamp down objections Democrats might raise.

“It seems like it would solve a lot of the politician divisions that are there, and it has in the database the types of things you’d want to look at to determine if somebody is qualified for voting,” he told the commission.

The idea didn’t impress Mr. Dunlap, who said harnessing the gun system to handle voter checks would be “a sterling example of the laws of unintended consequences.”

The commission also heard from voting experts who said that declining election participation rates have complicated explanations, and there isn’t an easy solution such as mail-in voting.

“Some of the removals of barriers to voting are not panaceas,” said Andrew Smith, a political scientist at the University of New Hampshire.

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