The American war effort in WW2 was characterized by one of the largest compulsory drafts in history. A staggering 50 million men were registered and nearly 10 million inducted.

There was just one problem. Circa 1940, we didn’t know how to mass-produce penicilin and contraceptives weren’t considered an important public health tool. Syphilis - which earned the moniker The Great Imitator (owing to the wide variety of symptoms that victims exhibited), claimed 6 out of every 100,000 deaths. In fact, a mere 20 years before - in the 20s - Syphilis earned a spot among the top 10 killers in the US.

These conditions meant that every inductee was subjected to a blood test - a brutal exercise in logistics for a rapidly expanding military.

Robert Dorfman, a Harvard economist, produced an elegant process to cut down on the number of blood tests needed and in the process produced a seminal paper in the field of group testing.

In this post, we’ll derive the results from that paper - which as you’ll observe boils down to simple algebra.

Today, group testing is leveraged in several domains. We’ll look at one such application of this technique that solves a neat problem in cryptography.