From 8290657e61738a93b7b6eb60966c49efbc4f0af8 Mon Sep 17 00:00:00 2001
From: couchot <couchot@couchot-laptop.(none)>
Date: Fri, 8 Jun 2012 11:29:54 +0200
Subject: [PATCH 1/1] ajout de fichiers

---
 emb.pdf                 | Bin 0 -> 10036 bytes
 emb.ps                  | 993 ++++++++++++++++++++++++++++++++++++++++
 ourapproach.tex         |  87 ++++
 rec.pdf                 | Bin 0 -> 9292 bytes
 rec.ps                  | 819 +++++++++++++++++++++++++++++++++
 schema.dot              |  36 ++
 schema2.dot             |  29 ++
 stc.tex                 |  85 ++++
 stc/exp/python/stc_r.py | 241 ++++++++++
 test.ps                 | 993 ++++++++++++++++++++++++++++++++++++++++
 10 files changed, 3283 insertions(+)
 create mode 100644 emb.pdf
 create mode 100644 emb.ps
 create mode 100644 ourapproach.tex
 create mode 100644 rec.pdf
 create mode 100644 rec.ps
 create mode 100644 schema.dot
 create mode 100644 schema2.dot
 create mode 100644 stc.tex
 create mode 100644 stc/exp/python/stc_r.py
 create mode 100644 test.ps

diff --git a/emb.pdf b/emb.pdf
new file mode 100644
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diff --git a/ourapproach.tex b/ourapproach.tex
new file mode 100644
index 0000000..5fc4f7e
--- /dev/null
+++ b/ourapproach.tex
@@ -0,0 +1,87 @@
+The flowcharts given in Fig.~\ref{fig:sch} summarize our steganography scheme denoted as 
+STABYLO for STeganography with cAnny, Bbs, binarY embedding at LOw cost.
+What follows successively details all the inner steps and flow inside 
+the embedding stage (Fig.\ref{fig:sch:emb}) 
+and inside the extraction one(Fig.~\ref{fig:sch:ext}).
+
+
+\begin{figure*}[t]
+  \begin{center}
+    \subfloat[Data Embedding.]{
+      \begin{minipage}{0.49\textwidth}
+        \begin{center}
+          \includegraphics[width=5cm]{emb.pdf}
+        \end{center}
+      \end{minipage}
+      \label{fig:sch:emb}
+    }%\hfill
+    \subfloat[Data Extraction.]{
+      \begin{minipage}{0.49\textwidth}
+        \begin{center}
+          \includegraphics[width=5cm]{rec.pdf}
+        \end{center}
+      \end{minipage}
+      \label{fig:sch:ext}
+    }%\hfill
+  \end{center}
+  \caption{The STABYLO Scheme.}
+  \label{fig:sch}
+\end{figure*}
+
+
+\subsection{Steganalysis}
+
+LSB : 
+"Adaptive steganalysis of Least Significant Bit replacement in grayscale natural images"
+
+Structural LSB Detectors:
+\verb+http://dde.binghamton.edu/download/structural_lsb_detectors/+
+
+Vainqueur du BOSS challenge 
+
+
+ensemble:
+
+
+G. Gül and F. Kurugollu. A new methodology in steganalysis : Breaking highly
+undetactable steganograpy (HUGO). In Information Hiding, 13th International
+Workshop, volume 6958 of LNCS, pages 71–84, Prague, Czech Republic, May 18–
+20, 2011. 
+
+
+\subsection{Data Embedding} 
+
+
+
+
+\subsubsection{Edge Based Image Steganography}
+Image Quality: Edge Image Steganography
+\JFC{Raphael, les fuzzy edge detection sont souvent utilisés. 
+  il faudrait comparer les approches en terme de nombre de bits retournés,
+  en terme de complexité. }
+
+
+Presentation des algos de detection de contour
+Caractéristiques
+
+Comparaison théoriques, références
+
+Algo de stegano basé juste sur cela : (pas de bbs, pas de stc, même message).
+
+Quels paramètres sont optimaux ? Combinaison ? 
+
+
+
+
+
+\subsubsection{Security Considerations}
+
+Security aspect:
+BBS-based cryptographic version of the message 
+
+\subsubsection{Minimizing Distortion with Syndrome-Treillis Codes} 
+
+\input{stc}
+
+
+\subsection{Data Extraction}
\ No newline at end of file
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diff --git a/schema.dot b/schema.dot
new file mode 100644
index 0000000..165432b
--- /dev/null
+++ b/schema.dot
@@ -0,0 +1,36 @@
+digraph start_up { 
+	node [style = rounded, shape = rect] IC [label="Image\nCover X "]
+	node [style = rounded, shape = rect] message [label="message"]
+	node [style = rounded, shape = rect] key 
+
+	node [style = rounded, shape = rect] PI [label="Parameter\nInstantiation"] 		 
+	node [style = rounded, shape = rect] encrypt [label="m=encryption(message)"] 		 
+	node [style = rounded, shape = rect] STC [label="y= STC(x,m)"] 		 
+	node [style = rounded, shape = rect] emb [label="stego=embedding(y,X)"] 		 
+
+	node [style = rounded, shape = rect] start end;
+	node [style = rounded, shape = rect] ED [label="x= LSB(7 bits\nEdge Detection)"]  
+	
+	node [style = "", shape = diamond] cond [label="Size of x\n enough for m"]; 
+	
+	start -> PI
+	start -> IC
+	start -> message
+	start -> key 
+
+	key ->  encrypt
+
+
+	message -> encrypt
+	IC -> ED
+	ED -> cond
+	encrypt -> cond
+	encrypt -> STC
+	cond -> STC [label="Yes"]
+	cond -> PI [label="No"]
+	
+	PI -> ED
+	STC -> emb
+	emb -> end
+	
+	 }
\ No newline at end of file
diff --git a/schema2.dot b/schema2.dot
new file mode 100644
index 0000000..4f47d83
--- /dev/null
+++ b/schema2.dot
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+digraph start_up { 
+	node [style = rounded, shape = rect] SI [label="Stego Image"]
+	node [style = "", shape = diamond] cond [label="Size of y\n enough"]; 
+	node [style = rounded, shape = rect] key 
+	node [style = rounded, shape = rect] start end;
+	node [style = rounded, shape = rect] PI [label="Parameter\nInstantiation"] 		 
+	node [style = rounded, shape = rect] STC [label="m = STCr(y,H)"] 		 
+	node [style = rounded, shape = rect] ED [label="(y,H)= LSB(7 bits\nEdge Detection)"]  
+	node [style = rounded, shape = rect] decrypt [label="message=decryption(m)"] 		 
+
+
+
+	start -> SI
+	start -> PI
+	PI -> ED 
+	start -> key 
+
+	SI -> ED
+	ED -> cond 
+	cond -> STC [label="Yes"]
+	cond -> PI [label="No"]
+	
+	STC -> decrypt
+	key -> decrypt
+	decrypt -> end
+	
+		
+	
+	 }
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diff --git a/stc.tex b/stc.tex
new file mode 100644
index 0000000..6570c73
--- /dev/null
+++ b/stc.tex
@@ -0,0 +1,85 @@
+Let 
+$x=(x_1,\ldots,x_n)$ be the $n$-bits cover vector of the image $X$, 
+$m$ be the message to embed and 
+$y=(y_1,\ldots,y_n)$ be the $n$-bits stego vector.
+The usual additive embbeding impact of replacing $x$ by $y$ in $X$
+is given by a distortion function 
+$D_X(x,y)= \Sigma_{i=1}^n \rho_X(i,x,y)$ where the function $\rho_X$
+expressed the cost of replacing $x_i$ by $y_i$ in $X$.
+Let us consider that $x$ is fixed: 
+this is for instance the LSBs of the image edge bits. 
+The objective is thus to find $y$ that minimizes $D_X(x,y)$.
+
+Hamming embedding proposes a solution to this problem. 
+Some steganographic 
+schemes~\cite{DBLP:conf/ih/Westfeld01,DBLP:conf/ih/KimDR06,DBLP:conf/mmsec/FridrichPK07} are based on this binary embedding.
+Furthermore this code provides a vector $y$ s.t. $Hy$ is equal to 
+$m$ for a given binary matrix $H$. 
+
+Let us explain this embedding on a small illustrative example where
+$\rho_X(i,x,y)$ is identically equal to 1,
+$m$ and $x$ are respectively  a 3 bits column
+vector and a 7 bits column vector. 
+Let then $H$ be the binary Hamming matrix  
+$$
+H = \left(
+\begin{array}{lllllll}
+ 0 & 0 & 0 & 1 & 1 & 1 & 1 \\
+ 0 & 1 & 1 & 0 & 0 & 1 & 1 \\
+ 1 & 0 & 1 & 0 & 1 & 0 & 1 
+\end{array}
+\right).
+$$
+The objective is to modify $x$ to get $y$ s.t. $m = Hy$.
+In this algebra, the sum and the product respectively correspond to
+the exclusive \emph{or} and to the \emph{and} Boolean operators.
+If $Hx$ is already equal to $m$, nothing has to be changed and $x$ can be sent.
+Otherwise we consider the difference $\delta = d(m,Hx)$ which is expressed 
+as a vector : 
+$$
+\delta = \left( \begin{array}{l}
+\delta_1 \\
+\delta_2 \\
+\delta_3
+\end{array} 
+\right)  
+\textrm{ where $\delta_i$ is 0 if $m_i = Hx_i$ and 1 otherwise.} 
+$$
+Let us thus consider the $j$th column of $H$ which is equal to $\delta$.   
+We denote by $\overline{x}^j$ the vector  we obtain by
+switching the $j$th component of $x$, 
+that is, $\overline{x}^j = (x_1 , \ldots, \overline{x_j},\ldots, x_n )$.
+It is not hard to see that if $y$ is $\overline{x}^j$, then 
+$m = Hy$.
+It is then possible to embed 3 bits in only 7 LSB of pixels by modifying
+1 bit at most.
+In the general case, when comunicating $n$ message bits in 
+$2^n-1$ pixels needs $1-1/2^n$ average changes. 
+
+
+
+Unfortunately, 
+
+
+for any given $H$, finding $y$ that solves $Hy=m$ and that 
+that minimizes $D_X(x,y)$ has exponential complexity with respect to $n$. 
+The Syndrome-Trellis Codes  (STC) 
+presented by Filler et al. in~\cite{DBLP:conf/mediaforensics/FillerJF10} 
+is a practical solution to this complexity. Thanks to this contribution,
+the solving algorithm has a linear complexity with resspect to $n$.
+
+First of all, Filler et al. compute the matrix $H$
+by placing a small sub-matrix $\hat{H}$ of size $h × w$ next
+to each other and shifted down by one row. 
+Thanks to this special form of $H$, one can represent
+every solution of  $m=Hy$ as a path through a trellis.
+
+Next, the  process of finding $y$ consists of a forward and a backward part:
+\begin{enumerate}
+\item Forward construction of the trellis that depends on $\hat{H}$, on $x$, on $m$, and on $\rho$;
+\item Backward determinization of $y$ which minimizes $D$ starting with 
+the complete path with minimal weight
+\end{enumerate} 
+Let us now give some details about these two parts.
+
+
diff --git a/stc/exp/python/stc_r.py b/stc/exp/python/stc_r.py
new file mode 100644
index 0000000..854c780
--- /dev/null
+++ b/stc/exp/python/stc_r.py
@@ -0,0 +1,241 @@
+from random import *
+import numpy as np
+from math import *
+import gc
+
+infinity = 100000000000
+
+
+
+# forward part
+
+
+def dec(ch,n):    
+    l = len(ch)
+    acc = 0
+    for i in xrange(l):
+        if ch[i]==1:
+            acc = acc + 2**(n-i-1)        
+    return acc
+
+
+def bin(elem,n):
+    """Convertit un nombre en binaire"""
+    q = -1
+    res = [0 for i in xrange(n)]
+    i = 1
+    while q != 0:
+        q = elem // 2
+        r = elem % 2
+        res[n-i] =  r
+        elem = q
+        i+=1
+    return res
+
+
+
+def xorb(a,b):
+    return 1 if a != b else 0
+
+def xor(e1,e2,h):
+    e1b,e2b  = bin(e1,h),bin(e2,h)
+    d = dec([xorb(e1b[j],e2b[j]) for j in xrange(h)],h)
+    return d
+
+def lit(d,(indx,indy)):
+    if (indx,indy) in d :
+        return d[(indx,indy)]
+    else :
+        return 0
+
+
+
+
+def forward(H_hat,x,message,lnm,rho):
+    (h,w) = int(log(max(H_hat),2))+1, len(H_hat)
+    path = dict() 
+    nbblock = lnm
+    wght = [infinity for _ in xrange(int(2**h))] 
+    wght[0]=0    
+    newwght = [0 for _ in xrange(int(2**h))]
+#    rho = 1
+#    rho= [1 for _ in xrange(len(x))]
+    indx,indm = 0,0
+    i=0
+    while i < nbblock: # pour chaque bit du message
+        for j in xrange(w):   # pour chaque colonne de H_hat
+            #print indx, "en entrant",wght
+            k = 0
+            while k < int(2**h): # pour chaque ligne de H
+                w0 = wght[k] + x[indx]*rho[indx]
+                w1 = wght[xor(k,H_hat[j],h)] + (1-x[indx])*rho[indx]
+                if w1 < w0 :
+                    path[(indx,k)] = 1 
+                else : 
+                    if (indx,k) in path:
+                        del path[(indx,k)]
+                newwght[k] = min(w0,w1)
+                k +=1 
+            indx +=1
+            wght = [t for t in newwght]
+            #print " apres calcul",wght
+
+        for j in xrange(int(2**(h-1))):   # pour chaque colonne de H
+            wght[j] = wght[2*j + message[indm]]
+        wght = wght[:int(pow(2,h-1))] + [infinity for _ in xrange(int(pow(2,h)-pow(2,h-1)))]
+        indm +=1
+        i +=1
+    start = np.argmin(wght)
+    return (start,path)
+
+
+def backward(start,H_hat,x,message,lnm,path):
+    (h,w) = int(log(max(H_hat),2))+1, len(H_hat)
+    indx,indm = len(x)-1,lnm-1
+    state = 2*start + message[indm]
+    indm -=1
+    # l'initialisation de state n'est pas optimale...
+    nbblock = lnm
+    y=np.zeros(len(x))
+    i=0
+    while i < nbblock:
+        l = range(w)
+        l.reverse()
+        for j in l:   # pour chaque colonne de H_hat
+            y[indx] = lit(path,(indx,state))
+            state = xor(state,y[indx]*H_hat[j],h)
+            indx -=1
+        state = 2*state + message[indm]
+        indm -=1 
+        i +=1
+    return [int(t) for t in y]
+
+    
+ 
+
+
+
+def trouve_H_hat(n,m,h):
+    assert h ==7 
+    alpha = float(n)/m
+    assert alpha >= 2 
+    index = min(int(alpha),9)
+    mat = {
+        2 : [71,109],
+        3 : [95, 101, 121],
+        4 : [81, 95, 107, 121],
+        5 : [75, 95, 97, 105, 117],
+        6 : [73, 83, 95, 103, 109, 123],
+        7 : [69, 77, 93, 107, 111, 115, 121],
+        8 : [69, 79, 81, 89, 93, 99, 107, 119],
+        9 : [69, 79, 81, 89, 93, 99, 107, 119, 125]
+        }[index]
+    return(mat, index*m)
+
+
+def stc(x,rho,message):
+    lnm = len(message)
+    (mat,taille_suff) = trouve_H_hat(len(x),len(message),7)
+    x_b = x[:taille_suff]
+    (start,path) = forward(mat,x_b,message,lnm,rho)
+    return (x_b,backward(start,mat,x_b,message,lnm,path),mat)
+
+
+
+
+
+def nbdif(x,y):
+    r,it = 0,0
+    l = len(y)
+    while it < l :
+        if x[it] != y[it] :
+            r +=1
+        it += 1
+    return float(r)/l 
+        
+
+
+
+
+
+def prod(H_hat,lnm,y):
+    (h,w) = int(log(max(H_hat),2))+1, len(H_hat)
+    i=0
+    H =[]
+    V=[0 for _ in range(len(y))]
+    sol=[]
+    while i < lnm: # pour chaque ligne 
+        V=[0 for _ in range(len(y))]    
+        k = max([(i-h+1)*w,0])
+        dec = max([i-h+1,0])
+        for j in xrange(min([i+1,h])): #nbre de blocks presents sur la ligne i
+            for l in xrange(w): # pour chaque collone de H_hat
+                V[k] = bin(H_hat[l],h)[h-i-1+j+dec]
+                k+=1
+                
+        sol.append(np.dot(np.array(V),np.array(y)))
+        i+=1
+        #H += [V]
+    #H = np.array(H)    
+    #y = np.array(y)
+    #print "dot",np.dot(H,y),H.shape
+    #print "sol",sol
+    return sol#list(np.dot(H,y))
+    
+def equiv(x,y): 
+    lx = len(x)
+    assert lx == len(y)
+    i=0
+    while i < lx :
+        if x[i] % 2 != y[i]%2 : 
+            return False
+        i += 1
+    return True
+        
+"""
+################
+
+x = [randint(0,1) for _ in xrange(65000)]
+rho = [randint(1,9) for _ in xrange(65000)]
+message = [randint(0,1) for _ in xrange(26000)]
+
+
+
+#(x_b,y,H_hat) = stc(x,rho,message)
+# x_b est la sous partie de x qui va etre modifiee
+# y est le vecteur des bits modifies
+# H_hat est la sous-matrice retenue qui est embarquee dans H  
+
+#print nbdif(x_b,y)
+
+#print message
+#print x
+#print rho
+#print y
+#message2 = [x%2 for x in prod(H_hat,len(message),y)]
+#print message2 
+print max([message[l]-message2[l] for l in xrange(len(message))])
+print equiv(message,message2)
+
+"""
+count = 0
+
+while count < 100 and eval :
+    lx = randint(500,1000)
+    x = [randint(0,1) for _ in xrange(lx)]
+    rho = [randint(1,9) for _ in xrange(lx)]
+
+    lm = randint(lx/10,lx/2)
+    message = [randint(0,1) for _ in xrange(lm)]
+    (x_b,y,H_hat) = stc(x,rho,message)
+    eval = equiv(message, prod(H_hat,len(message),y))
+    if not (eval):
+        print x
+        print message
+
+    count +=1
+    if count % 10 == 0 :
+        print count
+                     
+print count
+
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new file mode 100644
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