GKS FHE: Security Analysis

Paper 2026/2523

GKS FHE: Security Analysis

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.

Metadata

• Available format(s)

PDF

• Category
• Attacks and cryptanalysis
• Publication info
• Preprint.
• Keywords
• fully homomorphic encryptionprivate-key FHEAI trainingmachine learningprivate search
• Contact author(s)

•   jgraham @ zerofhe ai
  

Delaram Kahrobaei @ qc cuny edu marzougui soundes @ gmail com milos @ zerofhe ai vshpilrain @ ccny cuny edu

• History
• 2026-10-19: approved
• 2026-10-18: received
• See all versions
• Short URL
• https://ia.cr/2026/2523
• License

CC BY

BibTeX

@misc{cryptoeprint:2026/2523,
      author = {John Graham and Delaram Kahrobaei and Soundes Marzougui and Milos Pavlovic and Vladimir Shpilrain},
      title = {{GKS} {FHE}: Security Analysis},
      howpublished = {Cryptology {ePrint} Archive, Paper 2026/2523},
      year = {2026},
      url = {https://eprint.iacr.org/2026/2523}
}