The purpose of steganography is to conceal the very presence of secret information.

剛剛收到的 空中英語教室電子報 200 期, 內容剛好是在討論 very 的形容詞用法, 內容如下:

The U.N.'s Law of the Sea Treaty aims to resolve this very question. (p. 50, line 2)

句中的 very 是形容詞、比較不常見的用法，它有「正是」的強調意味。

例句：

-- The topic you brought up is the very thing we discussed at our last meeting.

-- Barbara realized that her children had done the very thing she feared: they had all moved far from home.

在我的印象中, 我所讀的 steganography papers 中, 的確常常出現這樣的用法:

例如, 在 Jessica Fridrich 所寫的論文 "A New Steganographic Method for Palette-Based Images" 的 Introduction 中, 第二句就是這樣用的:

The purpose of steganography is to conceal the very presence of secret information.

From StegoRN

另外, 在 The Code Breakers 這本書中, Chapter 16 CENSORS, SCRAMBLERS, AND SPIES (P. 513) 中的第一段也有這樣的用法:

CIPHER IS THE LANGUAGE OF SPIES - and usually they must talk in whispers. A spy's success, his very existence, depends on his not being seen or heard. Sending messages in obviously cryptographic form would alert counterespionage to him as effectively as wearing a cloak and dagger. Yet he must transmit, else he is useless. So he eschews the overt methods of secret communications for the covert. He resorts to open codes, hollow heels, invisible inks, microscopically small missives - the steganographic methods that conceal the very fact that a message is being sent. He seeks to communicate unnoticed.

From StegoRN

最近在看的這本書 "Steganography in Digital Media" 中, 第 2 頁的第 2 段, 也是有相同的用法:

Note that the hidden message is unrelated to the content of the letter, which only serve as a decoy or "cover" to hide the very fact that a secret message is being sent. ...

如果你用 "to conceal the very existence" 當關鍵字在 Google 中搜尋, 相信也可以搜尋到許多 steganography 相關的論文或文章呢!

Feature-Based Steganalysis for JPEG Images and Its Implications for Future Design of Steganographic Schemes

Author: Jessica Fridrich

Information Hiding Workshop 2004
Toronto, Ontario, Canada
23 - 25, May, 2004

Lecture Notes in Computer Science, Vol. 3200



Abstract

In this paper, we introduce a new feature-based steganalytic method for JPEG images and use it as a benchmark for comparing JPEG steganographic algorithms and evaluating their embedding mechanisms. The detection method is a linear classifier trained on feature vectors corresponding to cover and stego images. In contrast to previous blind approaches, the features are calculated as an L1 norm of the difference between a specific macroscopic functional calculated from the stego image and the same functional obtained from a decompressed, cropped, and recompressed stego image. The functionals are built from marginal and joint statistics of DCT coefficients. Because the features are calculated directly from DCT coefficients, conclusions can be drawn about the impact of embedding modifications on detectability. Three different steganographic paradigms are tested and compared. Experimental results reveal new facts about current steganographic methods for JPEGs and new design principles for more secure JPEG steganography.

Detecting LSB Steganography in Color and Gray-Scale Images (RS steganalysis)

Detecting LSB Steganography in Color and Gray-Scale Images
Jessica Fridrich, Miroslav Goljan, Rui Du
Magazine of IEEE Multimedia, Special Issue on Security,
October-November 2001, pp. 22-28.

這篇論文將一張影像中的連續像素切割成一個一個的 pixel group G = (x1, x2, ... xn)。
假設每一個 pixel group 的大小為 2*2, 那麼一張 384*256 大小的影像, 就會有 (384/2)*(256/2) = 24576 個 pixel groups。

針對每個 group, 根據其特性將會被分成 Regular, Singular, Unusable 等三類。用來分類的特性由兩個因素決定:

1. discrimination function f

discrimination function 的目的是評量一個 pixel group 的平坦性(smoothness) 或規則性(regularity)。一般來說, 如果 group 所包含的 noise 愈多, f(G) 就會越大。論文中舉了一個例子, 用相鄰兩個像素值差的總和, 當作 discrimination function 所得到值。

2. flipping: invertible operation F。

flipping 基本上是針對灰階值的一種排列方式(permutation), 且連坐兩次就會回復成原來的灰階值(2-cycles), 即 F(F(x)) = x。論文中定義了三種 flipping operation, 分別為 F1, F-1 及 F0。
The permutation F1: 0←→1, 2←→3, 4←→5, ..., 254 ←→ 255。
The permutation F-1: -1←→0, 1←→2, 3←→4, ..., 255←→256。
　F-1(x) = F1(x+1) -1 , for all x
The identity permutation F0:
　F0(x) = x, for all x

針對每一個 pixel group G, 首先計算 discrimination function f(G) 的值, 然後對 G 做 flipping operation F, 得到 F(G), 然後計算 f(F(G)), 藉由比較 f(G) 與 f(F(G)) 的大小關係, 就可以對 G 進行分類。

　Regular groups:　G 屬於 R <=> f(F(G)) > f(G)
　Singular groups:　G 屬於 R <=> f(F(G)) < f(G)　
　Unusable groups:　G 屬於 U <=> f(F(G)) = f(G)

F(G) 所代表的意思是針對 pixel group G = (x1, x2, ... xn) 中的每一個 xi, 都分別使用相同的 flipping operation F。要針對不同的 xi, 使用不同的 flipping operation F, 必須再提供一個 mask M 來指明。M 是一個 n-tuple 的向量, 每個值都由 -1, 0, 1 所組成。假設 n=4, M=( 0, 1, -1, 0),

FM(G) 所代表的意思就是:
對 x1 做 F0 的 flipping operation;
對 x2 做 F1 的 flipping operation;
對 x3 做 F-1 的 flipping operation;
對 x4 做 F0 的 flipping operation。

使用 FM 的用意是模擬不可逆雜訊干擾行為(invertible noise adding) 對 pixel values 的影響。

RM 表示在針對 FM , 影像中 regular group 數量所佔的百分比 (percent of all group);
SM 則是 singular group 數量所佔的百分比。因此,

　RM + SM ≤ 1　and　R-M + S-M ≤ 1 ( -M: negative mask )

針對作者所提出的方法, 有一個統計假設前提(statistical hypothesis)是:

　RM ~= R-M　and　SM ~= S-M









(未完待續)

Attacking the OutGuess

Jessica Fridrich, Miroslav Goljan & Dorin Hogea
"Attacking the OutGuess,"
ACM Workshop on Multimedia and Security 2002,
Juan-les-Pins, France, December 6, 2002





Abstract
In this paper, we describe new methodology for developing steganalytic methods for JPEG images. The proposed framework can be applied to virtually all current methods for JPEGs including OutGuess, F5, and J-Steg. It also enables accurate estimation of the length of the embedded secret message. The methodology is demonstrated on OutGuess 0.2.

這篇論文針對 OutGuess 0.2 隱藏工具提出一套攻擊方法。所提的分析架構, 不但可以運用到不同的JPEG影像隱藏工具, 亦可以正確地估算嵌入訊息的長度。

在這篇論文的第三節中提到 OutGuess 的特點, 與解釋為什麼 Chi-square attack 無法破解 OutGuess。

p2. left column
The OutGuess steganographic algorithm was proposed by Neils Provos to counter the statistical chi-square attack. In the first pass, similar to J-Steg, OutGuess embeds message bits along a random walk into the LSBs of coefficients while skipping 0’s and 1’s. After embedding, the image is processed again using a second pass. This time, corrections are made to the coefficients to make the stego image histogram match the cover image histogram. Because the chi-square attack is based on analyzing first-order statistics of the stego image, it cannot detect messages embedded using OutGuess. Provos also reports that the corrections are made in such a manner to avoid detection using his generalized chi-square attack.

本篇論文的核心觀念描述在底下這段文字:

P.2 right column
Because OutGuess introduces random changes into the quantized coefficients, the spatial discontinuities at the boundaries of all 8×8 blocks will increase. We will measure the discontinuity using the blockiness measure. For detection, we will inspect the increase of this blockiness measure after embedding a 100% message again using OutGuess. This increase will be smaller for the stego image than for the cover image because of the partial cancellation of changes. This difference will form the basis of our message length estimation.

由於 OutGuess 隨機改變量化後 DCT 係數的 LSBs, 增加了還原後 8*8 區塊的不連續性。J. Fridrich用一個 blockiness formula 來估算區塊不連續性。使用 OutGuess 藏入100% 的資料量後, 檢驗區塊不連續性的增加量。如果這張影像是偽裝影像(stego image), 區塊不連續性增加量是比原始掩護影像 (cover image) 來得小。這個差距就是用來估算嵌入資料量的基礎。

而論文中的 blockiness formula, 其實就是不同區塊間的相鄰像素間的色彩差距絕對值的總和。再求取嵌入資料量大小的過程中, 必須知道原始掩護影像的區塊不連續性, S(0)。J. Fridrich 經由實驗證明, 將偽裝影像裁去四列像素後所得的區塊不連續性和原始掩護影像的區塊不連續性值是相近的, 因此可以用來代替所需的 S(0)。

關於 Jsteg 的點點滴滴 (四) : J. Fridrich

Jessica Fridrich 在她 2006 年 Fundamentals of Steganography 課程, Lecture 4 投影片 中, P. 7 談到 Jsteg 的作法, 從投影片中我們清楚的知道 Jsteg 並沒有考慮到四捨五入所造成的影響。完全是針對四捨五入後的 DCT 係數根據要藏入的訊息去修改係數。