Paper 2026/316 Original: eprint.iacr.org/2026/316 ↗

GG-GSW: Chosen-Ciphertext Secure Leveled FHE From Gadget Trapdoors

Abstract

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.