Paper 2024/1532
Bitwise Garbling Schemes --- A Model with $\frac{3}{2}\kappa$-bit Lower Bound of Ciphertexts
Abstract
At Eurocrypt 2015, Zahur, Rosulek, and Evans proposed the model of Linear Garbling Schemes. This model proved a $2\kappa$-bit lower bound of ciphertexts for a broad class of garbling schemes. Since then, several methods have been developed that bypass this lower bound, albeit with a notable limitation: Their reliance on specifically correlated input wire labels restricts their applicability across most gates. At Crypto 2021, Rosulek and Roy presented the innovative "three-halves" garbling scheme in which AND gates cost $1.5\kappa+5$ bits and XOR gates are free. A noteworthy aspect of their scheme is the slicing-and-dicing technique, which is applicable universally to all AND gates when garbling a boolean circuit. Following this revelation, Rosulek and Roy presented several open problems. Our research primarily addresses one of them: ``Is $1.5\kappa$ bits optimal for garbled AND gates in a more inclusive model than Linear Garbling Schemes?'' In this paper, we propose the Bitwise Garbling Schemes, a model that seamlessly incorporates the slicing-and-dicing technique. Our key revelation is that $1.5\kappa$ bits is indeed optimal for arbitrary garbled AND gates in our model. Since Rosulek and Roy also suggested another problem which questions the necessity of free-XOR, we explore constructions without free-XOR and prove a $2\kappa$-bit lower bound. Therefore, sacrificing compatibility with free-XOR does not lead to a more efficient scheme.
Metadata
- Available format(s)
- Category
- Cryptographic protocols
- Publication info
- Preprint.
- Keywords
- Garbled circuit2PCLinear garbling scheme
- Contact author(s)
-
xf555233 @ mail ustc edu cn
hghu2005 @ ustc edu cn
xuchangh @ mail ustc edu cn - History
- 2024-10-04: approved
- 2024-09-30: received
- See all versions
- Short URL
- https://ia.cr/2024/1532
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2024/1532, author = {Fei Xu and Honggang Hu and Changhong Xu}, title = {Bitwise Garbling Schemes --- A Model with $\frac{3}{2}\kappa$-bit Lower Bound of Ciphertexts}, howpublished = {Cryptology {ePrint} Archive, Paper 2024/1532}, year = {2024}, url = {https://eprint.iacr.org/2024/1532} }