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arXiv:2309.13620v2 [cs.CV] 28 Nov 2023

PRIS: Practical robust invertible network for

image steganography

Hang Yang

, Yitian Xu

* Xuhua Liu

* Xiaodong Ma

College of Science, China Agricultural University, Beijing 100083, China

Abstract

Image steganography is a technique of hiding secret information inside another im-

age, so that the secret is not visible to human eyes and can be recovered when

needed. Most of the existing image steganography methods have low hiding robust-

ness when the container images aﬀected by distortion. Such as Gaussian noise and

lossy compression. This paper proposed PRIS to improve the r obustness of image

steganography, it based on invertible neural networks, and put two enhance mod-

ules before and after the extraction process with a 3-step training strategy. Moreover,

rounding error is considered which is always ignored by existing methods, but ac-

tually it is unavoidable in practical. A gradient approximation function (GAF) is

also proposed to overcome the undiﬀerentiable issue of rounding distortion. Exper-

imental results show that our PRI S outperforms the state-of-the-art robust image

steganography method in both robustness and practicability. Codes are available at

https://github.com/yanghangAI/PRIS, demonstration of our model in practical

at http://yanghang.site/hide/.

1 Introduction

Steganography is the art of concealing informatio n. The goal of steganogra-

phy is to hide a secret message within a host medium [1,2]. The host medium

containing the hidden secret message is called the container [3]. The container

is typically publicly visible, but the diﬀerence between the host and container

should be invisible to third parties. There are some good introductions to

steganography in [1,4,5]. Image steganography aims to hide message such as

image, audio, and text within a host image in an undetectable way [6], mean-

ing the host medium in image steganography is an image. Nowadays, image

Email address: xytshuxue@126.com, Tel.: +8610 62737077. (Yitian Xu

*).

steganography is widely used in ﬁelds such as copyright protection, digital

communication, information certiﬁcation, and more [7].

Traditional image steganographic methods have the ability to hide only a small

amount of information [8,9 ,1 0,11,12,13]. They conceal secret messages in the

spatial or adaptive domains [14] with capacities of 0.2∼4 bits per pixel (bpp).

In recent years, some researchers have attempted to hide an image conta ining

more information than the secret message in traditional image steganographic

methods within a host image [15,16,17,18,19,20]. They introduced deep learn-

ing into image steganography by using two separate networks to realize the

embedding and extraction processes. Lu [3] and Jing [21] achieved state-of-

the-art performance in image steganography by using an invertible network

to embed a secret image into a host image. Since the extraction process is the

inverse of the embedding process, the secret image can be fully recovered.

In practical applications, the container image is of ten subject to various forms

of attacks due to factors such as lossy image compression for storage savings.

These attacks can distort the container image, potentially aﬀecting the ability

to extract the secret information. Robustness refers to the ability of the secret

information to remain unchanged when the container is distorted [22]. In other

words, it measures how similar the secret and extracted messages will be when

the container image is attacked.

However, state-of-the-art image steganography methods [3,21] did not take

into account the eﬀect of container images being attacked. As a result, they

failed to extract secret images when container images were distorted. To ad-

dress this issue, Xu [6] proposed robust inver t ible image steganography. This

method improved the robustness of image steganography by taking image

distortion into account, allowing for the successful extraction of secret infor-

mation even when the container image is distorted.

Moreover, since the current mainstream deep learning frameworks have a nu-

merical precision of 32 bits, while images are usually 8 bits, there is an in-

evitable rounding error when saving the container images. However, to the

best of our knowledge, the existing deep steganography methods ignore this

problem [23,6,21,3], which is not practical in real application, we also give a

method to illustrate the importance to consider rounding error in section 3.7.

In this paper, we designed a practical robust invertible network called PRIS

based on HiNet [21]. We introduce two enhancement mo dules and a 3-step

training strategy into invertible neural network to improve its robustness. In

addition, we take rounding distortion into account and propose a g r adient

approximation f unction (GAF ) to deal with the undiﬀerentiable problem of

rounding operation. The main contributions are listed as follows:

1. A practical robust invertible network is proposed for image steganography

under diverse a t tacks.

2. We introduce a 3-step training strategy into our training process to achieve

a better ro bustness.

3. A gradient approximate function is proposed to solve the undiﬀerentiable

problem caused by rounding operation, and take rounding error into consider-

ation.

4. Experiments results demonstrate that our proposed PRIS outperforms the

existing state-of-the-art method RIIS in both robustness and practicability.

2 Related work

2.1 Traditional image steganography

Traditional image steganography can be divided into two categor ies based on

the whether the hiding process happen in spatial or frequency domain. Spatial

domain: The most popular spatial-based method called Least Signiﬁcant Bit

(LSB) [24,25], it changes n least signiﬁcant bits of host image to embed secret

messages. However, the change of picked bits make it easy t o be detected by

some steganalysis methods [9,26,27]. In addition, Pan [28] utilizes pixel value

diﬀerencing (PVD), Tsai [29] introduces histogram shifting, Nguyen [30] use

multiplebit-planes and Imaizumi [31] propose palettes in image steganography.

Frequency domain: Those methods hide secret messages in frequency do-

mains, such as discrete cosine transform (DCT) [10], discrete Fourier transform

(DFT) [13], and discrete wavelet transform (DWT) [8] domains. Although they

are more robust and undetectable than LSB methods, they still suﬀered from

limited payload capacity.

2.2 Deep learning-based image steganography

Recently, many researchers have a pplied deep learning methods to image

steganography and achieved better performance than traditional methods.

HiDDeN [32] and SteganoGAN [33] utilize the encoder-decoder architecture to

realize the embedding and extraction of secret messages and employ a third

network t o resist steganalysis adversarially. Shi [34] proposes Ssgan for im-

age steganography, which is ba sed on generative adversarial networks. Baluja

[17,15] and Zhang [16] hide a secret image of the same size as the host im-

age with deep learning method, achieve a much higher payload capacity than

traditional methods.

2.3 Invertible neural network

Dinh [35] proposed Invertible neural networ k (INN) in 2014. It learns a stable

bijective mapping between a data distribution p

and a latent distribution p

Unlike CycleGAN [36], which uses two generators and a cycle loss to achieve

bidirectional mapping, INN performs both f orward and backward propagation

within the same networ k, acting as both feature encoder and image generator.

INNs are also useful for estimating t he posterior of an inverse problem [37].

More ﬂexible INNs are built with masked convo lutions under some composi-

tion rules in [38]. An unbiased ﬂow-based generative model is proposed in [39].

Other works improve the coupling layer for density estimation, such as Glow

[40] and i-ResNet [41 ], resulting in better generation quality.

Lu [3], Jing [21] and Jia [42] introduced INN into image steganography. The

strict invertibility of INN just meets the requirement that embedding and

extraction are mutually inverse processes. Therefore they gain state-of-the-

art performance in image steganography. However, the strict invertibility also

means that when the container image is attacked, the noise is also transmitted

to the extracted image, which make it vulnerable to attack. Xu [6] proposed

robust invertible image steganography (RIIS) and improve the robustness of

the afor ementioned invertible neural netwo rks.

In the ﬁeld of image steganography, the invertible network has shown its great

potential. It achieves state-of-the-art performance by utilizing t he prior knowl-

edge that hiding and extraction are inverse processes [3,21], along with the

strict reversibility of its own network. However, due to its strictly reversible

nature, when the container image is perturbed, t he inverse process of its net-

work will also be perturbed. This implies that the extracted image will also be

distorted. To address this issue, we proposed our model PRIS, by introducing

two new modules: pre-enhance and post-enhance, which are added before and

after the extraction process respectively, and through a 3-step training strat-

egy, we improve its robustness to state-of-the-art level. Moreover, rounding

error is considered in our PRIS since it is unavoidable in practice, and a gradi-

ent approximate function is proposed to address the undiﬀerentiable problem

of rounding operation.

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