Consider the following strategic dilemma. You are a superpower that hopes to convert other nations to principles you hold vital—these might be individual liberty, private property, and free markets. There is another superpower out there that is hoping to do the same thing, to persuade other nations to embrace its principles—for example, social equality, state ownership, and centralized planning.

One day, you realize that this rival superpower has been busy creating international organizations and staging world congresses and festivals in the name of peace and democracy, and inviting people from other nations to participate.

These organizations and festivals are fronts. Their membership, their programs, and the political positions they enthusiastically adopt are all clandestinely orchestrated by the rival superpower, which is pumping large amounts of money into them. What’s more, in your view that rival superpower is not a peace-loving democracy at all. It’s a totalitarian regime. Yet its slogans attract unwary writers and artists, intellectuals, students, organized labor—people who believe in world peace and international coöperation.

You believe in those things, too. But you think that the slogans are being used to advance your rival’s interests, one of which is to rob you of your superpowers. What do you do? Doing nothing is not an option. Remember, you are a superpower.

The obvious response is to create your own international organizations and sponsor your own world congresses and festivals, and use them to promote your interests. Sadly, however, you cannot do this in a public and transparent way. For it happens that your citizens are not all that taken with the ideals of world peace and international coöperation, and they would not be pleased to see you spend their tax dollars to support the kind of people who advance that agenda. They would prefer to see their tax dollars spent on defense. In fact, they would prefer for there to be no tax dollars at all.

There is also the problem that one of your principles as a superpower is the belief that governments should not interfere with the activities of voluntary associations, such as writers’ congresses and student groups. You don’t believe in fronts. This is a key point of difference between you and your rival superpower. So your hands appear to be tied.

Unless you could do it all in secret. Suppose you directed taxpayer dollars through back channels, disguised as gifts from private benefactors and foundations, to organizations that operated internationally, and that reached out to groups in other countries in the name of the principles you believe in. You would want to be sure that the people running those organizations either didn’t know where the money was coming from or could be trusted to keep it a secret. You might need to pull strings occasionally to get the right people in charge and the right positions enthusiastically adopted.

Wouldn’t that be like creating fronts? Sort of. But here’s the thing: fundamentally, everyone would be on the same page. They just might not be knowingly on the same page. No one would be forced to do or say anything. After you succeeded in stripping your rival of its superpowers, there would no longer be a need for secrecy. Until that day arrived, however, national security might demand this tiny bite out of the principle of transparency. The only people who could object would be people who were already on the wrong side.

After the Second World War, our superpower solved this dilemma in exactly this way and on exactly this line of reasoning. From the more or less official start of the Cold War, Harry Truman’s speech to Congress in March, 1947, announcing his policy “to support free peoples who are resisting attempted subjugation by armed minorities or by outside pressures”—that is, Communist aggression—the United States created fronts and secretly infiltrated existing nongovernmental organizations in order to advance American interests abroad.

Almost exactly twenty years after Truman’s speech, in February, 1967, the government’s cover was spectacularly blown by a college dropout. The dropout’s name was Michael Wood, and the operation he exposed was the C.I.A.’s covert use of an organization called the National Student Association. The revelation had a cascading effect, and helped to mark the end of the first phase of the Cold War.

The C.I.A. had its eye on the N.S.A. from the start—both were born in 1947, a few months after Truman’s speech—and the relationship gained steadily in strength and intimacy until the day the secret became public. Its story is now told in detail for the first time, in Karen M. Paget’s “Patriotic Betrayal” (Yale).

“Patriotic Betrayal” is an amazing piece of research. Paget has industriously combed the archives and interviewed many of the surviving players, including former C.I.A. officials. And Paget herself is part of the story she tells. In 1965, her husband, a student-body president at the University of Colorado, became an officer in the N.S.A., and, as a spouse, she was informed of the covert relationship by two former N.S.A. officials who had become C.I.A. agents.

She was sworn to secrecy. The penalty for violating the agreement was twenty years. Paget describes herself back then as “an apolitical twenty-year-old from a small town in Iowa,” and she says that she was terrified. Fifty years later, she is still angry. She has channelled her outrage into as scrupulous an investigation of the covert relationship as the circumstances allow.

One circumstance is the fact that a good deal of material is classified. Paget was able to fish up bits and pieces using the Freedom of Information Act. But most of the iceberg is still underwater, and will probably remain there. So there is sometimes an aura of vagueness around who was calling the tune and why.

The vagueness was also there by design. It was baked into the covert relationship. There was a lot of winking and nodding; that’s what helped people believe they were on the same page. But it means that much of the history of what passed between the C.I.A. and the N.S.A. is irrecoverable. Still, “Patriotic Betrayal” is a conscientious attempt to take the full measure of an iconic piece of Cold War subterfuge.

It’s a dense book. Readers will be glad for the three-page guide in the back to abbreviations and acronyms. (There are also nearly ninety pages of endnotes, with more references accessible online.) Organizationally, the N.S.A.-C.I.A. affair was quite complex. There were a number of quasi-independent parts—another reason, besides the secrecy, that it was hard to see what was really going on.

The parts included the World Federation of Democratic Youth, or W.F.D.Y., a Soviet front organization created right after the war; the International Union of Students, or I.U.S., formed at a world congress of students in Prague in 1946, with a Czech Communist elected president; and the N.S.A. itself, which was founded at a student convention in Madison, Wisconsin, in 1947, in order to represent the United States in the I.U.S.

The Madison convention also created an N.S.A. subcommittee on international affairs and gave it authority to deal with international issues. The key move was the separation of the main N.S.A. office, which was in Madison, from the international division, which was housed in Cambridge, Massachusetts. It was the Cambridge branch of the N.S.A. that received most of the C.I.A.’s funding and did most of the C.I.A.’s bidding. Madison was kept out of the loop.