2022.sagews

# set up Key, PlainText("hold") and find Cipher 
d={0:"a",1:"b",2:"c",3:"d",4:"e",5:"f", 6:"g",7:"h",8:"i",9:"j",10:"k",11:"l", 12:"m",
  13:"n",14:"o",15:"p",16:"q", 17:"r",18:"s",19:"t",20:"u",21:"v", 22:"w",23:"x",24:"y",25:"z"} 
a={"a":0,"b":1,"c":2,"d":3,"e":4,"f":5, "g":6,"h":7,"i":8,"j":9,"k":10,"l":11, "m":12,
  "n":13,"o":14,"p":15,"q":16, "r":17,"s":18,"t":19,"u":20,"v":21, "w":22,"x":23,"y":24,"z":25} 
K=Matrix([[3,10],[5,7]]) 
print "key:"
print K
print
print "plaintext:"
print P
print
P=Matrix([[a["h"],a["o"]],[a["l"],a["d"]]]) 
C=(P*K) 
C=C.mod(26)
print "Ciphertext:" 
print C 
print


# Compute K inverse 
Mod(K.determinant(),26) 
Di=Mod(Mod(K.determinant(),26)^-1,26) 
Ki=Di*Matrix([[7,-10],[-5,3]]) 
print "Compute K inverse:"
print Ki
print
        
# Confirm that Ki is indeed the inverse of K 
print "Confirm that Ki is indeed the inverse of K: " 
print K*Ki     
print


# Get the plaintext from the cipher text usin 
# Ki 
P=C*Ki 
print "Get the plaintext from the cipher text using K:"
print (d[P[0][0]],d[P[0][1]],d[P[1][0]],d[P[1][1]])
print 


# Crack the hill cipher 
K=Matrix([[3,10],[5,7]]) 
P=Matrix([[a["h"],a["i"]],[a["l"],a["l"]],[a["c"],a["i"]],[a["p"],a["h"]],[a["e"],a["r"]]]) 
C=(P*K).mod(26) 
print "Crack the hill cipher:"
print C     
print



Y=Matrix([[9,22],[10,5]]) 
X=Matrix([[a["h"],a["i"]],[a["l"],a["l"]]]) 
print "Crack the hill cipher:"
print X    
print 
     


# Compute X inverse 
Di=Mod(Mod(X.determinant(),26)^-1,26) 
Xi=Di*Matrix([[11,-8],[-11,7]]) 
print "Compute X inverse"
print Xi*X     
print

print "Compute the Key" 
print Xi*Y

key: [ 3 10] [ 5 7] plaintext: [ 7 8] [11 11] [ 2 8] [15 7] [ 4 17] Ciphertext: [13 12] [22 1] Compute K inverse: [15 12] [19 25] Confirm that Ki is indeed the inverse of K: [1 0] [0 1] Get the plaintext from the cipher text using K: ('h', 'o', 'l', 'd') Crack the hill cipher: [ 9 22] [10 5] [20 24] [ 2 17] [19 3] Crack the hill cipher: [ 7 8] [11 11] Compute X inverse [1 0] [0 1] Compute the Key [ 3 10] [ 5 7]