Time-Synchronized Mutual Authentication via Orbital State Functions

Orbital State Function (OSF) based Time-Synchronized Mutual Authentication Protocol We introduce the Orbital State Function (OSF), a continuous-time keyed primitive whose evaluation traces a deterministic orbit on a 3-dimensional sphere as a function of wall-clock time. An OSF is parameterized by a secret key consisting of an initial position, a rotation axis, and an angular velocity; given only the current time, its output at the next microsecond is computationally unpredictable to any adversary lacking the key, despite the function being deterministic. Built on any OSF satisfying a min-entropy condition, we construct a 3-round time-synchronized mutual authentication protocol in which each party proves knowledge of its peer’s OSF by predicting the peer’s current state. Wall-clock time serves as an implicit challenge, eliminating the explicit challenge–response round trip of classical schemes. Under the random oracle model for the hash commitment, we prove authentication unforgeability with adversary advantage bounded by qH · 2⁻λ, where λ is the OSF’s output min-entropy. We instantiate the OSF concretely via quaternion rotation on a spherical shell in R³, parameterized by seven CSPRNG-generated floating-point values (a unit axis, an angular velocity, and a 3-dimensional initial position). A careful entropy analysis yields output min-entropy λ ≥ 159 bits, exceeding the 128-bit level of AES-128. Session data keys are derived via ephemeral Diffie–Hellman embedded in the same three rounds, providing forward secrecy. Authentication security reduces only to hash pre-image resistance and OSF key entropy; it is independent of integer factorization and discrete logarithm assumptions. Under the quantum random oracle model, the forgery advantage is bounded by O(qH² / 2^λ) via Grover’s algorithm, giving 79-bit post-quantum security for λ = 159. A deployed TypeScript implementation achieves sub-millisecond state computation and under 50ms mutual authentication on commodity hardware.