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DES-bucketing-proof.py
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DES-bucketing-proof.py
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import numpy
import random
import matplotlib.pyplot as plt
DesSbox = [
[
14, 4, 13, 1, 2, 15, 11, 8, 3, 10, 6, 12, 5, 9, 0, 7,
0, 15, 7, 4, 14, 2, 13, 1, 10, 6, 12, 11, 9, 5, 3, 8,
4, 1, 14, 8, 13, 6, 2, 11, 15, 12, 9, 7, 3, 10, 5, 0,
15, 12, 8, 2, 4, 9, 1, 7, 5, 11, 3, 14, 10, 0, 6, 13],
[
15, 1, 8, 14, 6, 11, 3, 4, 9, 7, 2, 13, 12, 0, 5, 10,
3, 13, 4, 7, 15, 2, 8, 14, 12, 0, 1, 10, 6, 9, 11, 5,
0, 14, 7, 11, 10, 4, 13, 1, 5, 8, 12, 6, 9, 3, 2, 15,
13, 8, 10, 1, 3, 15, 4, 2, 11, 6, 7, 12, 0, 5, 14, 9],
[
10, 0, 9, 14, 6, 3, 15, 5, 1, 13, 12, 7, 11, 4, 2, 8,
13, 7, 0, 9, 3, 4, 6, 10, 2, 8, 5, 14, 12, 11, 15, 1,
13, 6, 4, 9, 8, 15, 3, 0, 11, 1, 2, 12, 5, 10, 14, 7,
1, 10, 13, 0, 6, 9, 8, 7, 4, 15, 14, 3, 11, 5, 2, 12],
[
7, 13, 14, 3, 0, 6, 9, 10, 1, 2, 8, 5, 11, 12, 4, 15,
13, 8, 11, 5, 6, 15, 0, 3, 4, 7, 2, 12, 1, 10, 14, 9,
10, 6, 9, 0, 12, 11, 7, 13, 15, 1, 3, 14, 5, 2, 8, 4,
3, 15, 0, 6, 10, 1, 13, 8, 9, 4, 5, 11, 12, 7, 2, 14],
[
2, 12, 4, 1, 7, 10, 11, 6, 8, 5, 3, 15, 13, 0, 14, 9,
14, 11, 2, 12, 4, 7, 13, 1, 5, 0, 15, 10, 3, 9, 8, 6,
4, 2, 1, 11, 10, 13, 7, 8, 15, 9, 12, 5, 6, 3, 0, 14,
11, 8, 12, 7, 1, 14, 2, 13, 6, 15, 0, 9, 10, 4, 5, 3],
[
12, 1, 10, 15, 9, 2, 6, 8, 0, 13, 3, 4, 14, 7, 5, 11,
10, 15, 4, 2, 7, 12, 9, 5, 6, 1, 13, 14, 0, 11, 3, 8,
9, 14, 15, 5, 2, 8, 12, 3, 7, 0, 4, 10, 1, 13, 11, 6,
4, 3, 2, 12, 9, 5, 15, 10, 11, 14, 1, 7, 6, 0, 8, 13],
[
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],
]
def is_disjoint(v0, v1):
return not any(set(v0).intersection(set(v1)))
NB_rept = 15
for targeted_sbox in range (8):
# Generating I_0 and I_1 for each key guess
I = [[[] for j in range (2)] for x in range(64)]
for k in range (64):
for msg in range (64):
a = msg ^ k
bs = (bin(a)[2:]).zfill(6)
sbox_in = bs[0]+bs[5]+bs[1:5]
sbox_in_new = int(sbox_in,2)
sbox_out= DesSbox[targeted_sbox][sbox_in_new]
if sbox_out &1 == 0 :
I[k][0].append(msg)
else:
I[k][1].append(msg)
score = numpy.zeros ((64,33))
for GK in range (64): # For each possible value of a good key
for key in range (64): # For a fixed good key, compute the probability of disjoint sets for all possible key guesses (including the good one)
for msg_range in range (1,33):
for repet in range (NB_rept):
tmp_0 = random.sample(I[key][0], msg_range)
tmp_1 = random.sample(I[key][1], msg_range)
v_0 = []
v_1 = []
for i in range (len(tmp_0)):
a = tmp_0[i] ^ GK
bs = (bin(a)[2:]).zfill(6)
sbox_in = bs[0]+bs[5]+bs[1:5]
sbox_in_new = int(sbox_in,2)
sbox_out= DesSbox[targeted_sbox][sbox_in_new]&1
#v_0.append(sbox_out)
tmp = bin(random.randint(0,31))[2:] + str(sbox_out) # construct the 6 bits entries of S_2^j that takes the bucketing bit as input (which value equals to 0), the other 5 bits are generated at random
v_0.append(int(tmp,2))
a = tmp_1[i] ^ GK
bs = (bin(a)[2:]).zfill(6)
sbox_in = bs[0]+bs[5]+bs[1:5]
sbox_in_new = int(sbox_in,2)
sbox_out= DesSbox[targeted_sbox][sbox_in_new]&1
#v_1.append(sbox_out)
tmp = bin(random.randint(0,31))[2:] + str(sbox_out)# construct the 6 bits entries of S_2^j that takes the bucketing bit as input (which value equals to 1), the other 5 bits are generated at random
v_1.append(int(tmp,2))
if is_disjoint(v_0, v_1): score[key][msg_range] += 1
res = numpy.mean(score, axis=0)/(64*NB_rept)
res = res - 1/64 # remove the probability of the goog key
plt.grid(True)
plt.xlabel("Number of plaintexts in $I_0$ and $I_1$")
plt.ylabel("Probability that for an incorrect key guess \n the sets $V_0$ and $V_1$ are disjoints")
x = numpy.arange (1, 33)
plt.plot (x, res[1:], label='Sbox ' + str(targeted_sbox) )
plt.axhline(y = 1/64, linestyle = "--", label ="Prob = $2^{-6}$")
plt.legend(loc=1, ncol=2)
plt.show()
plt.savefig("effectiveness_proof_for_DES.pdf", format='pdf')