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arXiv · 2610.37061

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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John Graham, Soundes Marzougui, Miloš Pavlović, Vladimir Shpilrain. 2026-10-27. GKS Fully Homomorphic Encryption: Security Analysis. https://arxiv.org/abs/2610.37061

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