T.R. Hollcroft’s Problem

Abstract

JN-25 was the primary World War II Japanese naval cipher. It was introduced in 1939 and evolved throughout the war, presenting US Navy codebreakers with a succession of challenges. When JN-25N-62 was introduced on 25 July 1944, one question that arose for US Navy codebreakers was the function of two digits in the starting point indicator: did they represent a pair of single-digit numbers or a single two-digit number? US Navy codebreakers knew Japanese cipher clerks often chose an additive in the leftmost column of a page of additives as the starting point for the string of text additives. This lack of randomness enabled an attack on the indicator. Navy codebreakers used a statistical test to decide between the two possibilities. Construction of the necessary probability tables was assigned to Temple Rice Hollcroft, a mathematician on the faculty of Wells College. Hollcroft’s problem is documented in an internal Navy history, but that history raises almost as many questions as it answers. This article explores the construction of Hollcroft’s tables, how they were used, and why Hollcroft was selected to construct the tables.