Plausible Deniability in Fully Homomorphic Computation

2026-05-03

AI Summary

This work addresses the dual challenges of preserving computational privacy in untrusted cloud environments and enabling plausible deniability under coercion. To this end, it presents the first fully homomorphic computation framework with deniability support (PD-FHC). The framework embeds both genuine and multiple decoy computations into RGB images via steganography and processes them uniformly using Fredkin gate circuits. It formally defines medium-agnostic Deniable Computation Media (DCM) and Deniable Computation Schemes (DCS). Maintaining performance comparable to TFHE, the system demonstrates feasibility across image sizes from 128² to 512² and circuit complexities ranging from 5 to 289 gates, thereby achieving—for the first time—a fully homomorphic computation scheme that simultaneously guarantees computational privacy and provable plausible deniability.

Abstract

We introduce \emph{Plausible Deniability in Fully Homomorphic Computation} (PD-FHC), a framework enabling users to outsource Boolean computations to an untrusted cloud while maintaining both computational privacy against honest-but-curious providers and plausible deniability against coercive adversaries. We define the notion of a \emph{Deniable Computation Medium} (DCM) and a \emph{Deniable Computation Scheme} (DCS) as medium-independent abstractions, then instantiate them using RGB images with Fredkin-gate circuits. Multiple computation scenarios (one real, several decoys) are embedded at secret positions within cover images; the cloud applies identical operations to every pixel, processing all scenarios uniformly. Under coercion, the user reveals a decoy computation with verifiable results while the real computation remains hidden. We formalize multi-round coercion games with existence and intent distinguishing advantages, proving computational privacy with advantage $Θ(1/(n-1)!)$ and negligible existence-hiding advantage for the image instantiation. Our Python implementation, benchmarked across circuit sizes (5--289 gates) and image dimensions ($128^2$ to $512^2$), demonstrates competitive performance with TFHE for Boolean circuits while providing deniability that FHE fundamentally cannot offer.

Problem

• Plausible Deniability
• Fully Homomorphic Computation
• Computational Privacy
• Coercive Adversary
• Outsourced Computation

Innovation

• Plausible Deniability
• Fully Homomorphic Encryption
• Deniable Computation
• Fredkin Gate
• Coercion Resistance