## CryptoDB

### How to Garble Mixed Circuits that Combine Boolean and Arithmetic Computations

Authors: Hanjun Li , University of Washington Tianren Liu , Peking University Search ePrint Search Google Slides EUROCRYPT 2024 The study of garbling arithmetic circuits is initiated by Applebaum, Ishai, and Kushilevitz [FOCS'11], which can be naturally extended to mixed circuits. The basis of mixed circuits includes Boolean operations, arithmetic operations over a large ring and bit-decomposition that converts an arithmetic value to its bit representation. We construct efficient garbling schemes for mixed circuits. In the random oracle model, we construct two garbling schemes: - The first scheme targets mixed circuits modulo some $N\approx 2^b$. Addition gates are free. Each multiplication gate costs $O(\lambda \cdot b^{1.5})$ communication. Each bit-decomposition costs $O(\lambda \cdot b^{2} / \log{b})$. - The second scheme targets mixed circuit modulo some $N\approx 2^b$. Each addition gate and multiplication gate costs $O(\lambda \cdot b \cdot \log b / \log \log b)$. Every bit-decomposition costs $O(\lambda \cdot b^2 / \log b)$. Our schemes improve on the work of Ball, Malkin, and Rosulek [CCS'16] in the same model. Additionally relying on the DCR assumption, we construct in the programmable random oracle model a more efficient garbling scheme targeting mixed circuits over $\mathbb Z_{2^b}$, where addition gates are free, and each multiplication or bit-decomposition gate costs $O(\lambda_{DCR} \cdot b)$ communication. We improve on the recent work of Ball, Li, Lin, and Liu [Eurocrypt'23] which also relies on the DCR assumption.
##### BibTeX
@inproceedings{eurocrypt-2024-33914,
title={How to Garble Mixed Circuits that Combine Boolean and Arithmetic Computations},
publisher={Springer-Verlag},
author={Hanjun Li and Tianren Liu},
year=2024
}