On Black-Box Constructions of Time and Space Efficient Sublinear Arguments from Symmetric-Key Primitives
Theory of Cryptography(2023)
摘要
Zero-knowledge proofs allow a prover to convince a verifier of a statement without revealing anything besides its validity. A major bottleneck in scaling sub-linear zero-knowledge proofs is the high space requirement of the prover, even for NP relations that can be verified in a small space. In this work, we ask whether there exist complexity-preserving (i.e. overhead w.r.t time and space are minimal) succinct zero-knowledge arguments of knowledge with minimal assumptions while making only black-box access to the underlying primitives. We design the first such zero-knowledge system with sublinear communication complexity (when the underlying
$$\textsf {NP}$$
relation uses non-trivial space) and provide evidence why existing techniques are unlikely to improve the communication complexity in this setting. Namely, for every NP relation that can be verified in time T and space S by a RAM program, we construct a public-coin zero-knowledge argument system that is black-box based on collision-resistant hash-functions (CRH) where the prover runs in time
$$\widetilde{O}(T)$$
and space
$$\widetilde{O}(S)$$
, the verifier runs in time
$$\widetilde{O}(T/S+S)$$
and space
$$\widetilde{O}(1)$$
and the communication is
$$\widetilde{O}(T/S)$$
, where
$$\widetilde{O}()$$
ignores polynomial factors in
$$\log T$$
and
$$\kappa $$
is the security parameter. As our construction is public-coin, we can apply the Fiat-Shamir heuristic to make it non-interactive with sample communication/computation complexities. Furthermore, we give evidence that reducing the proof length below
$$\widetilde{O}(T/S)$$
will be hard using existing symmetric-key based techniques by arguing the space-complexity of constant-distance error correcting codes.
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关键词
space efficient sublinear arguments,black-box,symmetric-key
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