Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Complex Domain Approach for Reversible Data Hiding and Homomorphic Encryption: General Framework and Application to Dispersed Data

David Megias

TL;DR

This paper presents H[i]dden, a novel complex-domain framework for reversible data hiding that intrinsically mixes host data with watermarks using Gaussian integers, achieving perfect reversibility and scalable watermark capacity. It integrates two cryptographic instantiations: H[i]dden-EG, which extends ElGamal to Gaussian integers for joint RDH and encryption of individual data, and H[i]dden-AggP, which applies a component-wise Paillier scheme to enable privacy-preserving aggregation across multiple sensors. The schemes leverage the complex-domain algebra to realize simultaneous integrity, provenance, and confidentiality in dispersed data environments, such as IoT/WSN. The work also provides a detailed complexity analysis and security discussion, and suggests future directions toward broader homomorphic options and multimedia extensions.

Abstract

Ensuring the trustworthiness of data from distributed and resource-constrained environments, such as Wireless Sensor Networks or IoT devices, is critical. Existing Reversible Data Hiding (RDH) methods for scalar data suffer from low embedding capacity and poor intrinsic mixing between host data and watermark. This paper introduces Hiding in the Imaginary Domain with Data Encryption (H[i]dden), a novel framework based on complex number arithmetic for simultaneous information embedding and encryption. The H[i]dden framework offers perfect reversibility, in-principle unlimited watermark size, and intrinsic data-watermark mixing. The paper further introduces two protocols: H[i]dden-EG, for joint reversible data hiding and encryption, and H[i]dden-AggP, for privacy-preserving aggregation of watermarked data, based on partially homomorphic encryption. These protocols provide efficient and resilient solutions for data integrity, provenance and confidentiality, serving as a foundation for new schemes based on the algebraic properties of the complex domain.

Complex Domain Approach for Reversible Data Hiding and Homomorphic Encryption: General Framework and Application to Dispersed Data

TL;DR

This paper presents H[i]dden, a novel complex-domain framework for reversible data hiding that intrinsically mixes host data with watermarks using Gaussian integers, achieving perfect reversibility and scalable watermark capacity. It integrates two cryptographic instantiations: H[i]dden-EG, which extends ElGamal to Gaussian integers for joint RDH and encryption of individual data, and H[i]dden-AggP, which applies a component-wise Paillier scheme to enable privacy-preserving aggregation across multiple sensors. The schemes leverage the complex-domain algebra to realize simultaneous integrity, provenance, and confidentiality in dispersed data environments, such as IoT/WSN. The work also provides a detailed complexity analysis and security discussion, and suggests future directions toward broader homomorphic options and multimedia extensions.

Abstract

Ensuring the trustworthiness of data from distributed and resource-constrained environments, such as Wireless Sensor Networks or IoT devices, is critical. Existing Reversible Data Hiding (RDH) methods for scalar data suffer from low embedding capacity and poor intrinsic mixing between host data and watermark. This paper introduces Hiding in the Imaginary Domain with Data Encryption (H[i]dden), a novel framework based on complex number arithmetic for simultaneous information embedding and encryption. The H[i]dden framework offers perfect reversibility, in-principle unlimited watermark size, and intrinsic data-watermark mixing. The paper further introduces two protocols: H[i]dden-EG, for joint reversible data hiding and encryption, and H[i]dden-AggP, for privacy-preserving aggregation of watermarked data, based on partially homomorphic encryption. These protocols provide efficient and resilient solutions for data integrity, provenance and confidentiality, serving as a foundation for new schemes based on the algebraic properties of the complex domain.

Paper Structure

This paper contains 25 sections, 30 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Plan and Contributions of the Paper
  3. Background
  4. Reversible Data Hiding
  5. Homomorphic Encryption
  6. ElGamal Encryption
  7. Paillier Encryption
  8. Reversible Watermarking Approach on the Complex Domain
  9. Basic Definitions
  10. Proposed Reversible Watermarking Scheme
  11. Data Aggregation
  12. Homomorphic Encryption on the Complex Domain
  13. ElGamal Encryption over Gaussian Integers
  14. Numerical example
  15. Component-wise Paillier Encryption of Gaussian Integers
  16. ...and 10 more sections

Figures (2)

  • Figure 1: Representatives of Gaussian integers $\,(\mathop{\mathrm{\mathrm{mod}}}\nolimits 7)$, or $\mathbb Z[i]_7$.
  • Figure 2: "Canonical" epresentatives of Gaussian integers $\,(\mathop{\mathrm{\mathrm{mod}}}\nolimits 7)$, or $\mathbb Z[i]_7$.

Theorems & Definitions (18)

  • Definition 1
  • Definition 2
  • Remark 1
  • Definition 3
  • Definition 4
  • Definition 5
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • ...and 8 more