NSA Releases 1966 Secret Study on “Coupon Collecting and Cryptology” After Nine-Year FOIA Wait

The NSA released a 1966 study titled “Coupon Collecting and Cryptology” after nine years of FOIA requests. The paper was written by Marie Capozza and published in the NSA Technical Journal in the Fall of 1966. It examines the coupon collector’s problem, a classic probability question about how long it takes to collect all types of coupons. The study was made publicly available through FOIA, despite previous attempts to locate a copy.

The study details how the coupon collector’s problem applies to cryptology, specifically testing whether sequences used in cryptographic systems behave randomly. It uses mathematical models to determine the expected number of selections needed to collect all possible symbols. For example, with ten possible coupons, the expected number of selections is approximately 29.29. The same principles apply to decimal digits and 26 letters. The paper also discusses how these models can be used to test the randomness of sequences in cryptographic systems.

The study’s findings are relevant to cryptologists and security professionals, as they provide a framework for evaluating the randomness of generated sequences. It explains that while the coupon collector’s problem is a theoretical model, it can be used to assess the statistical behavior of real-world sequences. The paper also highlights how the methodology is not unique to the NSA, as Robert E. Greenwood previously used similar techniques in 1955. The study’s practical significance lies in its ability to detect non-random behavior in random-number generators, which is crucial for ensuring cryptographic security.

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