As an important technique to achieve covert communication, steganography has developed greatly in pursuit of the secrecy of concealment suggested by Shannon. The most widely used scheme is called adaptive steganography which is composed of two phases: the distortion calculation phase and the adaptive steganographic coding phase. Conventionally, adaptive steganography assumes a noise-free lossless channel between the sender and the receiver. However, in real-world applications, the stego (cover media with secret messages embedded) would suffer from various lossy operations and be modified during transmission, leading to extraction error at the receiver. In this paper, robust adaptive steganographic coding is considered. We formalize the problem to be a problem of finding the maximum embedding rate of a special communication system with a normalized adaptive distortion function and a non-stationary memoryless sequence of discrete channels such that the secret message can be communicated without error. The theoretical rate-distortion bound of the problem is established which is a great leap forward in the research field of robust steganography. By modeling the noisy channels in real-world applications into non-stationary discrete memoryless channels (DMCs), our bound can be used to evaluate the existing robust methods and will serve as the ultimate goal for the design of new practical robust adaptive steganographic coding algorithms.
Apr 8, 2025
Steganography is the art of covert communication that pursues the secrecy of concealment. In adaptive steganography, the most commonly used framework of steganography, the sender embeds a "secret message" signal within another "cover" signal with respect to a certain adaptive distortion function that measures the distortion incurred, contributing to the composite "stego" signal that resembles the cover, and the receiver extracts the "secret message" signal from the stego. When the communication channel between the sender and the receiver is noisy, robust steganography is needed, in which robust adaptive steganographic coding plays a central role. The existing robust adaptive steganographic coding methods can only provide very limited robustness, and they fail when the communication channel is bad. To ensure the success of covert communication, we propose a reliable robust adaptive steganographic coding scheme based on nested polar codes that possesses the highest robustness among the existing algorithms while the security performance is also maintained. Theoretically, we show that for the most important binary embedding, in the special case where the communication channel is a Binary Symmetric Channel (BSC), the proposed scheme is optimal under the constant distortion profile as the cover length N tends to infinity through powers of two when the design embedding rate is large enough. Experimentally, our method is capable of making sure the perfect extraction of the secret message in situations where the embedding rate is large or the communication channel is bad, while the existing algorithms are not applicable in these scenarios.
Dec 3, 2024
Steganographic coding is an essential part of adaptive steganography. There are only two practical near-optimal codes in the context of adaptive steganography so far: Syndrome-Trellis Codes (STCs) based on linear convolutional codes and Steganographic Polar Codes (SPCs) based on polar codes. It can be noticed that both STCs and SPCs are based on channel codes. Like the need for the variety of cryptographic algorithms, to make steganography practical and secure, it is important to devise more adaptive steganographic codes to create more choices for users. Moreover, we want to solve the long-lasting problem of whether lossy source codes-based near-optimal adaptive steganographic coding exists. In this paper, we consider using Low-Density Generator-Matrix (LDGM) codes in adaptive steganography where a new algorithm is proposed. First, we describe the framework of our LDGM codes-based steganographic coding algorithm and establish rigorous upper bounds on average embedding efficiency for individual LDGM steganographic codes with a given information bit degree distribution under the constant distortion profile. Then, we give a provably optimal method of distortion incorporation for adaptive steganography and provide the corresponding log-domain Belief Propagation Guided Decimation (log-BPGD) algorithm to minimize the additive distortion. The syndrome coding technique is applied to realize definitive encoding and decoding of the secret message. We report experiments for various distortion profiles, payload rates, and code lengths. The results verify the near-optimal performance of the proposed method, by which the possibility of designing near-optimal adaptive steganographic coding methods based on lossy source coding is confirmed.
Dec 13, 2023
Steganography aims to hide information in cover media where steganographic coding acts as a vital part. None of the existing steganographic coding algorithms have been proved to be optimal so far. Recently, capacity-achieving polar codes have been used to devise steganographic coding algorithms which are evaluated by experimental simulations without theoretical analysis. In this paper, we prove that under the constant distortion profile, polar codes-based steganographic coding methods could achieve the theoretical rate-distortion bound for additive steganography when the code length goes to infinity.
Nov 3, 2022