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SparSamp: Efficient Provably Secure Steganography Based on Sparse Sampling

Yaofei Wang, Gang Pei, Kejiang Chen, Jinyang Ding, Chao Pan, Weilong Pang, Donghui Hu, Weiming Zhang

TL;DR

SparSamp introduces a provably secure steganography method for generative models that embeds messages without distorting the underlying probability distributions. It achieves this via message-driven sampling with MRNs and a sparse, index-based embedding scheme that yields $O(1)$ per-sampling-step complexity while preserving generation speed. The approach demonstrates high embedding speeds across text, image, and audio models, maintains low or zero KL divergence from the cover distributions, and remains compatible with token disambiguation techniques to handle TA. Empirical results show SparSamp outperforms prior PSS methods on speed and capacity while maintaining security, with practical potential for real-time covert communication in diverse AIGC tasks.

Abstract

Steganography embeds confidential data within seemingly innocuous communications. Provable security in steganography, a long-sought goal, has become feasible with deep generative models. However, existing methods face a critical trade-off between security and efficiency. This paper introduces SparSamp, an efficient provably secure steganography method based on sparse sampling. SparSamp embeds messages by combining them with pseudo-random numbers to obtain message-derived random numbers for sampling. It enhances extraction accuracy and embedding capacity by increasing the sampling intervals and making the sampling process sparse. SparSamp preserves the original probability distribution of the generative model, thus ensuring security. It introduces only $O(1)$ additional complexity per sampling step, enabling the fastest embedding speed without compromising generation speed. SparSamp is designed to be plug-and-play; message embedding can be achieved by simply replacing the sampling component of an existing generative model with SparSamp. We implemented SparSamp in text, image, and audio generation models. It can achieve embedding speeds of up to 755 bits/second with GPT-2, 5046 bits/second with DDPM, and 9,223 bits/second with WaveRNN.

SparSamp: Efficient Provably Secure Steganography Based on Sparse Sampling

TL;DR

SparSamp introduces a provably secure steganography method for generative models that embeds messages without distorting the underlying probability distributions. It achieves this via message-driven sampling with MRNs and a sparse, index-based embedding scheme that yields per-sampling-step complexity while preserving generation speed. The approach demonstrates high embedding speeds across text, image, and audio models, maintains low or zero KL divergence from the cover distributions, and remains compatible with token disambiguation techniques to handle TA. Empirical results show SparSamp outperforms prior PSS methods on speed and capacity while maintaining security, with practical potential for real-time covert communication in diverse AIGC tasks.

Abstract

Steganography embeds confidential data within seemingly innocuous communications. Provable security in steganography, a long-sought goal, has become feasible with deep generative models. However, existing methods face a critical trade-off between security and efficiency. This paper introduces SparSamp, an efficient provably secure steganography method based on sparse sampling. SparSamp embeds messages by combining them with pseudo-random numbers to obtain message-derived random numbers for sampling. It enhances extraction accuracy and embedding capacity by increasing the sampling intervals and making the sampling process sparse. SparSamp preserves the original probability distribution of the generative model, thus ensuring security. It introduces only additional complexity per sampling step, enabling the fastest embedding speed without compromising generation speed. SparSamp is designed to be plug-and-play; message embedding can be achieved by simply replacing the sampling component of an existing generative model with SparSamp. We implemented SparSamp in text, image, and audio generation models. It can achieve embedding speeds of up to 755 bits/second with GPT-2, 5046 bits/second with DDPM, and 9,223 bits/second with WaveRNN.

Paper Structure

This paper contains 29 sections, 1 theorem, 5 equations, 8 figures, 10 tables, 4 algorithms.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Deep Generative Models
  4. Information-theoretic Security of Steganography
  5. Attempts to Provably Secure Steganography in the AIGC Era
  6. SparSamp Methodology
  7. Message Embedding via Message-Driven Sampling
  8. Decoding ambiguity
  9. Conflict
  10. Sparse Sampling
  11. Message Embedding as Index Embedding
  12. Achieving $O(1)$ time complexity
  13. Overview of SparSamp
  14. Advantages
  15. Dealing with Token Ambiguity
  16. ...and 14 more sections

Key Result

Theorem 1

For any polynomial-time distinguisher $\mathcal{A}$, it is computationally infeasible to distinguish between samples drawn from $\mathcal{P}_i$ using $r_i$ and using $r_i(m)$.

Figures (8)

  • Figure 1: A graphical depiction of steganography.
  • Figure 2: A generation process of LLM
  • Figure 3: An example of sampling based on $\mathbf{MRN}$s. The initial pseudo-random number is $r_i = 0.575$. The message length $l_m$ to be embedded is 3, and the $\mathbf{MRN}$s are $r_i(xxx)$.
  • Figure 4: Sampling based on different number/length ($l_m$) of $\mathbf{MRN}$s/message. The red arrow represents sampling that causes decoding ambiguity.
  • Figure 5: An example of embedding based on Sparse Sampling.
  • ...and 3 more figures

Theorems & Definitions (2)

  • Theorem 1
  • Proof 1