Paper 2026/316
GG-GSW: Chosen-Ciphertext Secure Leveled FHE From Gadget Trapdoors
, Universität der Bundeswehr MünchenAbstract
We present a simple leveled fully homomorphic encryption (FHE) scheme that achieves IND-CCA1 security in the standard model without relying on SNARKs. Our construction combines the gadget trapdoors introduced by Micciancio and Peikert [Eurocrypt 2012] with the GSW leveled FHE scheme [Gentry, Sahai, Waters, Crypto 2013]. We make only minimal changes to GSW to obtain security: ciphertext size remains similar and the homomorphic operations are unchanged. We prove IND-CCA1 security under a new delayed-target LWE assumption. We provide evidence for its hardness in two ways: under a lattice knowledge assumption, we give a reduction from standard LWE; for a restricted parameter regime, we give a quantum reduction from the one-more inhomogeneous short integer solution assumption. Finally, using the randomized evaluation technique from Bourse et al. [Crypto 2016], we obtain IND-CPA-D security for branching programs using only polynomial noise flooding and without requiring statistical correctness.
Note: The previous version contained an incorrect IND-CCA1 security proof. This revision replaces it with a proof under a new delayed-target LWE assumption.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Preprint.
- Keywords
- Fully homomorphic encryptionChosen-ciphertext securityGadget TrapdoorsCPA-D security
- Contact author(s)
- jerome nguyen @ unibw de
- History
- 2026-09-21: last of 2 revisions
- 2026-02-18: received
- See all versions
- Short URL
- https://ia.cr/2026/316
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2026/316,
author = {Jérôme Nguyen},
title = {{GG}-{GSW}: Chosen-Ciphertext Secure Leveled {FHE} From Gadget Trapdoors},
howpublished = {Cryptology {ePrint} Archive, Paper 2026/316},
year = {2026},
url = {https://eprint.iacr.org/2026/316}
}
