AES_cpa_sca_1x.py

# CPA SCA practice on AES S-box based on Hamming distances: single byte implementation

import random

s_box = [
    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]

# Hamming weight of x
def count1s(x):
    y = 0
    while(x>0):
        if x%2==1:
            y+=1
        x=x//2
    return y

# SIMULATE MEASUREMENTS
# ---------------------

# number of choosen plain texts
run_length = 150

# pick any random number between 0 and 255
key_byte = random.randint(0,255)

# pick some random numbers you like to run hacking with
choosen_plain_texts = [random.randint(0,255) for i in range(run_length)]

# calculate relevant (yet noiseless) leakages by summing the number of switching bits from one trial to the other
# (frankly this model assumes that chosen plaintext processings follow one another, meanwhile in a real life
# unprotected AES implemenatation this may only be valid for series of 16 bytes for example in an 8 bit uC)

leakages = []
for i in range(len(choosen_plain_texts)-1):
    leakages.append(count1s(s_box[key_byte ^ choosen_plain_texts[i]] ^ s_box[key_byte ^ choosen_plain_texts[i+1]]))

# HACK IT
# -------

#calculating correlations with diverse hypothesises on assumed key values
most_likely_key = 0
highest_correlation = 0
for assumed_key in range(256):

    # hypothesises of Hamming weight transitions for a particular assumed key and with the given chosen plain text series
    # (all transitions between any two bytes for any possible key assumption would be large to compute, so the hypothesises
    # get re-computed for every possible key and only for the actual choosen plain text transitions)
    hypothesis = []
    for i in range(len(choosen_plain_texts)-1):
        hypothesis.append(count1s(s_box[assumed_key ^ choosen_plain_texts[i]] ^ s_box[assumed_key ^ choosen_plain_texts[i+1]]))

    # calculate correlation of hypotheis with measurement
    correlation = 0
    for i in range(len(leakages)):
        correlation += hypothesis[i] * leakages[i]
    if correlation > highest_correlation:
        highest_correlation = correlation
        most_likely_key = assumed_key

print('real key:', key_byte)
print('most likely key:', most_likely_key)