GKS FHE: Security Analysis

A preprint posted to the Cryptology ePrint Archive on October 19, 2026 presents a formal security analysis of the Gribov-Kahrobaei-Shpilrain (GKS) private-key fully homomorphic encryption scheme. The paper, 2026/2523, is authored by John Graham, Delaram Kahrobaei, Soundes Marzougui, Milos Pavlovic and Vladimir Shpilrain, and states that GKS requires no bootstrapping or de-linearization, produces bit-exact decryption, supports native encrypted search and scales to unbounded depth. The work is filed under the archive's attacks and cryptanalysis category and lists AI training, machine learning and private search among its keywords.

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} }