Communication with Extraterrestrial Intelligence: the NSA cryptologist paper

Lambros D. Callimahos was one of the most important figures in postwar American cryptology. A flautist by early training, he became a legendary instructor at the NSA, where he ran the agency advanced cryptanalysis course, the CA-400, that trained generations of codebreakers. He worked alongside William Friedman, the founder of modern American cryptanalysis. When a man of Callimahos's standing inside the NSA wrote about decoding alien messages, it was not a hobbyist's daydream. It was a senior practitioner applying the discipline of his agency to a problem he considered real and, in his framing, probably overdue.

The paper grew out of a panel discussion held at the 1965 IEEE Conference on Military Electronics in Washington, on September 23, 1965. Callimahos sat on that panel as the cryptologist. The other panelists were a linguist, a physicist, an astronomer, and John C. Lilly, the neuroscientist famous for attempting to communicate with dolphins. The moderator was the director of information services for the Air Force Office of Scientific Research. The paper was then published in the NSA internal journal, where it remained until declassification.

Callimahos begins from the scientific consensus of his day: that the galaxy almost certainly contains a vast number of stars capable of supporting life, and that advanced civilizations, if they exist, are probably far ahead of us. He reasons that any civilization trying to reach us would first send attention-getting signals, simple mathematical sequences such as the counting numbers or the primes, designed to stand out from random cosmic noise. He notes the work of Project Ozma, the 1960 attempt by astronomer Frank Drake to detect intelligent signals from two nearby stars, and the specific radio frequency, the 21 centimeter hydrogen line, that researchers proposed as a universal meeting point any technological civilization would recognize.

He then turns to his real subject. Once a signal is recognized, how do we extract meaning from it. Callimahos coins a phrase for this: "inverse cryptography." Ordinary cryptography hides meaning. Inverse cryptography is the opposite discipline, the art of designing a message to be as easy as possible for an unknown mind to understand. The burden, he argues, falls on the sender to be clever, not on the recipient to be ingenious. Mathematics is the natural starting point because number is the most universal concept available to any intelligence.

The paper does something most documents on this subject never attempt. It shows the work. Callimahos presents two fully decoded examples. The first is a raster message, a string of 1271 binary digits devised by Bernard Oliver after a 1961 conference at Green Bank. Because 1271 has only two prime factors, 31 and 41, the receiver is led to arrange the bits in a grid, and a picture emerges: a sun, eight planets, two figures identified as bisexual and mammalian, the chemistry of carbon-based life, and a figure pointing to the planet the senders inhabit.

The second example is Callimahos's own. He constructs a message of 30 transmissions using 32 arbitrary symbols, the kind of signal that might arrive from another world, and then walks through how a cryptologist would crack it: first recovering the integers, then arithmetic, then the concept of zero, then powers and roots, then the constants pi and e, and finally words and concepts, until the reader is, in his phrase, understanding "pure Venerean." He leaves the reader a challenge: to formulate questions such as the proof of Fermat's Last Theorem for transmission back. The full symbol key and solution are in the paper. They are transcribed on the primary documents page.

This is not a claim that aliens have visited. Callimahos makes no such claim, and neither does this site. What the document establishes is something quieter and harder to dismiss: that the United States signals intelligence agency took the prospect of extraterrestrial contact seriously enough that one of its master cryptologists published a technical treatment of how to decode an alien transmission, in the agency own classified journal, as a professional exercise. The interest was institutional. The treatment was rigorous. The document is authentic and released by the NSA itself. That is the record, and it is far stranger for being so sober.

The complete paper, transcribed word for word, including the opening declaration, the Project Ozma discussion, the Oliver raster message and its interpretation, Callimahos's own 30-transmission worked example, the full symbol and code-value key, and the encoded statements of Fermat's Last Theorem and Goldbach's Conjecture. First full searchable HTML transcription.