I Prove, Therefore I Am: Spatiotemporal Multi-Party Computation
Researchers propose spatiotemporal MPC that keeps location and time private yet physically consistent.
The paper initiates spatiotemporal multiparty computation, where private inputs can include physical facts such as location, time, or trajectory. It defines arguments of spatiotemporal knowledge so an extractor recovers a point only if the prover can complete an auxiliary physical verification protocol. Constructions provide UC-secure commit-and-prove under LWE against quantum provers without pre-shared entanglement, and in the QROM against provers with unbounded entanglement. UC-secure spatiotemporal MPC then follows from semi-honest post-quantum MPC, including quantum functionalities with classical spatiotemporal input.
- Defines UC security for spatiotemporal multiparty computation.
- CRS construction uses LWE against quantum provers.
- QROM variant allows unbounded pre-shared entanglement.
- UC spatiotemporal MPC follows from semi-honest post-quantum MPC.
Full article241 words · extracted from arxiv.org · click to collapse
Secure multiparty computation (MPC) enables mutually distrustful parties to compute on private digital inputs. We initiate the study of spatiotemporal MPC, extending this paradigm to functionalities whose inputs additionally depend on physical facts such as the parties' locations, times, or trajectories. Such protocols must simultaneously hide spatiotemporal information and ensure its physical consistency: a malicious party should not be able to make the functionality operate on a spatiotemporal input inconsistent with its actual physical state. The main conceptual challenge is to formulate extraction of spatiotemporal information within the simulation-based security framework. We introduce arguments of spatiotemporal knowledge, following the principle "I prove, therefore I am:" rather than defining physical presence directly through a mathematical relation, we define it operationally through the ability to complete a sound spatiotemporal verification protocol. Accordingly, an extractor recovers a spatiotemporal point from a successful prover and certifies its physical validity by using the extracted prover to succeed in an auxiliary spatiotemporal verification protocol. Building on this notion, we define universally composable (UC) security for spatiotemporal MPC, capturing privacy, physical consistency, and composability. We provide constructions achieving this new MPC notion. We first construct UC-secure commit-and-prove of spatiotemporal knowledge: in the CRS model under LWE against quantum provers without pre-shared entanglement, and in the QROM against quantum provers with unbounded pre-shared entanglement. Using these protocols, we obtain UC-secure spatiotemporal MPC from semi-honest post-quantum MPC. We also extend our framework to support quantum functionalities with classical spatiotemporal input.
Text extracted automatically; images, tables and formatting may be missing. Original: https://arxiv.org/abs/2609.26448