Algebraic Cipher Types: Confidentiality Trade-offs in Type Constructors over Trapdoor Computing

I study the confidentiality costs of applying products, sums, and function types to cipher values. The paper examines the trade-off between hiding a sum type’s tag and allowing an untrusted machine to pattern-match on it, then uses orbit closure to bound the information exposed by available operations. It describes expression-tree and cipher-machine realizations and evaluates a cipher Boolean specialization on a 20 Newsgroups search task. The PDF below contains the full argument and its assumptions.