By David E. Sanger, Reid J. Epstein and Michael Wines

Amid growing warnings about the security of American voting systems, many states are rushing to address vulnerabilities exposed by the 2016 election, even as intelligence officials worry they are fighting the last battle and are not sufficiently focused on a new generation of threats headed into 2020.

Delaware has replaced its voting machines to assure paper backup that would provide a record in case of a breach. South Carolina’s State Election Commission said this month that it would introduce a paper-based voting system in January and planned to “build additional layers of security designed to harden the new system.”

Yet Florida, home of the United States’ best-known presidential balloting problems, like hanging chads in 2000 and still mysterious Russian activity in 2016, once again seems far behind.

And the fear among American intelligence officials is that the federal government and the 50 states may be making the classic mistake of believing their adversaries will use the same techniques again.

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“No one expects the Russians will use their old playbook” in the next election, said Suzanne Spaulding, who oversaw election security at the Department of Homeland Security during the Obama administration and is now looking at how Russia is expanding its targets to undermine confidence in the American judicial system.

Other officials point to evidence that Iran, having seen how cheap and easy it is to create election-year chaos in a Western democracy, is already experimenting with the possibilities.

So while the states are thinking about how to ensure every voter can confirm their selections on paper, and in the best case track an encrypted ballot to make sure it is counted, federal officials are war-gaming emerging risks.