Paper 2024/392

Heuristic Ideal Obfuscation Based on Evasive LWR

Zhuang Shan, School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
Leyou Zhang, School of Mathematics and Statistics, Xidian University, Xi’an 710126, China
Qiqi Lai, School of Computer Science, Shaanxi Normal University, Xi’an 710121, China

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.

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Ideal obfuscationSplit FHEMultilinear mapsLattice problem reductionEvasive Lattice
Contact author(s)
arcsec30 @ 163 com
lyzhang @ mail xidian edu cn
laiqq @ snnu edu cn
2024-05-31: last of 2 revisions
2024-03-04: received
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      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},
      note = {\url{}},
      url = {}
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