Paper 2024/392
Heuristic Ideal Obfuscation Based on Evasive LWR
Abstract
This paper introduces a heuristic ideal obfuscation scheme grounded in the lattice problems, which differs from that proposed by Jain, Lin, and Luo ([JLLW23], CRYPTO 2023). The approach in this paper follows a methodology akin to that of Brakerski, Dottling, Garg, and Malavolta ([BDGM20], EUROCRYPT 2020) for building indistinguishable obfuscation (iO). The proposal is achieved by leveraging a variant of learning with rounding (LWR) to build linearly homomorphic encryption (LHE) and employing {\em Evasive LWR} to construct multilinear maps. Initially, we reprove the hardness of LWR using the prime number theorem and the fixed-point theorem, showing that the statistical distance between $\lfloor As\rfloor_p$ and $\lfloor u\rfloor_p$ does not exceed $\exp\left(-\frac{n\log_2n\ln p}{\sqrt{5}}\right)$ when the security parameter $q>2^{n}p$. Additionally, we provide definitions for {\em Evasive LWR} and {\em composite homomorphic pseudorandom function} (cHPRF), and based on these, we construct multilinear maps, thereby establishing the ideal obfuscation scheme proposed in this paper.
Metadata
- Available format(s)
-
PDF
- Category
- Foundations
- Publication info
- Preprint.
- Keywords
- Ideal obfuscationSplit FHEMultilinear mapsLattice problem reductionEvasive Lattice
- Contact author(s)
-
arcsec30 @ 163 com
lyzhang @ mail xidian edu cn
laiqq @ snnu edu cn - History
- 2024-05-31: last of 2 revisions
- 2024-03-04: received
- See all versions
- Short URL
- https://ia.cr/2024/392
- License
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CC BY
BibTeX
@misc{cryptoeprint:2024/392,
author = {Zhuang Shan and Leyou Zhang and Qiqi Lai},
title = {Heuristic Ideal Obfuscation Based on Evasive {LWR}},
howpublished = {Cryptology {ePrint} Archive, Paper 2024/392},
year = {2024},
url = {https://eprint.iacr.org/2024/392}
}