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PreprintCC BY 4.0arXiv

GKS Fully Homomorphic Encryption: Security Analysis

  • John Graham
  • Soundes Marzougui
  • Miloš Pavlović
  • Vladimir Shpilrain
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Abstract

All traditional encryption schemes share a fundamental operational vulnerability: encrypted data must be decrypted before it can be used. Fully homomorphic encryption eliminates this vulnerability by enabling computation directly on encrypted data, but existing FHE schemes impose substantial practical constraints that limit deployment. This paper presents a formal security analysis of the Gribov-Kahrobaei-Shpilrain (GKS) private-key FHE scheme. GKS requires no bootstrapping or de-linearization, produces bit-exact decryption, supports native encrypted search, and scales to unbounded depth.

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Cite

BibTeXRIS
BibTeX
@misc{graham2026fully,
  title = {{GKS Fully Homomorphic Encryption: Security Analysis}},
  author = {John Graham and Soundes Marzougui and Miloš Pavlović and Vladimir Shpilrain},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37061},
  eprint = {2610.37061},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37061},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - GKS Fully Homomorphic Encryption: Security Analysis
AU  - John Graham
AU  - Soundes Marzougui
AU  - Miloš Pavlović
AU  - Vladimir Shpilrain
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37061
UR  - https://arxiv.org/abs/2610.37061
AB  - All traditional encryption schemes share a fundamental operational vulnerability: encrypted data must be decrypted before it can be used. Fully homomorphic encryption eliminates this vulnerability by enabling computation directly on encrypted data, but existing FHE schemes impose substantial practical constraints that limit deployment. This paper presents a formal security analysis of the Gribov-Kahrobaei-Shpilrain (GKS) private-key FHE scheme. GKS requires no bootstrapping or de-linearization, produces bit-exact decryption, supports native encrypted search, and scales to unbounded depth.
ER  -