International Association for Cryptologic Research

International Association
for Cryptologic Research


Efficient Laconic Cryptography from Learning With Errors

Nico Döttling , Helmholtz Center for Information Security (CISPA)
Dimitris Kolonelos , IMDEA Software Institute & Universidad Politécnica de Madrid
Russell W. F. Lai , Aalto University
Chuanwei Lin , Aarhus University
Giulio Malavolta , Max Planck Institute for Security and Privacy
Ahmadreza Rahimi , Max Planck Institute for Security and Privacy
DOI: 10.1007/978-3-031-30620-4_14 (login may be required)
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Presentation: Slides
Conference: EUROCRYPT 2023
Abstract: Laconic cryptography is an emerging paradigm that enables cryptographic primitives with sublinear communication complexity in just two messages. In particular, a two-message protocol between Alice and Bob is called \emph{laconic} if its communication and computation complexity are essentially independent of the size of Alice's input. This can be thought of as a dual notion of fully-homomorphic encryption, as it enables ``Bob-optimized'' protocols. This paradigm has led to tremendous progress in recent years. However, all existing constructions of laconic primitives are considered only of \emph{theoretical interest}: They all rely on non-black-box cryptographic techniques, which are highly impractical. This work shows that non-black-box techniques are not necessary for basic laconic cryptography primitives. We propose a \emph{completely algebraic} construction of laconic encryption, a notion that we introduce in this work, which serves as the cornerstone of our framework. We prove that the scheme is secure under the standard Learning With Errors assumption (with polynomial modulus-to-noise ratio). We provide proof-of-concept implementations for the first time for laconic primitives, demonstrating the construction is indeed practical: For a database size of $2^{50}$, encryption and decryption are in the order of single digit \emph{milliseconds}. Laconic encryption can be used as a black box to construct other laconic primitives. Specifically, we show how to construct: \begin{itemize} \item Laconic oblivious transfer \item Registration-based encryption scheme \item Laconic private-set intersection protocol \end{itemize} All of the above have essentially optimal parameters and similar practical efficiency. Furthermore, our laconic encryption can be preprocessed such that the online encryption step is entirely combinatorial and therefore much more efficient. Using similar techniques, we also obtain identity-based encryption with an unbounded identity space and tight security proof (in the standard model).
  title={Efficient Laconic Cryptography from Learning With Errors},
  author={Nico Döttling and Dimitris Kolonelos and Russell W. F. Lai and Chuanwei Lin and Giulio Malavolta and Ahmadreza Rahimi},