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**2024/781**

**Title:**

Doubly-Efficient Batch Verification in Statistical Zero-Knowledge

**Authors:**
Or Keret, Ron D. Rothblum, Prashant Nalini Vasudevan

**Abstract:**

A sequence of recent works, concluding with Mu et al. (Eurocrypt, 2024) has shown that every problem \Pi admitting a non-interactive statistical zero-knowledge proof (NISZK) has an efficient zero-knowledge batch verification protocol. Namely, an NISZK protocol for proving that x_1,\dots,x_k \in \Pi with communication that only scales poly-logarithmically with k. A caveat of this line of work is that the prover runs in exponential-time, whereas for NP problems it is natural to hope to obtain a doubly-efficient proof - that is, a prover that runs in polynomial-time given the k NP witnesses.

```
In this work we show that every problem in $NISZK \cap UP$ has a doubly-efficient interactive statistical zero-knowledge proof with communication $poly(n,\log(k))$ and $poly(\log(k),\log(n))$ rounds. The prover runs in time $poly(n,k)$ given access to the $k$ UP witnesses. Here $n$ denotes the length of each individual input, and UP is the subclass of NP relations in which YES instances have unique witnesses.
This result yields doubly-efficient statistical zero-knowledge batch verification protocols for a variety of concrete and central cryptographic problems from the literature.
```

**ePrint:**
https://eprint.iacr.org/2024/781

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