## 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 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 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 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 milliseconds. Laconic encryption can be used as a black box to construct other laconic primitives. Specifically, we show how to construct: Laconic oblivious transferRegistration-based encryption schemeLaconic private-set intersection protocol 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).

Original language | English |
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Title of host publication | Advances in Cryptology – EUROCRYPT 2023 - 42nd Annual International Conference on the Theory and Applications of Cryptographic Techniques, 2023, Proceedings |

Editors | Carmit Hazay, Martijn Stam |

Publisher | Springer |

Pages | 417-446 |

Number of pages | 30 |

ISBN (Print) | 978-3-031-30619-8 |

DOIs | |

Publication status | Published - 2023 |

MoE publication type | A4 Conference publication |

Event | Annual International Conference on the Theory and Applications of Cryptographic Techniques - Lyon, France Duration: 23 Apr 2023 → 27 Apr 2023 Conference number: 42 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Publisher | Springer |

Volume | 14006 LNCS |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Conference

Conference | Annual International Conference on the Theory and Applications of Cryptographic Techniques |
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Abbreviated title | EUROCRYPT |

Country/Territory | France |

City | Lyon |

Period | 23/04/2023 → 27/04/2023 |