Pairing-based Succinct Half-Chosen VOLE

Succinct Non-Interactive Half-Chosen VOLE allows a sender with a vector $\boldsymbol x$ of length $n$ and a receiver with a scalar $y$ to establish a pair of additive shares of $\boldsymbol x \cdot y$, by simultaneous exchange of succinct messages. Recent works construct NIHC-VOLE with $O(n^{2/3} \lambda)$ communication from various assumptions (Abram, Roy and Scholl, Eurocrypt 24) and poly-logarithmic communication from LWE (Abram, Malavolta and Roy, STOC 25).

We explore how bilinear pairings can improve group-based NIHC-VOLE schemes. • In the public setup setting, our scheme has online communication of $O(\sqrt{n \log n})$ group elements. The scheme relies on a new BDDH-like assumption. • In the designated receiver setting, our scheme has online communication of only 3 group elements and reusable offline communication of $O(n)$ group elements. The scheme relies on the bilinear power DDH assumption.