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Security Analysis of Thumbnail-Preserving Image Encryption and a New Framework

Dong Xie, Zhiyang Li, Shuangxi Guo, Fulong Chen, Peng Hu

TL;DR

This work identifies thumbnail collisions as a critical security risk in thumbnail-preserving encryption (TPE) and analyzes their probability across blocks and images. It introduces the multi-factor thumbnail-preserving encryption (MFTPE) framework, which preserves multiple statistical factors within image blocks to reduce thumbnail collisions. Three concrete constructions—preserving the sum with the geometric mean, the sum with the range, and the sum with the weighted mean—are proposed, with theoretical collision-probability reductions and practical efficiency demonstrated. Experiments on the Helen dataset show strong robustness against noise and face-detection attacks and confirm lossless decryption, highlighting the method's practicality for privacy-preserving cloud image storage.

Abstract

As a primary encryption primitive balancing the privacy and searchability of cloud storage images, thumbnail preserving encryption (TPE) enables users to quickly identify the privacy personal image on the cloud and request this image from the owner through a secure channel. In this paper, we have found that two different plaintext images may produce the same thumbnail. It results in the failure of search strategy because the collision of thumbnail occurs. To address this serious security issues, we conduct an in-depth analysis on the collision probabilities of thumbnails, and then propose a new TPE framework, called multi-factor thumbnail preserving encryption (MFTPE). It starts from the collision probability of two blocks, extend to the probabilities of two images and ultimately to N images. Then, we in detail describe three specific MFTPE constructions preserving different combinations of factors, i.e., the sum and the geometric mean, the sum and the range, and the sum and the weighted mean. The theoretical and experimental results demonstrate that the proposed MFTPE reduces the probability of thumbnails, exhibits strong robustness, and also effectively resists face detection and noise attacks.

Security Analysis of Thumbnail-Preserving Image Encryption and a New Framework

TL;DR

This work identifies thumbnail collisions as a critical security risk in thumbnail-preserving encryption (TPE) and analyzes their probability across blocks and images. It introduces the multi-factor thumbnail-preserving encryption (MFTPE) framework, which preserves multiple statistical factors within image blocks to reduce thumbnail collisions. Three concrete constructions—preserving the sum with the geometric mean, the sum with the range, and the sum with the weighted mean—are proposed, with theoretical collision-probability reductions and practical efficiency demonstrated. Experiments on the Helen dataset show strong robustness against noise and face-detection attacks and confirm lossless decryption, highlighting the method's practicality for privacy-preserving cloud image storage.

Abstract

As a primary encryption primitive balancing the privacy and searchability of cloud storage images, thumbnail preserving encryption (TPE) enables users to quickly identify the privacy personal image on the cloud and request this image from the owner through a secure channel. In this paper, we have found that two different plaintext images may produce the same thumbnail. It results in the failure of search strategy because the collision of thumbnail occurs. To address this serious security issues, we conduct an in-depth analysis on the collision probabilities of thumbnails, and then propose a new TPE framework, called multi-factor thumbnail preserving encryption (MFTPE). It starts from the collision probability of two blocks, extend to the probabilities of two images and ultimately to N images. Then, we in detail describe three specific MFTPE constructions preserving different combinations of factors, i.e., the sum and the geometric mean, the sum and the range, and the sum and the weighted mean. The theoretical and experimental results demonstrate that the proposed MFTPE reduces the probability of thumbnails, exhibits strong robustness, and also effectively resists face detection and noise attacks.

Paper Structure

This paper contains 34 sections, 7 theorems, 25 equations, 17 figures, 5 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Backgrounds
  3. Motivation
  4. Contribution
  5. Organization
  6. Related work
  7. Approximate TPE
  8. Ideal TPE
  9. Preliminaries
  10. Nonce-Based Encryption
  11. Format-Preserving Encryption
  12. Thumbnail-Preserving Encryption
  13. $\Phi_{d}^{-1}(s, n)$ and $\Psi_{d}(s, n)$
  14. Collision probability of thumbnails in TPE
  15. Multiple random blocks
  16. ...and 19 more sections

Key Result

Theorem 1

Suppose that there exist a block with $n$ pixels $B_1$ and $s_1=sum(B_1)$, where $s_1$ represent the sum of pixels in $B_1$. Then, for a random block $B_2$ with $n$ pixels, the collision probability of $B_1$ and $B_2$ is

Figures (17)

  • Figure 1: Comparison of different methods balancing the privacy and the serachability of could images.
  • Figure 2: Different images with the same thumbnail
  • Figure 3: The encryption process of the MFTPE framework.
  • Figure 4: The substitution process of the MFTPE scheme when preserving the sum and the range.
  • Figure 5: The ciphertext images under the MFTPE framework preserving the sum and the geometric mean
  • ...and 12 more figures

Theorems & Definitions (13)

  • Definition 1: PRP security bellare2009format
  • Definition 2: Nonce-respecting tajik2019balancing
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Corollary 1
  • Theorem 3
  • proof
  • Theorem 4
  • ...and 3 more