She warned state and county officials “further delay is not tolerable” in “confronting and tackling the challenges before the state’s election balloting system.”

The motion was filed in August by election integrity advocates seeking to compel Georgia Secretary of State Brian Kemp to abandon the state’s centrally run system of paperless electronic voting. They argued a failure to do so would deprive Georgia’s 6.8 million voters of their constitutional right to vote and the machines themselves were vulnerable to hacking — especially by foreign governments like Russia.

Switching to paper at this late date, state and county officials argued last week in court, would throw the election into chaos and cause voter confusion. The state has 2,600 precincts across 159 counties.

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The judge was sympathetic to the plaintiffs’ arguments about security, but in the end felt the risks of converting the system with fewer than eight weeks before Election Day outweighed the security threat.

“While [the] plaintiffs have shown the threat of real harms to their constitutional interests, the eleventh-hour timing of their motions and an instant grant of the paper ballot relief requested could just as readily jeopardize the upcoming elections, voter turnout, and the orderly administration of the election,” Totenberg wrote in a 46-page opinion.

The ruling comes as the nation is gripped by concern Russia or other foreign governments will interfere in this year’s election as Moscow did in 2016. As a result, warnings from experts — including the National Academies of Sciences — about the vulnerabilities of computerized voting machines have become more insistent.

“With this ruling behind us, we will continue our preparations for a secure, orderly election in November and move forward with [a bipartisan commission’s] work to responsibly upgrade Georgia’s secure — but aging — voting system,” Kemp said in a statement Tuesday. “As I have said many times over, our state needs a verifiable paper trail, but we cannot make such a dramatic change this election cycle.”

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Though Totenberg denied the motion for a preliminary injunction for November, she has not yet ruled on the underlying claims, which seek to wean Georgia entirely off paperless touch screen machines.

And she vowed to expedite the schedule.

“The 2020 elections are around the corner,” she said. “If a new balloting system is to be launched in Georgia in an effective manner, it should address democracy’s critical need for transparent, fair, accurate and verifiable election processes that guarantee each citizen’s fundamental right to cast an accountable vote.”

The plaintiffs said they will continue to press their claims.

“We are not deterred in our fight for the right to vote, for that is the heart of this matter,” said Donna Price, director of Georgians for Verified Voting, one of two groups that brought the legal action.

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“We fully expect to prevail in the end,’’ said Robert A. McGuire, an attorney for the plaintiff group Coalition for Good Governance.

The judge noted Georgia, the first state in the country to adopt direct-recording electronic (DRE) touch screen machines in 2002, is now one of only five states in which electronic voting is entirely paperless — with no independent paper ballot or audit record.

The plaintiffs last week called expert witnesses who testified to the problems with such machines. Computer scientist Alex Halderman of the University of Michigan demonstrated for the court how a malware-laced memory card inserted into a DRE machine of the sort Georgia uses can alter election results.

The plaintiffs also drew on written testimony from computer expert Logan Lamb, who had alerted the executive director of the state’s Center for Election Systems of a separate vulnerability in a server that forms part of the election system. He discovered that flaw — and the exposure online of the personal data of more than 6 million voters — in August 2016, three months before the presidential election. Six months later, both problems persisted, Lamb said.

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The plaintiffs “shine a spotlight on the serious security flaws and vulnerabilities in the state’s DRE system — including unverifiable election results, outdated software susceptible to malware and viruses and a central server that was already hacked multiple times,” wrote Totenberg, a judge in the Northern District of Georgia.

Yet those arguments “have hardly been rebutted” by the defendants “except via characterizations of the issues raised as entirely hypothetical and baseless.”

She chided the defendants for having “buried their heads in the sand” on the security problems.

“The defendants may have won this battle, but they’re ultimately going to lose the war because the judge will ensure that a secure, verifiable system is in place for the next elections in 2020,” said David Cross, an attorney for Georgians for Verified Voting.