Zero-Knowledge Proofs in Sublinear Space (2509.05326v1)

Abstract: Modern zero-knowledge proof (ZKP) systems, essential for privacy and verifiable computation, suffer from a fundamental limitation: the prover typically uses memory that scales linearly with the computation's trace length T, making them impractical for resource-constrained devices and prohibitively expensive for large-scale tasks. This paper overcomes this barrier by constructing, to our knowledge, the first sublinear-space ZKP prover. Our core contribution is an equivalence that reframes proof generation as an instance of the classic Tree Evaluation problem. Leveraging a recent space-efficient tree-evaluation algorithm, we design a streaming prover that assembles the proof without ever materializing the full execution trace. The approach reduces prover memory from linear in T to O(sqrt(T)) (up to O(log T) lower-order terms) while preserving proof size, verifier time, and the transcript/security guarantees of the underlying system. This enables a shift from specialized, server-bound proving to on-device proving, opening applications in decentralized systems, on-device machine learning, and privacy-preserving technologies.