Nearly three years after NSA whistleblower Edward Snowden gave journalists his trove of documents on the intelligence community’s broad and powerful surveillance regime, the public is still missing some crucial, basic facts about how the operations work.

Surveillance researchers and privacy advocates published a report on Wednesday outlining what we do know, thanks to the period of discovery post-Snowden — and the overwhelming amount of things we don’t.

The NSA’s domestic surveillance was understandably the initial focus of public debate. But that debate never really moved on to examine the NSA’s vastly bigger foreign operations.

“There has been relatively little public or congressional debate within the United States about the NSA’s overseas surveillance operations,” write Faiza Patel and Elizabeth Goitein, co-directors of the Brennan Center for Justice’s Liberty and National Security Program, and Amos Toh, legal adviser for David Kaye, the U.N. special rapporteur on the right to freedom of opinion and expression.

The central guidelines the NSA is supposed to follow while spying abroad are described in Executive Order 12333, issued by President Ronald Reagan in 1981, which the authors describe as “a black box.”

Just Security, a national security law blog, and the Brennan Center for Justice are co-hosting a panel on Thursday on Capitol Hill to discuss the policy, where the NSA’s privacy and civil liberties officer, Rebecca Richards, will be present.

And the independent government watchdog, the Privacy and Civil Liberties Oversight Board, which has authored in-depth reports on other NSA programs, intends to publish a report on 12333 surveillance programs “this year,” according to spokesperson Jen Burita.

In the meantime, the authors of the report came up with a list of questions they say need to be answered to create an informed public debate.

1. How far does the law go?

The authors ask: How does the NSA actually interpret the law — most of which is public — and use it to justify its tactics? Are there any other laws governing overseas surveillance that are still hidden from public view?

When Congress discovered how the NSA was citing Section 215 of the Patriot Act as giving it the authority to vacuum up massive amounts of information about American telephone calls, many were shocked. One of the Patriot Act’s original authors, Rep. Jim Sensenbrenner, R-Wis., has repeatedly said the NSA abused what was meant to be a narrow law.

“The public deserves to know how the agencies interpret their duties and obligations under the Constitution and international law,” the authors write.

2. Who’s watching the spies?

How can we know there’s proper oversight of the intelligence community, both internally and through Congress? Does Congress even know what it’s funding, especially when intelligence work is contracted out to the private sector?

Lawmakers have complained that they learned more about NSA spying from the media and Snowden than from classified hearings.

3. How much foreign spying ends up in domestic courts?

The authors wonder how evidence collected through foreign spying is used in court, and whether or not “targets” of the surveillance are told about the NSA’s search when that search finds data that can be used against them.

Officials told New York Times reporter Charlie Savage that “in practice … the government already avoids” introducing evidence obtained directly from 12333 intercepts “so as not to have to divulge the origins of the evidence in court.” “But the officials contend,” Savage wrote, “that defendants have no right to know if 12333 intercepts provided a tip from which investigators derived other evidence.”

4. How many words don’t mean what we think they mean?

Some of the report’s questions focus on the NSA’s use of language when it describes different programs. Though words like “collection” and “gathering” sound synonymous to us, the NSA could be using them differently, leading to misinterpretation of what the agency is actually doing. “Is the term ‘collection’ interpreted differently from the terms ‘interception,’ ‘gathering,’ and ‘acquisition’?” the authors ask.

5. Where does it end?

When the NSA says a search is “targeted,” could the agency still be sweeping up a lot of information? And not just about foreigners?

Does the agency use vague search terms like “ISIS” or “nuclear” when combing through communications, thereby grabbing up data from millions of innocent people simply discussing the news?

And how much American data is swept up, either on purpose or incidentally, when Americans talk with friends overseas, or their messages are routed through other countries due to the way the internet works?

“The fact that [12333 programs] are conducted abroad rather than at home makes little difference in an age where data and information flows are unconstrained by geography, and where the constitutional rights of Americans are just as easily compromised by operations in London as those in Los Angeles,” the authors write.

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