The classified mathematical papers of A. A. Albert: a glimpse into the application of mathematics to cryptologic problems during the 1950s and 1960s

Abstract

Abraham Adrian Albert “A cubed” (1905–1972) was an algebraist best known academically for his study of associative and non-associative algebras. By the 1940s he had also developed an interest in cryptology and its relationship to mathematics. Throughout the following two decades, Albert would participate in several mathematics programs to study and advise on cryptanalysis. In particular, Albert’s work with the National Security Agency (NSA) set a framework for the development of cryptology as a mathematical discipline. This research aims to present a timeline for and the breadth of Albert’s promotion of cryptology in the post-WWII American mathematical community and to examine, for the first time, reports Albert authored under contract with the NSA. In doing so, we hope to better understand the relationship between the NSA and academic mathematicians at the time of writing. The reports, released in 2020 by the NSA in response to a 2010 Freedom of Information Act request, have been arranged by the author into eleven collections based on content. Each collection will be introduced with their ideas and results given in a roughly chronological order. These collections span ideas in group theory, field theory, matrix algebra, and geometry, most often with application to cryptological systems.