Pairing-based Succinct Half-Chosen VOLE

Liqiang Liu; Tianren Liu; Luojian Wei

Paper 2026/1922

Pairing-based Succinct Half-Chosen VOLE

Liqiang Liu, Peking University

Tianren Liu

, Peking University

Luojian Wei, Peking University

Abstract

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.

Metadata

Available format(s): PDF
Category: Cryptographic protocols
Publication info: Preprint.
Keywords: Bilinear Pairings Vector Oblivious Linear Evaluation
Contact author(s): lql @ pku edu cn
trl @ pku edu cn
luojianwei @ pku edu cn
History: 2026-09-10: approved; 2026-09-08: received; See all versions
Short URL: https://ia.cr/2026/1922
License: CC BY

BibTeX

@misc{cryptoeprint:2026/1922,
      author = {Liqiang Liu and Tianren Liu and Luojian Wei},
      title = {Pairing-based Succinct Half-Chosen {VOLE}},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/1922},
      year = {2026},
      url = {https://eprint.iacr.org/2026/1922}
}