Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Provably Secure Public-Key Steganography Based on Admissible Encoding

Xin Zhang, Kejiang Chen, Na Zhao, Weiming Zhang, Nenghai Yu

TL;DR

This work addresses the challenge of provably secure public-key steganography on elliptic curves without the curve-parameter restrictions or half-point usage of prior EC methods. It introduces admissible encoding, constructed via the tensor square of well-distributed elliptic-curve encodings (Icart, SW, SWU), to produce a surjective mapping from a finite-field domain to $E(\mathbb{F}_p)$ with a sampleable inverse, enabling pseudorandom public-key ciphertexts under IND$-$CPA in the random-oracle model. The framework yields universal applicability across curve types, full utilization of curve points (including pairing-friendly ones), and concrete instances on $\text{P-384}$, $\text{secp256k1}$, and $\text{P-256}$, supported by both statistical tests and steganalysis experiments. Together, these results broaden the practical scope of provably secure covert communication and pave the way for integrating such primitives into higher-level protocols like group key exchange and deterministic cryptographic schemes.

Abstract

The technique of hiding secret messages within seemingly harmless covertext to evade examination by censors with rigorous security proofs is known as provably secure steganography (PSS). PSS evolves from symmetric key steganography to public-key steganography, functioning without the requirement of a pre-shared key and enabling the extension to multi-party covert communication and identity verification mechanisms. Recently, a public-key steganography method based on elliptic curves was proposed, which uses point compression to eliminate the algebraic structure of curve points. However, this method has strict requirements on the curve parameters and is only available on half of the points. To overcome these limitations, this paper proposes a more general elliptic curve public key steganography method based on admissible encoding. By applying the tensor square function to the known well-distributed encoding, we construct admissible encoding, which can create the pseudo-random public-key encryption function. The theoretical analysis and experimental results show that the proposed provable secure public-key steganography method can be deployed on all types of curves and utilize all points on the curve.

Provably Secure Public-Key Steganography Based on Admissible Encoding

TL;DR

This work addresses the challenge of provably secure public-key steganography on elliptic curves without the curve-parameter restrictions or half-point usage of prior EC methods. It introduces admissible encoding, constructed via the tensor square of well-distributed elliptic-curve encodings (Icart, SW, SWU), to produce a surjective mapping from a finite-field domain to with a sampleable inverse, enabling pseudorandom public-key ciphertexts under INDCPA in the random-oracle model. The framework yields universal applicability across curve types, full utilization of curve points (including pairing-friendly ones), and concrete instances on , , and , supported by both statistical tests and steganalysis experiments. Together, these results broaden the practical scope of provably secure covert communication and pave the way for integrating such primitives into higher-level protocols like group key exchange and deterministic cryptographic schemes.

Abstract

The technique of hiding secret messages within seemingly harmless covertext to evade examination by censors with rigorous security proofs is known as provably secure steganography (PSS). PSS evolves from symmetric key steganography to public-key steganography, functioning without the requirement of a pre-shared key and enabling the extension to multi-party covert communication and identity verification mechanisms. Recently, a public-key steganography method based on elliptic curves was proposed, which uses point compression to eliminate the algebraic structure of curve points. However, this method has strict requirements on the curve parameters and is only available on half of the points. To overcome these limitations, this paper proposes a more general elliptic curve public key steganography method based on admissible encoding. By applying the tensor square function to the known well-distributed encoding, we construct admissible encoding, which can create the pseudo-random public-key encryption function. The theoretical analysis and experimental results show that the proposed provable secure public-key steganography method can be deployed on all types of curves and utilize all points on the curve.
Paper Structure (24 sections, 9 theorems, 38 equations, 3 figures, 4 tables, 8 algorithms)

This paper contains 24 sections, 9 theorems, 38 equations, 3 figures, 4 tables, 8 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Provably Secure Steganography
  4. Generative Model and Provably Secure Steganography
  5. Provable Secure Public-Key Steganography
  6. Definition
  7. Existing Constructions
  8. Elliptic Curve Hash and Admissible Encoding
  9. Admissible Encoding
  10. Instantiation
  11. Definition
  12. Our Proposed Method
  13. Provably Secure Public-Key Steganography Framework Based on Admissible encoding
  14. Well-distributed Encoding Strengthen to Admissible Encoding
  15. Provably Secure Public-key Steganography Framework Based on Admissible Encoding
  16. ...and 9 more sections

Key Result

Lemma 1

Consider the tensor square function $f^{\otimes 2}$ defined as Def. Def_tensor_exponent fucntion, if $f$ is a $B$-well-distributed encoding, and is both computable and $\epsilon^\prime$-sampleable, where $B$ is a constant and $\epsilon^\prime$ is negligible relative to the security parameter, then $

Figures (3)

  • Figure 1: Diagram of the public-key steganography system.
  • Figure 2: The theoretical framework of our public-key steganography system.
  • Figure 3: The hardness of distinguishing between $H_0$ and $H_3$.

Theorems & Definitions (22)

  • Definition 1
  • Definition 2
  • Definition 3
  • Definition 4
  • Definition 5
  • Definition 6
  • Definition 7
  • Definition 8
  • Definition 9
  • Lemma 1
  • ...and 12 more