import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
import math
mpl.rc("figure", facecolor="white")
hamming_weight = lambda x: bin(x).count('1')
xor = lambda x,y: (x ^ y) % 256
average = lambda x: sum(x) / len(x)
def get_hamming_weight_table(inputs):
    A = []
    for ith_input in inputs:
        A.append([hamming_weight(sbox[xor(ith_input, k)]) for k in xrange(1,257)])
    return np.array(A)
def correlation(x, y):
    n = len(x)
    avg_x = average(x)
    avg_y = average(y)
    dx = dy = dp = dxpow = dypow = 0
    for i in xrange(n):
        dx = x[i] - avg_x
        dy = y[i] - avg_y
        dp += dx * dy
        dxpow += dx * dx
        dypow += dy * dy
    return dp / math.sqrt(dxpow * dypow)
input_data_path = 'inputs8.dat'
input_t_path = 'T8.dat'
nr_observations = np.arange(0, 55, 1)
nr_samples = np.arange(0, 600, 1)
T = np.loadtxt(input_t_path, delimiter=',')
Inputs = np.loadtxt(input_data_path, delimiter=',', dtype=(int))
sbox =[0x63, 0x7c, 0x77, 0x7b, 0xf2, 0x6b, 0x6f, 0xc5, 0x30, 0x01, 0x67, 0x2b, 0xfe, 0xd7, 0xab, 0x76, 0xca, 0x82, 0xc9, 0x7d, 0xfa, 0x59, 0x47, 0xf0, 0xad, 0xd4, 0xa2, 0xaf, 0x9c, 0xa4, 0x72, 0xc0, 0xb7, 0xfd, 0x93, 0x26, 0x36, 0x3f, 0xf7, 0xcc, 0x34, 0xa5, 0xe5, 0xf1, 0x71, 0xd8, 0x31, 0x15, 0x04, 0xc7, 0x23, 0xc3, 0x18, 0x96, 0x05, 0x9a, 0x07, 0x12, 0x80, 0xe2, 0xeb, 0x27, 0xb2, 0x75, 0x09, 0x83, 0x2c, 0x1a, 0x1b, 0x6e, 0x5a, 0xa0, 0x52, 0x3b, 0xd6, 0xb3, 0x29, 0xe3, 0x2f, 0x84, 0x53, 0xd1, 0x00, 0xed, 0x20, 0xfc, 0xb1, 0x5b, 0x6a, 0xcb, 0xbe, 0x39, 0x4a, 0x4c, 0x58, 0xcf, 0xd0, 0xef, 0xaa, 0xfb, 0x43, 0x4d, 0x33, 0x85, 0x45, 0xf9, 0x02, 0x7f, 0x50, 0x3c, 0x9f, 0xa8, 0x51, 0xa3, 0x40, 0x8f, 0x92, 0x9d, 0x38, 0xf5, 0xbc, 0xb6, 0xda, 0x21, 0x10, 0xff, 0xf3, 0xd2, 0xcd, 0x0c, 0x13, 0xec, 0x5f, 0x97, 0x44, 0x17, 0xc4, 0xa7, 0x7e, 0x3d, 0x64, 0x5d, 0x19, 0x73, 0x60, 0x81, 0x4f, 0xdc, 0x22, 0x2a, 0x90, 0x88, 0x46, 0xee, 0xb8, 0x14, 0xde, 0x5e, 0x0b, 0xdb, 0xe0, 0x32, 0x3a, 0x0a, 0x49, 0x06, 0x24, 0x5c, 0xc2, 0xd3, 0xac, 0x62, 0x91, 0x95, 0xe4, 0x79, 0xe7, 0xc8, 0x37, 0x6d, 0x8d, 0xd5, 0x4e, 0xa9, 0x6c, 0x56, 0xf4, 0xea, 0x65, 0x7a, 0xae, 0x08, 0xba, 0x78, 0x25, 0x2e, 0x1c, 0xa6, 0xb4, 0xc6, 0xe8, 0xdd, 0x74, 0x1f, 0x4b, 0xbd, 0x8b, 0x8a, 0x70, 0x3e, 0xb5, 0x66, 0x48, 0x03, 0xf6, 0x0e, 0x61, 0x35, 0x57, 0xb9, 0x86, 0xc1, 0x1d, 0x9e, 0xe1, 0xf8, 0x98, 0x11, 0x69, 0xd9, 0x8e, 0x94, 0x9b, 0x1e, 0x87, 0xe9, 0xce, 0x55, 0x28, 0xdf, 0x8c, 0xa1, 0x89, 0x0d, 0xbf, 0xe6, 0x42, 0x68, 0x41, 0x99, 0x2d, 0x0f, 0xb0, 0x54, 0xbb, 0x16]
for i in xrange(0,599):
    plt.plot(nr_observations,T[i])
plt.xlim([0, 54])
plt.xlabel('Samples')
plt.ylabel('Power Trace')
plt.show()
HW = get_hamming_weight_table(Inputs)
plt.plot(nr_samples,HW[:,0])
plt.xlim([0, 600])
plt.xlabel('N')
plt.ylabel('Hamming Weight')
plt.show()

Corr = []

for o in xrange(0, 256):
    Corr.append([correlation(HW[:,o],T[:,t]) for t in xrange(0,55)])
Corr = np.array(Corr)
for i in xrange(0,256):
    plt.plot(nr_observations,Corr[i])
plt.xlim([0, 54])

plt.xlabel('Samples')
plt.ylabel('Correlation')
plt.show()
for i in xrange(0,256):
    if (len([q for q in Corr[i] if q > 0.2]) > 0):
        print('The best matched key is: ', i+1) # +1 since keyspace 1 <= k >= 256 and the array is 0-indexed
        plt.plot(nr_observations,Corr[i])
plt.xlim([0, 54])

plt.xlabel('Samples')
plt.ylabel('Correlation')
plt.show()