Paper 2025/605

Laconic Cryptography with Preprocessing

Abstract

Laconic cryptography focuses on designing two-message protocols that allow secure computation on large datasets while minimizing communication costs. While laconic cryptography protocols achieve asymptotically optimal communication complexity for many tasks, their concrete efficiency is prohibitively expensive due to the heavy use of public-key techniques or the non-black-box of cryptographic primitives. In this work, we initiate the study of "laconic cryptography with preprocessing", introducing a model that includes an offline phase to generate database-dependent correlations, which are then used in a lightweight online phase. These correlations are conceptually simple, relying on linear-algebraic techniques. This enables us to develop a protocol for private laconic vector oblivious linear evaluation (plvOLE). In such a protocol, the receiver holds a large database $$, and the sender has two messages $$ and $$, along with an index $$. The receiver learns the value $$ without revealing other information. Our protocol, which draws from ideas developed in the context of private information retrieval with preprocessing, serves as the backbone for two applications of interest: laconic private set intersection (lPSI) for large universes and laconic function evaluation for RAM-programs (RAM-LFE). Based our plvOLE protocol, we provide efficient instantiations of these two primitives in the preprocessing model.

Note: This work replaces https://eprint.iacr.org/2024/1555. This is a repost, as the techniques in this work have substantially changed.