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milp_model_3_gen.py
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import argparse
from copy import deepcopy
rho_val = [[0, 36, 3, 105, 210], [1, 300, 10, 45, 66], [190, 6, 171, 15, 253], [28, 55, 153, 21, 120], [91, 276, 231, 136, 78]]
def constraint(n, w, rounds, bs):
print("Minimize")
#Objective Function
for r in range(rounds):
for y in range(5):
for z in range(16):
if y==4 and z==15 and r==rounds-1:
print(f'A_{r}_{y}_{z}')
else:
print(f"A_{r}_{y}_{z} + ", end="")
print("\n\nSubject To")
x_list = [[[ f'x_0_{k}_{j}_{i}' for i in range(16)] for j in range(5)] for k in range(5)]
#print(len(i_list[0]))
#for i in range(16):
# print(f'{i_list[0][1][i]}')
for i in range(5):
for j in range(5):
for k in range(16):
if i == 4 and j ==4 and k == 15:
print(f'{x_list[i][j][k]} >= 1')
else:
print(f'{x_list[i][j][k]} + ', end="")
print("\n")
for rnd in range(1, rounds) :
y_list = [[[ f'y_{rnd}_{k}_{j}_{i}' for i in range(16)] for j in range(5)] for k in range(5)]
##inequalities for Computing parity bits
for i in range(5):
for k in range(16):
for j in range(5):
if j ==4 :
print(f'{x_list[i][j][k]} + p_{rnd}_{i}_{k} - 2 d_{rnd}_{i}_{k} >= 0')
else:
print(f'{x_list[i][j][k]} + ', end="")
#print('*'*100)
print("")
for i in range(5):
for k in range(16):
for j in range(5):
print(f'd_{rnd}_{i}_{k} - {x_list[i][j][k]} >= 0')
print(f"d_{rnd}_{i}_{k} - p_{rnd}_{i}_{k} >= 0")
# parity bits inequality done, now for theta
print("")
for i in range(5):
for k in range(16):
for j in range(5):
print(f'{x_list[i][j][k]} + p_{rnd}_{(i-1)%5}_{k} + p_{rnd}_{(i+1)%5}_{(k-1)%16} + {y_list[i][j][k]} - 2 e_{rnd}_{i}_{j}_{k} >= 0')
print(f'e_{rnd}_{i}_{j}_{k} - {x_list[i][j][k]} >= 0')
print(f'e_{rnd}_{i}_{j}_{k} - p_{rnd}_{(i-1)%5}_{k} >= 0')
print(f'e_{rnd}_{i}_{j}_{k} - p_{rnd}_{(i+1)%5}_{(k-1)%16} >= 0')
print(f'e_{rnd}_{i}_{j}_{k} - {y_list[i][j][k]} >= 0')
for i in range(5):
for j in range(5):
for k in range(16):
if i==4 and j==4 and k==15:
print(f'{y_list[i][j][k]} >= 1')
else:
print(f'{y_list[i][j][k]} + ', end="")
# rho permutation
tmp = [[[ f'0' for i in range(16)] for j in range(5)] for k in range(5)]
for i in range(5):
for j in range(5):
for k in range(16):
tmp[i][j][k] = y_list[i][j][(k+rho_val[i][j])%16]
y_list = deepcopy(tmp)
#pi permutation
tmp2 = [[[ f'0' for i in range(16)] for j in range(5)] for k in range(5)]
for i in range(5):
for j in range(5):
for k in range(16):
tmp2[j][(2*i + 3*j)%5][k] = y_list[i][j][k]
y_list = deepcopy(tmp2)
#sbox chi
z_list = [[[ f'z_{rnd}_{k}_{j}_{i}' for i in range(16)] for j in range(5)] for k in range(5)]
print("")
for j in range(5):
for k in range(16):
for i in range(5):
print(f'- {y_list[i][j][k]} + A_{rnd}_{j}_{k} >= 0')
print("")
for j in range(5):
for k in range(16):
for i in range(5):
if i ==4:
print(f'{y_list[i][j][k]} - A_{rnd}_{j}_{k} >= 0')
else:
print(f'{y_list[i][j][k]} + ', end="")
print("")
for k in range(16):
for j in range(5):
print(f'5 {z_list[0][j][k]} + 5 {z_list[1][j][k]} + 5 {z_list[2][j][k]} + 5 {z_list[3][j][k]} + 5 {z_list[4][j][k]} - {y_list[0][j][k]} - {y_list[1][j][k]} - {y_list[2][j][k]} - {y_list[3][j][k]} - {y_list[4][j][k]} >= 0 ')
print(f'5 {y_list[0][j][k]} + 5 {y_list[1][j][k]} + 5 {y_list[2][j][k]} + 5 {y_list[3][j][k]} + 5 {y_list[4][j][k]} - {z_list[0][j][k]} - {z_list[1][j][k]} - {z_list[2][j][k]} - {z_list[3][j][k]} - {z_list[4][j][k]} >= 0 ')
print("")
for k in range(16):
for j in range(5):
print(f'{y_list[0][j][k]} + {y_list[1][j][k]} + {y_list[2][j][k]} + {y_list[3][j][k]} + {y_list[4][j][k]} + {z_list[0][j][k]} + {z_list[1][j][k]} + {z_list[2][j][k]} + {z_list[3][j][k]} + {z_list[4][j][k]} - {bs} f_{rnd}_{j}_{k} >= 0')
for i in range(5):
print(f'f_{rnd}_{j}_{k} - {z_list[i][j][k]} >= 0')
print(f'f_{rnd}_{j}_{k} - {y_list[i][j][k]} >= 0')
x_list = deepcopy(z_list)
#print("*"*100)
print("")
# [trial] hardcoding a constraint for optimum solution for 2 rounds
for r in range(rounds):
for j in range(5):
for k in range(16):
if r == rounds-1 and j == 4 and k == 15:
print(f'- A_r_{j}_{k} + 4 >= 0 ')
else:
print(f'- A_r_{j}_{k} ', end="")
print("")
print("Binary\n\n")
for i in range(5):
for j in range(5):
for k in range(16):
print(f"x_0_{i}_{j}_{k}")
for r in range(1, rounds):
for i in range(5):
for k in range(16):
print(f'p_{r}_{i}_{k}')
print(f'd_{r}_{i}_{k}')
for r in range(1, rounds):
for j in range(5):
for k in range(16):
print(f'f_{r}_{j}_{k}')
for r in range(1, rounds):
for i in range(5):
for j in range(5):
for k in range(16):
print(f'e_{r}_{i}_{j}_{k}\n y_{r}_{i}_{j}_{k}')
if __name__ == '__main__':
parser = argparse.ArgumentParser()
parser.add_argument('--r', dest='round')
args = parser.parse_args()
constraint(64, 4, int(args.round), 2)