# GKS Fully Homomorphic Encryption: Security Analysis

DevFeed: [GKS Fully Homomorphic Encryption: Security Analysis](<https://devfeed.tech/articles/gks-fully-homomorphic-encryption-security-analysis-103375.md>)

Original publisher: [Read original article](<https://arxiv.org/abs/2610.37061>)

Author: John Graham, Soundes Marzougui, Milo\\v{s} Pavlovi\\'c, Vladimir Shpilrain

Published: 2026-10-28T04:00:00Z

Content type: article

Language: en

Sources: [arXiv: Cryptography and Security](<https://devfeed.tech/sources/arxiv-cryptography-and-security.md>)

Topics: [FHE](<https://devfeed.tech/topics/fhe.md>), [homomorphic encryption](<https://devfeed.tech/topics/homomorphic-encryption.md>)

Tags: [analysis](<https://devfeed.tech/tags/analysis.md>), [bootstrapping](<https://devfeed.tech/tags/bootstrapping.md>), [cryptography](<https://devfeed.tech/tags/cryptography.md>), [cs-cr](<https://devfeed.tech/tags/cs-cr.md>), [encryption](<https://devfeed.tech/tags/encryption.md>), [fhe](<https://devfeed.tech/tags/fhe.md>), [homomorphic-encryption](<https://devfeed.tech/tags/homomorphic-encryption.md>), [math-ra](<https://devfeed.tech/tags/math-ra.md>), [private-key](<https://devfeed.tech/tags/private-key.md>), [search](<https://devfeed.tech/tags/search.md>), [security](<https://devfeed.tech/tags/security.md>), [vulnerability](<https://devfeed.tech/tags/vulnerability.md>)

## AI overview

The paper presents a formal security analysis of the Gribov-Kahrobaei-Shpilrain (GKS) private-key fully homomorphic encryption scheme. The abstract says GKS supports computation on encrypted data without bootstrapping or de-linearization, offers bit-exact decryption and native encrypted search, and scales to unbounded depth. The supplied text does not provide the analysis or its security findings, so those cannot be summarized here.

## Source excerpt

arXiv:2610.37061v1 Announce Type: new 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.