通用波域嵌入算法UNIWARD：2014年信息安全研究

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本文档标题为《001-隐写算法-2014-S-UNIWARD-EURASIP14_Universal_Distortion_Function_》，发表于2014年《EURASIP Journal on Information Security》。作者是Vojtěch Holub、Jessica Fridrich和Tomáš Denemark。文章主要探讨的是隐写术在数字媒体等实际对象中的应用，特别是设计一种通用的嵌入策略，即Universal Wavelet Relative Distortion (UNIWARD)算法。 UNIWARD算法的核心在于设计一个有效的嵌入策略，目标是在尽可能不改变原始数据（cover image）的情况下，最小化由嵌入数据（payload）引起的感知失真。实践中，隐写师面临的挑战是如何设计出既能保证信息隐藏容量又能保持高统计检测难度的失真函数。UNIWARD算法的独特之处在于它将失真计算基于方向滤波器银行分解（directional filter bank decomposition）下的系数变化。这种方向性使得嵌入的变化仅限于图像中那些对人类视觉感知影响较小的区域，从而提高隐藏的隐蔽性。具体来说，UNIWARD算法的工作流程包括以下几个步骤： 1. 对输入的覆盖图像进行方向滤波器银行分解，这有助于区分不同频率和方向的信息。 2. 计算每个子带（sub-band）内系数相对于原始值的相对变化，这些变化被用来嵌入秘密信息。 3. 将嵌入的数据分配到各个子带中，通过调整系数以最小化总体失真，同时尽量保持视觉上的自然。 4. 由于滤波器选择的特性，这种方法导致的失真在视觉上不易察觉，提高了隐写术的伪装性。该论文的贡献在于提供了一种通用的嵌入方法，能够在任意域（如JPEG、DCT等）中使用，这对于需要适应不同类型媒体的隐写应用具有重要意义。通过UNIWARD，隐写实践者能够针对不同的数据类型和应用场景优化他们的隐藏策略，同时保持足够的安全性。此外，文章还可能讨论了算法的性能评估、对抗分析以及潜在的应用案例，以证明其在实际隐写系统中的有效性。这篇研究论文是关于隐写领域的创新性工作，着重于开发一个能够在多种媒体领域实现高隐蔽性和有效性的一体化失真函数设计。这对于进一步推动隐写技术的发展，特别是在安全通信和数字取证等领域具有重要的理论价值和实践意义。

Holub et al. EURASIP Journal on Information Security 2014, 2014:1 Page 3 of 13

http://jis.eurasipjournals.com/content/2014/1/1

quantized coefficients in this structure with X and Y to

obtain the cover and stego images, respectively. This way,

we guarantee that both images were created using the

same JPEG compressor and that all that we will be detect-

ing are the embedding changes rather than compressor

artifacts.

3 Universal distortion function UNIWARD

In this section, we provide a general description of the

proposed universal distortion function UNIWARD and

explain how it can be used to embe d in the JPEG

and the side-informed JPEG domains. The distortion

depends on the choice of a directional filter bank and one

scalar parameter whose purpose is stabilizing the numer-

ical computations. The distortion design is finished in

Se ction 5, which investigates the effect of the filter bank

and the stabilizing constant on empirical security.

Since r ich models [18,20-22] currently used in ste-

ganalysis are capable of detecting changes along ‘clean

edges’ that can be well fitted using lo cally polynomial

models, whenever possible the embedding algorithm

should embed into textured/noisy areas that are not eas-

ily modellable in any direction. We quantify this u sing

outputs of a directional filter bank and construct the

distortion function in this manner.

3.1 Directional filter bank

By a directional filter bank, we underst and a set of three

linear shift-invariant filters represented with their ker-

nels

B ={K

(1)

, K

(2)

, K

(3)

}. They are used to evaluate the

smoothness of a given image X along the horizontal, ver-

tical, and diagonal directions by computing the so-called

directional residuals W

(k)

= K

(k)

 X,where‘’isa

mirror-padded convolution so that W

(k)

has again n

elements. The mirror padding prevents introducing

embe dding artifact s at the image boundary.

While it is possible to use arbitrary filter banks, we

will exclusively use kernels built from one-dimensional

low-pass (and high-pass) wavelet decomposition filters h

(and g):

(1)

= h · g

, K

(2)

= g · h

, K

(3)

= g · g

.(2)

In this case, the filters correspond, respectively, to two-

dimensional LH, HL, and HH wavelet directional hig h-

pass filters, and the residuals coincide with the first-level

undecimated wavelet LH, HL, and HH directional decom-

position of X. We constrained ourselves to wavelet filter

banks b ecause wavelet representations are known to pro-

vide good decorrelation and energy compactification for

images of natural scenes (see, e.g., Chapter 7 in [23]).

3.2 Distortion function (non-side-informed embedding)

We are now ready to describe the universal distortion

function. We do so first for embedding that does not use

any precover. Given a pair of cover and stego images,

X and Y, represented in the spatial (pixel) domain, we

will denote with W

(k)

(X) and W

(k)

(Y), k = 1, 2, 3, u ∈

{1, ..., n

}, v ∈{1, ..., n

}, their corresponding uvth

wavelet coefficient in the kth subband of the first decom-

position level. The UNIWARD distortion function is the

sum of relative changes of all wavelet coefficients with

respect to the cover image:

D(X, Y) 



k=1



u=1



v=1

(k)

(X) − W

(k)

(Y)|

σ +|W

(k)

(X)|

,(3)

where σ>0 is a constant stabilizing the numerical

calculations .

The ratio in (3) is smaller when a large cover wavelet

coefficient is changed (where texture and e dges appear).

Embe dding changes are discouraged in regions where

(k)

(X)| is small for at least one k, which corresponds to

a direction along which the content is modellable.

F or JPEG images, the distortion between the two arrays

of quantized DCT coefficients, X and Y,iscomputedby

first decompressing the JPEG files to the spatial domain,

and evaluating the distor tion betwe en the decompressed

images, J

−1

(X) and J

−1

(Y), in the same manner as in (3):

D(X, Y)  D



−1

(X), J

−1

(Y)



.(4)

Note that the distortion (3) is non-additive because

changing pixel X

will affect s × s wavelet coefficients,

where s × s is the size of the 2D wavelet support. Also,

changing a JPEG coefficient X

will affect a block of

8 × 8 pixels and therefore a block of (8 + s − 1) × (8 +

s − 1) wavelet coefficients. It is thus apparent that when

changing neighboring pixels (or DCT coefficients), the

embedding changes ‘interact,’ hence the non-additivity of

3.3 Distortion function (JPEG side-informed embedding)

By side-informed embedding in JPEG domain, we under-

stand the following general principle. Given the raw DCT

coefficient D

obtained from the precover P, the embed-

der has the choice of rounding D

up or down to modulate

its parity (usually the least significant bit of the rounded

value). We denote with e

=|D

− X

|, e

∈[0, 0.5], the

rounding error for the ijth co efficient when compressing

the precover P to the cover image X. Rounding ‘to the

other side’ leads to an embedding change, Y

= X

sign(D

− X

), which corresponds to a ‘rounding error ’

1−e

. Thus, every embedding change increases the distor-

tion with respect to the precover by the difference between

both rounding errors: |D

− Y

|−|D

− X

|=1 − 2e

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