Laconic cryptography focuses on designing two-message protocols that allow secure computation over 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 heavy use of public-key techniques or non-black-box cryptographic primitives. In this work, we initiate the study of \emph{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 $\mathsf{DB}$ , and the sender has two messages $v$ and $w$ along with an index $i$ . The receiver learns the value $v \cdot \mathsf{DB}_i + w$ without revealing any 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 on our plvOLE protocol, we provide efficient instantiations of these two primitives in the preprocessing model.Laconic cryptography focuses on designing two-message protocols that allow secure computation over 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 heavy use of public-key techniques or non-black-box cryptographic primitives. In this work, we initiate the study of \emph{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 $\mathsf{DB}$, and the sender has two messages $v$ and $w$ along with an index $i$. The receiver learns the value $v \cdot \mathsf{DB}_i + w$ without revealing any 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 on our plvOLE protocol, we provide efficient instantiations of these two primitives in the preprocessing model.

Jun 23, 20260 citations

The Future of Cryptography

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Public-Key Encryption with Quantum Keys

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arXiv:2306.07698Lecture notes in computer scienceJan 1, 202321 citations

\mathsf{DB}

, and the sender has two messages

v

and

w

along with an index

i

. The receiver learns the value

v \cdot \mathsf{DB}_i + w

without revealing any 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 on our plvOLE protocol, we provide efficient instantiations of these two primitives in the preprocessing model.