[Paper Review] Fully Homomorphic Image Processing

William Fu, Raymond Tzer Pin Lin+1 more|arXiv (Cornell University)|Oct 8, 2018

Cryptography and Data Security10 references4 citations

TL;DR

This paper presents a fully homomorphic encryption (FHE)-based framework for secure image processing, enabling homomorphic JPEG encoding, decoding, and image resizing on encrypted data using Microsoft's SEAL library. The key contribution is demonstrating feasible, privacy-preserving image computation on resource-constrained clients by offloading processing to the cloud while minimizing client-side encryption overhead through compressed image handling.

ABSTRACT

Fully homomorphic encryption has allowed devices to outsource computation to third parties while preserving the secrecy of the data being computed on. Many images contain sensitive information and are commonly sent to cloud services to encode images for different devices. We implement image processing homomorphically that ensures secrecy of the image while also providing reasonable overhead. We first present some previous related work, as well as the fully homomorphic encryption scheme we use. Then, we introduce our schemes for JPEG encoding and decoding, as well as schemes for bilinear and bicubic image resizing, as well as some data and analysis of our homomorphic schemes. Finally, we outline several issues with the homomorphic evaluation of proprietary algorithms, and how a third party can gain information on the algorithm through noise.

Motivation & Objective

• To enable secure outsourcing of image processing tasks to untrusted cloud servers while preserving data confidentiality.
• To reduce client-side computational overhead by homomorphically processing compressed images (e.g., JPEG) rather than raw, uncompressed images.
• To implement homomorphic image resizing (bilinear and bicubic) and run-length decoding for JPEG decompression using FHE.
• To analyze the feasibility and performance of homomorphic image processing under practical constraints of FHE schemes.
• To address functional privacy leaks where noise behavior in FHE can leak information about the computation's structure.

Proposed method

• The authors use Microsoft's SEAL library to implement the Fan-Vercauteren FHE scheme with fractional polynomial encoding for real-number arithmetic.
• Image data is encoded as polynomials in the ring R_t = Z_t/(x^n + 1), with coefficients representing digits in a chosen base B for fractional representation.
• Homomorphic JPEG encoding is implemented by applying the DCT to encrypted blocks and approximating quantized coefficients using a Fourier series expansion.
• Run-length decoding is approximated via a Fourier series to handle step functions in compressed data, with convergence controlled by the number of terms used.
• Image resizing is performed homomorphically using bilinear and bicubic interpolation formulas evaluated on encrypted pixel values.
• Noise flooding and 'soak-spin-repeat' techniques are applied to prevent side-channel leakage of algorithmic structure from noise budget behavior.

Experimental results

Research questions

• RQ1 Can JPEG encoding and decoding be securely performed homomorphically on encrypted images using FHE?
• RQ2 Is homomorphic image resizing (bilinear and bicubic) computationally feasible with current FHE performance?
• RQ3 To what extent does homomorphic decompression of compressed images reduce client-side encryption overhead?
• RQ4 Can noise behavior in FHE results leak information about the underlying computation, and how can this be mitigated?
• RQ5 How do approximation errors in Fourier-based decompression affect image fidelity under homomorphic evaluation?

Key findings

• Homomorphic JPEG encoding and decoding are feasible using Fourier series approximations, with image quality improving as the number of Fourier terms increases.
• With 64 Fourier terms, the decompressed image was visually indistinguishable from the original, demonstrating high fidelity in homomorphic decompression.
• Homomorphic image resizing was successfully implemented and benchmarked on standard-sized images using a desktop computer, proving feasibility under current FHE performance.
• The use of compressed image formats for homomorphic processing significantly reduces the amount of data that must be encrypted on the client side.
• Noise-based side-channel attacks on FHE can leak structural information about the computation, such as the number of layers in a neural network.
• Techniques like noise flooding and 'soak-spin-repeat' effectively obscure noise behavior and prevent leakage of functional information from the server.