Added files quantum attacks on 2EM.

Added files related to Quantum Attacks on EM cipher.
bshakya77 · Feb 12, 2024 · dab7f24 · dab7f24
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diff --git a/source_code/notebooks/EM_Attacks/library.py b/source_code/notebooks/EM_Attacks/library.py
@@ -0,0 +1,188 @@
+#!/usr/bin/python3
+import qcircuits as qc
+import numpy as np
+import sys
+def Circuits(x):
+    #print("*********** Circuit Input: (x) ****************")
+    #print(x)
+    CNOT = qc.CNOT()
+    X = qc.PauliX()
+    toffoli = qc.operators.Toffoli()
+    #----------------------------------------------------
+    #First copy
+    for i in range(0,10):
+        #print("\n******* x before ********\n")
+        #print(x)
+        x = CNOT(x,qubit_indices = [i,i+10])
+        #print("\n******* x after ********\n")
+        #print(x)
+    #------------------------------------------------------
+    #Adding the key
+    x = X(x,qubit_indices = [10])
+    x = X(x,qubit_indices = [13])
+    x = X(x,qubit_indices = [19])
+    #-----------------------------------------------------
+    #Permutation over the first register
+    x = toffoli(x,qubit_indices = [0,1,2])
+    x = toffoli(x,qubit_indices = [1,2,3])
+    x = toffoli(x,qubit_indices = [2,3,4])
+    x = toffoli(x,qubit_indices = [3,4,5])
+    x = toffoli(x,qubit_indices = [4,5,6])
+    x = toffoli(x,qubit_indices = [5,6,7])
+    x = toffoli(x,qubit_indices = [6,7,8])
+    x = toffoli(x,qubit_indices = [8,9,0])
+    x = toffoli(x,qubit_indices = [9,0,1])
+    #-----------------------------------------------------
+    #Permutation over the second register
+    x = toffoli(x,qubit_indices = [10,11,12])
+    x = toffoli(x,qubit_indices = [11,12,13])
+    x = toffoli(x,qubit_indices = [12,13,14])
+    x = toffoli(x,qubit_indices = [13,14,15])
+    x = toffoli(x,qubit_indices = [14,15,16])
+    x = toffoli(x,qubit_indices = [15,16,17])
+    x = toffoli(x,qubit_indices = [16,17,18])
+    x = toffoli(x,qubit_indices = [18,19,10])
+    x = toffoli(x,qubit_indices = [19,10,11])
+    #-----------------------------------------------------
+    #Compute P(x) xor P(x xor k)
+    for i in range(0,10):
+        x = CNOT(x,qubit_indices = [i,i + 10])
+    #------------------------------------------------------
+    #Adding the second key
+    x = X(x,qubit_indices = [10])
+    x = X(x,qubit_indices = [16])
+    x = X(x,qubit_indices = [17])
+    x = X(x,qubit_indices = [19])
+    #------------------------------------------------------
+    return x
+
+def SimonEM():
+    X = qc.PauliX()
+    #print("\n******* Pauli X ********\n")
+    #print(X)
+    #print("\n******* CNOT ********\n")
+    CNOT = qc.CNOT()
+    #print(CNOT)
+    #print("\n******* toffoli ********\n")
+    toffoli = qc.operators.Toffoli()
+    #print(toffoli)
+    H10 = qc.operators.Hadamard(d = 10)
+    #print("\n******* Hadamard Gate ********\n")
+    #print(H10)
+    phi = qc.positive_superposition(d = 10)
+    #print("\n******* positive superposition ********\n")
+    #print(phi)
+    ksi = qc.zeros(10)
+    #print("\n******* ksi qubit ********\n")
+    #print(ksi)
+    Phi = phi*ksi
+    #print("\n******* Phi = phi * ksi ********\n")
+    #print(Phi)
+    Phi = Circuits(Phi)
+    #We apply the inverse of the Permutation
+    #--------------------------------------------------------
+    Phi = toffoli(Phi,qubit_indices = [9,0,1])
+    Phi = toffoli(Phi,qubit_indices = [8,9,0])
+    Phi = toffoli(Phi,qubit_indices = [6,7,8])
+    Phi = toffoli(Phi,qubit_indices = [5,6,7])
+    Phi = toffoli(Phi,qubit_indices = [4,5,6])
+    Phi = toffoli(Phi,qubit_indices = [3,4,5])
+    Phi = toffoli(Phi,qubit_indices = [2,3,4])
+    Phi = toffoli(Phi,qubit_indices = [1,2,3])
+    Phi = toffoli(Phi,qubit_indices = [0,1,2])
+    #--------------------------------------------------------
+    #We measure the last register
+    Phi.measure(qubit_indices = [10,11,12,13,14,15,16,17,18,19],remove = True)
+    #On applique la transformé de Hadamard sur les premier registres
+    Phi = H10(Phi,qubit_indices = [0,1,2,3,4,5,6,7,8,9])
+    #--------------------------------------------------------
+    #We measure the first register
+    Phi.measure(qubit_indices = [0,1,2,3,4,5,6,7,8,9],remove = False)
+    return Phi
+
+
+def  QubitToVector(v):
+    for t in range(0,len(v)):
+        if((v[t] == 1) or (v[t] == -1)):
+            indice = t
+            break
+        else:
+            pass
+    x = bin(t)
+    return x
+
+def ReduceM(M):
+    Index = []
+    count = 0
+    for i in range(0,len(M)):
+        count = 0
+        for j in range(0,10):
+            if(M[i,j] == 1):
+                count += 1
+        if(count == 0):
+            Index.append(i)
+    for i in range(len(Index) - 1,-1,-1):
+        M = np.delete(M,(Index[i]), axis =0)
+    return M
+
+def pivot_index(M,i):
+    n = len(M)
+    j = i
+    for k in range(i + 1,n):
+        if(M[k,i] > M[i,i]):
+            j = k
+            return j
+    return i
+
+def pivot_indexH(M,i):
+    j = i
+    for k in range(i,0,-1):
+        if(M[k,i] > M[i,i]):
+            j = k
+            return j
+    return i
+
+def swapline(M,i,j):
+    for k in range(0,10):
+        tmp = M[i,k]
+        M[i,k] = M[j,k]
+        M[j,k] = tmp
+
+def transvection_lines(M,i,k,factor):
+    for j in range(0,10):
+        M[k,j] = (M[k,j] + M[i,j]*factor)%2
+
+def gauss(M):
+    for i in range(0,10):
+        ipiv =  pivot_index(M,i)
+        if(ipiv != i):
+            swapline(M,i,ipiv)
+        for k in range(i + 1,len(M)):
+            factor = M[k,i]
+            transvection_lines(M,i,k,factor)
+    return M
+
+def gaussH(M):
+    for i in range(9,1,-1):
+        ipiv = pivot_indexH(M,i)
+        if(ipiv != i):
+            swapline(M,i,ipiv)
+        for k in range(i - 1,0,-1):
+            factor = M[k,i]
+            transvection_lines(M,i,k,factor)
+    return M
+
+def solver(M):
+    #print("M:", M)
+    for i in range(1,1024):
+        tmp = bin(i)[2:]
+        l = [int(i) for i in tmp]
+        while(len(l) != 10):
+            l = [0] + l
+        arr = np.array(l)
+        #print("ARR:", arr)
+        hyp = M.dot(arr)
+        #print("hyp:", hyp)
+        if(all(x%2 == 0 for x in hyp)):
+            print("Array Found !!")
+            return arr
diff --git a/source_code/notebooks/EM_Attacks/main.py b/source_code/notebooks/EM_Attacks/main.py
@@ -0,0 +1,41 @@
+#!/usr/bin/python3
+import qcircuits as qc
+import numpy as np
+import library as lib
+import sys
+import time
+
+s = []
+
+for i in range(0,15):
+    phi = lib.SimonEM()
+    print("********** phi ************") #10 qubit tensor
+    print(phi)
+    v = phi.to_column_vector()
+    x = lib.QubitToVector(v)
+    #print("*******x before ******\n", x)
+    while(len(x) < 12):
+        x = x[:2] + '0' + x[2:]
+        #print("\n*******x after******\n", x)
+    s.append([int(d) for d in x[2:]])
+    #print("\n********s array*******\n")
+    #print(s)
+M = np.array(s,dtype=object)
+#print("\n********Reduced Matrix*******\n")
+#print(M)
+B = lib.gauss(M)
+#print("\n********Gaussian Elimination*******\n")
+#print(B)
+C = lib.gaussH(B)
+#print("\n********Hermitian*******\n")
+#print(C)
+N  = lib.ReduceM(C)
+#print("\n********Reduced Matrix*******\n")
+#print(N)
+if(len(N) < 9):
+    print("No solution")
+    sys.exit(False)
+else:
+    k = lib.solver(N)
+    print(k)
+    sys.exit(True)