# GKS FHE: Security Analysis

> Source: <https://eprint.iacr.org/2026/2523>
> Published: 2026-10-18 00:47:03+00:00

#### Paper 2026/2523

### [GKS FHE: Security Analysis](https://eprint.iacr.org/2026/2523.pdf)

##### 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](https://eprint.iacr.org/2026/2523.pdf)
- Category
- [Attacks and cryptanalysis](https://eprint.iacr.org/search?category=ATTACKS)
- Publication info
- Preprint.
- Keywords
- [fully homomorphic encryption](https://eprint.iacr.org/search?q=fully%20homomorphic%20encryption)[private-key FHE](https://eprint.iacr.org/search?q=private-key%20FHE)[AI training](https://eprint.iacr.org/search?q=AI%20training)[machine learning](https://eprint.iacr.org/search?q=machine%20learning)[private search](https://eprint.iacr.org/search?q=private%20search)
- 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](https://eprint.iacr.org/archive/versions/2026/2523)
- Short URL
- [https://ia.cr/2026/2523](https://ia.cr/2026/2523)
- License
- 
[CC BY](https://creativecommons.org/licenses/by/4.0/)

**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}
}
```