That time the U.S. government banned a math book over national security

There is something fundamentally absurd about banning a math book.

Mathematical knowledge has a certain democratic nature, so to speak: it belongs to no one in particular, though we’re not always aware of it. “No one can own it, no one can claim ownership over a formula or an idea,” argues Edward Frenkel. In a landmark 1972 case the U.S. Supreme Court even had to conclude:

A scientific truth, or its mathematical expression, is not a patentable invention. … A principle, in the abstract, is a fundamental truth; an original cause; a motive; these cannot be patented, as no one can claim an exclusive right in any of them. … He who discovers a hitherto unknown phenomenon of nature has no right to a monopoly over it that the law recognizes.

Although Albert Einstein proposed it, supported by the efforts of so many others, E=mc² belongs to no one. Even so, mathematics isn’t exactly like physics — making that argument would require a detour through the foundations of math and taking a stand in the debate over platonism about its objects, i.e., whether its truths are discovered or invented — but it’s enough to acknowledge that most practitioners act as if mathematical objects have an independent reality, even if in some contexts they subscribe to formalist positions.

Cryptography is a branch of mathematics that draws on structures, theories, and algorithms — like algebra and number theory — to encode and protect information. Although today the word “crypto” is tossed around casually — mainly thanks to cryptocurrencies, but also because of digital encryption — for a long time cryptography was almost exclusively under the control of state agencies like the National Security Agency (NSA) in the United States, which maintained a strict monopoly on knowledge and research in the field, actively suppressing any open discussion, going so far as to restrict the circulation of math texts as if they were state secrets.

Although the history of efforts to secure communications — for spies, military leaders, and diplomats, but also of an industrial nature — can be traced back thousands of years to ancient Rome, it took on crucial importance with long-distance communications during the conflicts of the last century. To a large extent, the development of digital computing owes itself to the need to encrypt one’s own messages and decrypt those of the enemy.

After the pivotal role these capabilities played in World War II, states relied on the secrecy of their theoretical advances as a strategic advantage over their enemies. But in the 1970s, during the timid early years of what would become personal computing, a civilian quest began for the knowledge needed to develop strategies or methods to protect private information.

Although “nature loves to hide”, discoveries often happen independently. For instance, a few years after mathematicians working for British intelligence were forced to keep secret their invention of public-key cryptography, in 1976 two other American mathematicians arrived at the same result as their colleagues. Therein lies the beauty of mathematical knowledge: “You can hide a formula, but you can’t prevent others from discovering it,” Frenkel sums up.

In 1977, with the invention of the RSA algorithm, which not only allowed the exchange of encrypted messages without a prior shared secret key, but also let them be signed to verify their authenticity unambiguously, it became possible for anyone to communicate securely and verifiably, without relying on intermediaries or central authorities.

This milestone turned cryptography into a tool of individual liberty, which a decade later would give rise to the cypherpunk movement — whose name derives from the work of William Gibson — which, from a libertarian perspective, is grounded in the principles of decentralization, individual autonomy, and rejection of centralized authorities. These principles would, decades later, motivate the development of cryptocurrencies aimed at creating decentralized, censorship-resistant money.

Throughout the 1980s, despite the NSA’s persistent attempts to suppress any research, this movement grew notably through exchanges on pre-web discussion forums and conferences where ideas and experiments were shared. The NSA went so far as to invoke arms-trafficking regulations to control the “export” of cryptographic knowledge, aiming to prevent it from becoming popular beyond government use. In short: they were concerned about the existence of private communications the government lacked the technical ability to spy on.

This tension reached a breaking point in 1989, when Ralph Merkle, a researcher at Xerox PARC, received a suppression request from the NSA for a paper on encryption algorithms, citing national security concerns. The work, however, had made its way to John Gilmore, a hacker and civil liberties activist, who posted it on a discussion group, defying government control and rendering its censorship system useless. Within hours, thousands of people around the world had access to a copy of the document, both in digital form and in physical printouts.

In response, the NSA was forced to rescind its original request to suppress the publication, marking one of the first episodes in which the Internet imposed limits on attempts to control information — a turning point in the growing tension between intelligence agencies and the independent cryptographic community seeking the free flow of knowledge.

Gilmore was one of the early employees of Sun Microsystems, which left him with a small fortune when he left the company. In 1990, together with John Perry Barlow, Grateful Dead lyricist, he founded the Electronic Frontier Foundation (EFF), an NGO dedicated to defending civil liberties in the digital age, and he was particularly keen on ensuring that cryptographic knowledge became part of the public domain.

As Steven Levy recounts, when a few years later Gilmore became obsessed with obtaining a series of cryptography manuals written during World War II by William F. Friedman, the pioneer of cryptanalysis and a central figure in the creation of the NSA, he once again ran into the wall of government secrecy. These books had been declassified in 1975 but then reclassified in 1982 during the Reagan administration. His first attempt to obtain them using the Freedom of Information Act (FOIA) wasn’t even answered.

Gilmore’s intentions were always explicit: make copies and distribute them to promote knowledge of cryptography, an essential tool for protecting privacy in the nascent digital age — something unacceptable to the NSA, which consistently held the same mathematically untenable position: private communications must be vulnerable to the good guys (themselves) so they can protect us from the bad guys.

Meanwhile, Gilmore decided to sue the NSA, but when a friend tipped him off that he’d found two of the manuals in a couple of libraries, he informed the judge that these supposedly secret documents were already in circulation. Gilmore never imagined he would face the threat of prison just for borrowing a couple of books from a library, but as it turned out, certain mathematical knowledge was indeed forbidden.

The government notified him that distributing Friedman’s texts would violate the Espionage Act, carrying a possible sentence of up to ten years in prison. The NSA, the most powerful electronic spy agency on the planet, had effectively threatened to imprison someone for taking a couple of cryptography manuals from a public library. The dispute hit the press in November 1992 and two days later an NSA spokesperson announced that the agency had declassified the writings once again. But the government’s argument crumbled before an unbeatable logic: you cannot reclassify as secret something that is already public. You cannot put the genie back in the bottle.

The argument was that making these manuals, which were over fifty years old, public would endanger national security. Apparently some countries were still using encryption systems based on Friedman’s techniques, and if they discovered that the United States knew how to break them, they would change them. The fact that a foreign power might be using half-century-old methods described in manuals available at a public library in Virginia was an uncomfortable question the NSA preferred not to address.

This incident wasn’t just a squabble over some old manuals; it was a pivotal event in what would come to be known as the “crypto wars” — the clash of two irreconcilable worldviews. On one side, for the NSA, the art of encrypting and decrypting was a weapon, like missiles or tanks, and its control had to remain exclusively in the hands of the State (that is, the United States of America). Any dissemination of robust cryptographic knowledge was a threat capable of eroding its ability to surveil adversaries (and, as we later learned, citizens and allies, too). On this point they were right.

On the other side was the vision of the growing community of academics, hackers, and libertarians. For them, as Steven Levy chronicles in his book *Crypto* (2001), the migration of our lives to the digital domain — emails, banking transactions, private conversations — created an unprecedented surface of vulnerability. Privacy, a right that in the analog world was guaranteed with whispers, sealed envelopes, and locked doors, now required a new kind of protection: strong, widely available encryption free of arbitrary restrictions.

For the NSA, this ideal was a catastrophe. The notion that the ability to keep secrets even from the State could be a freely accessible tool, and that guys like Gilmore, armed with a library card and a photocopier, could stand up to them publicly and noisily, demanded a change in strategy for which they were not well prepared.

This clash of visions persists even today. The debate over cryptography has shifted, but the fundamental tension remains the same. Governments around the world, including that of the United States, insist on the need for “backdoors” in encryption systems. As Frenkel denounces, the NSA itself has been accused of deliberately undermining encryption standards by promoting mathematical formulas (like certain elliptic curves) that appear secure but harbor vulnerabilities known only to the agency.

A backdoor is, by definition, a universal weakness. You cannot build a door that opens only for the “good guys.” Any deliberate shortcut will be exploited, sooner or later, by those it was meant to keep out, making us all more vulnerable. Demanding weak cryptography is like proposing we all use locks that the police can open with a master key, forgetting that thieves can learn to make one, too.

The case of the Friedman manuals laid bare that security through obscurity is an illusion. True security in the digital world, as Shawn Rosenheim argues in *The Cryptographic Imagination* (1995), comes not from keeping knowledge secret, but from making it public, from subjecting algorithms to the scrutiny of thousands of minds in order to find and fix their flaws. This is the same argument that gets made over and over in the face of governmental ineptitude, as was the case with the Single Electronic Ballot in Argentina.

The path for civilian technology is open source, public scrutiny, strong cryptography. These are not whims propped up by unbounded curiosity, but a democratic necessity.

Mathematics doesn’t care about state secrets.

A first edition copy of Several Machine-Ciphers, Publication №20 from the Riverbank Laboratories, authored by pioneering cryptologist William F. Friedman.

This text was originally published in 2025 in Spanish.

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