Data Encryption Standard Made With Key Sizes of 14 Bits

Today I would like to share you the power of cryptography.

I made this software 2011 in Eindhoven, Netherlands (country of cryptography) where I was having my exchange studies at the time.

The software is about the Data Encryption Standard or DES, however you like to call it.

DES With 14 Bits

Data Encryption Standard is the old queen of cryptography, which eventually got caught for being too easy to solve. There is a great article in Wikipedia about the topic and how it has influenced modern cryptography.

What I did was kinda experiment if I could code this thing together with some tweaking to the original Standard. DES was created to encrypt with key sizes of 56 bits and block sizes of 64 bits doing 16 rounds of crypting in total.

To learn the standard and the basics of cryptography, I chose to do it with key sizes of 14 bits and block sizes of 16 bits doing 2 rounds of crypting in total. I actually succeeded on this and did a little software with Python to prove it.

Mathematics

Here are the mathematics from my version of the Data Encryption Standard.

Permutations

PC1 = [12, 5, 14, 1, 10, 2, 6,

9, 15, 4, 13, 7, 11, 3]

PC2 = [ 6, 11, 4, 8, 13, 3,

12, 5, 1, 10, 2, 9]

IP = [ 2, 14, 6, 10,

12, 8, 16, 4,

5, 13, 3, 9,

11, 1, 15, 7]

IP-1 = [ 14, 1, 11, 8,

9, 3, 16, 6,

12, 4, 13, 5,

10, 2, 15, 7]

E = [ 8, 1, 2, 3, 4, 5,

4, 5, 6, 7, 8, 1]

S = [

[ 4, 11, 2, 14, 15, 0, 8, 13, 3, 12, 9, 7, 5, 10, 6, 1,

13, 0, 11, 7, 4, 9, 1, 10, 14, 3, 5, 12, 2, 15, 8, 6,

1, 4, 11, 13, 12, 3, 7, 14, 10, 15, 6, 8, 0, 5, 9, 2,

6, 11, 13, 8, 1, 4, 10, 7, 9, 5, 0, 15, 14, 2, 3, 12],

[13, 2, 8, 4, 6, 15, 11, 1, 10, 9, 3, 14, 5, 0, 12, 7,

1, 15, 13, 8, 10, 3, 7, 4, 12, 5, 6, 11, 0, 14, 9, 2,

7, 11, 4, 1, 9, 12, 14, 2, 0, 6, 10, 13, 15, 3, 5, 8,

2, 1, 14, 7, 4, 10, 8, 13, 15, 12, 9, 0, 3, 5, 6, 11]

]

P = [ 6, 4, 7, 3,

5, 1, 8, 2]

Calculations

We choose a sub key K’ of 12 bits

1	000110 110000

Calculations of F(R, K’) as R = 1011 0110

E(R) = 010110 101101

K (+) E(R) = 010000 011101

S7(B1)S8(B2) = 0011 1001

F(R, K') = 0101 1010

We choose a key K of 16 bits

1	0100 0110 0100 1001

And calculate the two keys K1 and K2

K+ = 0000 1110 0011 00

C0 = 0000111

D0 = 0001100

C1 = 0111000

D1 = 1100000

C2 = 1000011

D2 = 0000110

K1 = 001101000011

K2 = 100010101000

We choose an input I of 15 bits (e.g. the ASCI-coding of the characters ‘v’ and ‘b’)

1	0111 0110 0110 0001

And encrypt I using the DESHI-algorithm where we use the given IP and the calculated K1, K2 and IP-1.

IP = 1011 0001 0010 1011

L0 = 1011 0001

R0 = 0010 1011

R1 = L0 (+) F(R0, K1)

E(R0) = 100101 010110

K1 = 001101000011

K1 (+) E(R0) = 101000 010101

S7(B1) S8(B2) = 1100 0110

F(R, K’) = 1010 0101

R1 = L0 (+) F(R0, K1) = 0001 0100

L1 = R0 = 0010 1011

R2 = L0 (+) F(R1, K2)

E(R1) = 000010 101000

K2 = 1000010 101000

K2 (+) E(R1) = 100000 000000

S7(B1) S8(B2) = 0001 1101

F(R, K’) = 1100 1010

R2 = L1 (+) F(R1, K2) = 1110 0001

L2 = R0 = 0001 0100

R2L2 = 1110 0001 0001 0100

IP-1 = 1101 0100 1000 0100

Software

Program is made with Python version 3.2. The program can probably be run if the system has 3.0 or newer version of Python, but only tested with 3.2. The latest version can be downloaded from: http://www.python.org/download/. The program can be used in Linux or Windows as long as there is Python installed into the system.

Here are some screenshots with the same examples as used in the earlier handwritten DES encryption.

After clicking the encrypt button.

After clicking the decrypt button

Usage

This was just an experiment if I could learn DES and some cryptography, this software should not be used in real life situations. The method I used actually made DES weaker against attacks because I did it with less bits than the usual version. I hope maybe someone may find this information useful and maybe learn some cryptography. In my opinion it’s a really complex world and so much different from traditional software development, because of the mathematics that are included.

Source Code

Here is the source code for this software. To run the software, just copy/paste the code into .py file and run it.

100

101

102

103

104

105

106

107

108

109

110

111

112

113

114

115

116

117

118

119

120

121

122

123

124

125

126

127

128

129

130

131

132

133

134

135

136

137

138

139

140

141

142

143

144

145

146

147

148

149

150

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

181

182

183

184

# GNU GPL

# des.py - Python version used: 3.2

from tkinter import * # UI tool import

from tkinter.messagebox import showerror # copies showerror

fieldnames = ('key', 'message', 'cipher', 'binary')

pc1 = [12, 5, 14, 1, 10, 2, 6,

9, 15, 4, 13, 7, 11, 3]

leftshifts = [3, 3]

pc2 = [ 6, 11, 4, 8, 13, 3,

12, 5, 1, 10, 2, 9]

ip = [ 2, 14, 6, 10,

12, 8, 16, 4,

5, 13, 3, 9,

11, 1, 15, 7]

e = [ 8, 1, 2, 3, 4, 5,

4, 5, 6, 7, 8, 1]

s = [

[ 4, 11, 2, 14, 15, 0, 8, 13, 3, 12, 9, 7, 5, 10, 6, 1,

13, 0, 11, 7, 4, 9, 1, 10, 14, 3, 5, 12, 2, 15, 8, 6,

1, 4, 11, 13, 12, 3, 7, 14, 10, 15, 6, 8, 0, 5, 9, 2,

6, 11, 13, 8, 1, 4, 10, 7, 9, 5, 0, 15, 14, 2, 3, 12],

[13, 2, 8, 4, 6, 15, 11, 1, 10, 9, 3, 14, 5, 0, 12, 7,

1, 15, 13, 8, 10, 3, 7, 4, 12, 5, 6, 11, 0, 14, 9, 2,

7, 11, 4, 1, 9, 12, 14, 2, 0, 6, 10, 13, 15, 3, 5, 8,

2, 1, 14, 7, 4, 10, 8, 13, 15, 12, 9, 0, 3, 5, 6, 11]

]

p = [ 6, 4, 7, 3,

5, 1, 8, 2]

ip1 = [ 14, 1, 11, 8,

9, 3, 16, 6,

12, 4, 13, 5,

10, 2, 15, 7]

def makeWidgets(): # makeWidgets function

global entries

window = Tk()

window.title('DES')

form = Frame(window)

form.pack()

entries = {}

for(ix, label) in enumerate(fieldnames): # creation of labels and entries into two columns

lab = Label(form, text=label)

ent = Entry(form, width=50)

lab.grid(row=ix, column=0)

ent.grid(row=ix, column=1)

entries[label] = ent

Button(window, text='Encrypt', command=en).pack(side=TOP) # encrypt button, click takes to function en()

Button(window, text='Decrypt', command=de).pack(side=TOP) # decrypt button, click takes to function de()

return window

def stringToBits(data): # string to bits function

data = [ord(c) for c in data] # creates unicodes to list

result = []

for ch in data:

i = 7

while i >= 0: # bit selection

if ch & (1 << i) != 0:

result.append(1)

else:

result.append(0)

i -= 1

return result # returns a list of created bits

def bitsToString(bits): # bits to string function

strinG = []

position = 0

a = 0

while position < len(bits):

a += bits[position] << (7 - (position % 8))

if (position % 8) == 7:

strinG.append(a)

a = 0

position += 1

return ''.join([chr(a) for a in strinG]) # returns a string of characters made from bytes

def permutate(table, block): # permutation function

return list(map(lambda x: block[x], table)) # returns the permutated list

def createSubkeys(key, pc1, pc2, leftshifts): # subkeys creation

key = permutate(pc1, [0] + stringToBits(key)) # pc1 permutation

i = 0

L = key[:7] # slices the permutation into LEFT and RIGHT

R = key[7:]

subkeys = []

while i < 2:

j = 0

while j < leftshifts[i]: # leftshifts the bits from beginning to end

L.append(L[0])

del L[0]

R.append(R[0])

del R[0]

j += 1

subkeys.append(permutate(pc2, [0] + L + R)) # pc2 permutation

i += 1

return subkeys

def des(message, ip, e, s, p, ip1, subkeys, crypt): # des function

if not message:

return ""

if len(message) % 2 != 0:

showerror(title='Error', message='The message or encrypted data must be a multiple of 16 bits!')

return ""

a = 0

result = []

while a < len(message):

cryptob = stringToBits(message[a:a+2]) # gets part of the string and turns it to bits

ipresult = permutate(ip, [0] + cryptob) # ip permutation

L = ipresult[:8] # slices the variable into LEFT and RIGHT

R = ipresult[8:]

if crypt == 'en': # sets the variables for the encryption or decryption

it = 0

itadd = 1

if crypt == 'de':

it = 1

itadd = -1

i = 0

while i < 2: # encryption

R2 = R[:]

R = permutate(e, [0] + R) # E permutation

R = list(map(lambda x, y: x ^ y, R, subkeys[it])) # XOR the permutation

B = [R[:6], R[6:]] # slices the permutation into list B[0] and B[1]

k = 0

bg = [0] * 8

position = 0

while k < 2:

f = (B[k][0] << 1) + B[k][5] # for clarification << means left shifting and >> right shifting

g = (B[k][1] << 3) + (B[k][2] << 2) + (B[k][3] << 1) + B[k][4]

h = s[k][(f << 4) + g] bg[position] = (h & 8) >> 3

bg[position + 1] = (h & 4) >> 2

bg[position + 2] = (h & 2) >> 1

bg[position + 3] = h & 1

position += 4

k += 1

R = permutate(p, [0] + bg) # P permutation

R = list(map(lambda x, y: x ^ y, R, L)) # XOR the permutation

L = R2

i += 1

it += itadd

ip1result = permutate(ip1, [0] + R + L) # ip-1 permutation

result.append(bitsToString(ip1result)) # adds the crypted part as string to result

a += 2

return ''.join(result) # returns result list as one joined string

def en(): #encrypt click

crypt_click('en')

def de(): #decrypt click

crypt_click('de')

def crypt_click(crypttype): #process of encryption or decryption depending of the click

key = entries['key'].get() # gets the key from the UI

if not key:

showerror(title='Error', message='You have to enter a key!')

else:

if len(key) % 2 != 0:

showerror(title='Error', message='The key must be 16 bits!')

else:

subkeys = createSubkeys(key, pc1, pc2, leftshifts) # creation of subkeys in createSubkeys() functions

if crypttype == 'en': # sets the variables to message or to cipher depending on what the user clicked

textfrom = 'message'

textto = 'cipher'

entries['cipher'].delete(0, END)

else:

textfrom = 'cipher'

textto = 'message'

messageOrCipher = entries[textfrom].get() # gets message or cipher

result = des(messageOrCipher, ip, e, s, p, ip1, subkeys, crypttype) # actual result from the des() function

binary = ''.join(map(str, stringToBits(result))) # makes the binary of the result

entries[textfrom].delete(0, END) # UI entry delete

entries[textto].insert(0, result) # UI entry insert

entries['binary'].delete(0, END)

entries['binary'].insert(0, binary)

window = makeWidgets() # creates the UI

window.mainloop() # mainloop of the UI to get actions