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Provably Robust and Secure Steganography in Asymmetric Resource Scenario

Minhao Bai, Jinshuai Yang, Kaiyi Pang, Xin Xu, Zhen Yang, Yongfeng Huang

TL;DR

A novel provably robust and secure steganography framework for the asymmetric resource setting where only the encoder is high-resource and accessible to powerful models while the decoder can only read the stegano-graphic carriers without any other model's input.

Abstract

To circumvent the unbridled and ever-encroaching surveillance and censorship in cyberspace, steganography has garnered attention for its ability to hide private information in innocent-looking carriers. Current provably secure steganography approaches require a pair of encoder and decoder to hide and extract private messages, both of which must run the same model with the same input to obtain identical distributions. These requirements pose significant challenges to the practical implementation of steganography, including limited access to powerful hardware and the intolerance of any changes to the shared input. To relax the limitation of hardware and solve the challenge of vulnerable shared input, a novel and practically significant scenario with asymmetric resource should be considered, where only the encoder is high-resource and accessible to powerful models while the decoder can only read the steganographic carriers without any other model's input. This paper proposes a novel provably robust and secure steganography framework for the asymmetric resource setting. Specifically, the encoder uses various permutations of distribution to hide secret bits, while the decoder relies on a sampling function to extract the hidden bits by guessing the permutation used. Further, the sampling function only takes the steganographic carrier as input, which makes the decoder independent of model's input and model itself. A comprehensive assessment of applying our framework to generative models substantiates its effectiveness. Our implementation demonstrates robustness when transmitting over binary symmetric channels with errors.

Provably Robust and Secure Steganography in Asymmetric Resource Scenario

TL;DR

A novel provably robust and secure steganography framework for the asymmetric resource setting where only the encoder is high-resource and accessible to powerful models while the decoder can only read the stegano-graphic carriers without any other model's input.

Abstract

To circumvent the unbridled and ever-encroaching surveillance and censorship in cyberspace, steganography has garnered attention for its ability to hide private information in innocent-looking carriers. Current provably secure steganography approaches require a pair of encoder and decoder to hide and extract private messages, both of which must run the same model with the same input to obtain identical distributions. These requirements pose significant challenges to the practical implementation of steganography, including limited access to powerful hardware and the intolerance of any changes to the shared input. To relax the limitation of hardware and solve the challenge of vulnerable shared input, a novel and practically significant scenario with asymmetric resource should be considered, where only the encoder is high-resource and accessible to powerful models while the decoder can only read the steganographic carriers without any other model's input. This paper proposes a novel provably robust and secure steganography framework for the asymmetric resource setting. Specifically, the encoder uses various permutations of distribution to hide secret bits, while the decoder relies on a sampling function to extract the hidden bits by guessing the permutation used. Further, the sampling function only takes the steganographic carrier as input, which makes the decoder independent of model's input and model itself. A comprehensive assessment of applying our framework to generative models substantiates its effectiveness. Our implementation demonstrates robustness when transmitting over binary symmetric channels with errors.
Paper Structure (37 sections, 5 theorems, 41 equations, 8 figures, 4 tables, 2 algorithms)

This paper contains 37 sections, 5 theorems, 41 equations, 8 figures, 4 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Preliminaries
  4. Channel
  5. Steganography
  6. Security
  7. Correctness
  8. Robustness against Substitution
  9. Related Work
  10. Theoretical Steganography
  11. Practical Steganography
  12. Method
  13. Settings of Asymmetric Resource Scenario
  14. Steganography in Asymmetric Resource Scenario
  15. Construction
  16. ...and 22 more sections

Key Result

Lemma 1

$X_1, X_2, \cdot\cdot\cdot , X_n$ are independent and identical random variables, and each $X_i$ is bounded by $[l,h], r \in [0,1]$. Let $X = \frac{1}{n}\sum_{i=1}^n X_i$ and $\mu = \mathbb{E}[X_i]$, the probability that the sample mean $X$ deviates from the theoretical mean $\mathbb{E}[X]$ up to $t

Figures (8)

  • Figure 1: An overview of our steganography system.
  • Figure 2: 2 trivial permutations of the distribution of symbol $a$ and $b$.
  • Figure 3: Games used in the proof.
  • Figure 4: Relationship between error bound $P_e$ ($0.1 \sim 0.5$) and bit error rate.
  • Figure 5: Capacity of different functions.
  • ...and 3 more figures

Theorems & Definitions (10)

  • Definition 1: Computational Security
  • Definition 2: Correctness
  • Definition 3: $e$-Robustness against substitution
  • Definition 4: Steganography in asymmetric resource scenario
  • Definition 5: Correctness in asymmetric resource scenario
  • Lemma 1: Hoeffding's inequality
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4