Welcome to the resource topic for
**2024/216**

**Title:**

Rate-1 Fully Local Somewhere Extractable Hashing from DDH

**Authors:**
Pedro Branco, Nico Döttling, Akshayaram Srinivasan, Riccardo Zanotto

**Abstract:**

Somewhere statistically binding (SSB) hashing allows us to sample a special hashing key such that the digest statistically binds the input at m secret locations. This hash function is said to be somewhere extractable (SE) if there is an additional trapdoor that allows the extraction of the input bits at the m locations from the digest.

```
Devadas, Goyal, Kalai, and Vaikuntanathan (FOCS 2022) introduced a variant of somewhere extractable hashing called rate-1 fully local SE hash functions. The rate-1 requirement states that the size of the digest is $m + \mathsf{poly}(\lambda)$ (where $\lambda$ is the security parameter). The fully local property requires that for any index $i$, there is a "very short" opening showing that $i$-th bit of the hashed input is equal to $b$ for some $b \in \{0,1\}$. The size of this opening is required to be independent of $m$ and in particular, this means that its size is independent of the size of the digest. Devadas et al. gave such a construction from Learning with Errors (LWE).
In this work, we give a construction of a rate-1 fully local somewhere extractable hash function from Decisional Diffie-Hellman (DDH) and BARGs. Under the same assumptions, we give constructions of rate-1 BARG and RAM SNARG with partial input soundness whose proof sizes are only matched by prior constructions based on LWE.
```

**ePrint:**
https://eprint.iacr.org/2024/216

See all topics related to this paper.

Feel free to post resources that are related to this paper below.

**Example resources include:**
implementations, explanation materials, talks, slides, links to previous discussions on other websites.

For more information, see the rules for Resource Topics .