Paper 2026/1061

S4 Is All You Need

Abstract

A fully shuffled permutation of four cards suffices to implement 1-of-2 Oblivious Transfer at a rate of one transfer per shuffle. After dealing two cards to Alice and one to Bob, Alice deterministically selects item from a threefold partition of the edges of a tetrahedron, at which point OT is established. Unlike decades of 2-player computation results employing restricted permutations (as in den Boer's groundbreaking Five Card Trick) and artificial decks with repeated symbols, the "Tetrahedral OT" is the first to achieve two-party secret computations using a fully-shuffled set of unique elements. New "tenancy" and "narrowing" techniques are developed. Design patterns and protocol generation parameters are presented, along with some insightful but less efficient choices. The geometric symmetries behind the Tetrahedral OT protocol open up connections from Oblivious Transfer to Secret Key Exchange protocols as well. Decoupling information-theoretic permutations from computational one-wayness provides systematic access to broader and novel MPC protocol design, insight and simplification.