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• W4313002842 abstract "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." @default.
• W4313002842 created "2023-01-05" @default.
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• W4313002842 date "2022-01-01" @default.
• W4313002842 modified "2023-10-18" @default.
• W4313002842 title "On Black-Box Constructions of Time and Space Efficient Sublinear Arguments from Symmetric-Key Primitives" @default.
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• W4313002842 doi "https://doi.org/10.1007/978-3-031-22318-1_15" @default.
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