extract.py

#!/usr/bin/env python3

import sys
import binascii
import itertools
import collections

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
]

# shift row permutation on indexes
shift_rows = [
    0, 13, 10, 7,
    4, 1, 14, 11,
    8, 5, 2, 15,
    12, 9, 6, 3,
]

# indexes for every column
cols = [
    (0, 1, 2, 3),
    (4, 5, 6, 7),
    (8, 9, 10, 11),
    (12, 13, 14, 15)
]

def inv_perm(perm):
    inv = [0] * len(perm)
    for i in range(len(perm)):
        inv[perm[i]] = i
    return inv

sboxI = inv_perm(sbox)

def mult(a, b):
    assert 0x100 > a >= 0
    assert 0x100 > b >= 0

    r = 0
    p = 0b100011011

    while b:
        if b & 1:
            r ^= a

        a <<= 1
        b >>= 1

        if a >> 8:
            a ^= p

    return r

def mix_column(v):
    assert len(v) == 4

    r1 = mult(2, v[0]) ^ mult(3, v[1]) ^ v[2] ^ v[3]
    r2 = v[0] ^ mult(2, v[1]) ^ mult(3, v[2]) ^ v[3]
    r3 = v[0] ^ v[1] ^ mult(2, v[2]) ^ mult(3, v[3])
    r4 = mult(3, v[0]) ^ v[1] ^ v[2] ^ mult(2, v[3])

    return (r1, r2, r3, r4)

def mix_fault(d, row):
    col = [0, 0, 0, 0]
    col[row] = d
    return mix_column(col)

Ds = []

for row in range(4):
    for d in range(1, 0x100):
        Ds.append(mix_fault(d, row))

def recover(ct_correct, ct_fault, I, K):
    assert len(I) == 4
    assert len(ct_correct) == len(ct_fault) == 16

    def solve(xA, xB, D):
        ks = []
        for k in range(0x100):
            if D == sboxI[xA ^ k] ^ sboxI[xB ^ k]:
                ks.append(k)
        assert len(ks) in (0, 2, 4)
        return ks

    for D in Ds:
        # calculate candiates for each byte
        ks = [[], [], [], []]
        for j, i in enumerate(I):
            ks[j] = solve(ct_correct[i], ct_fault[i], D[j])
            if len(ks[j]) == 0:
                break

        # expand the cross product to get full 32-bit keys
        for k in itertools.product(*ks):
            K[k] += 1

def diff(s1, s2):
    idx = set([])
    for i in range(len(s1)):
        if s1[i] != s2[i]:
            idx.add(i)
    return frozenset(idx)

if __name__ == '__main__':
    # sample file
    with open(sys.argv[1], 'r') as f:
        samples = map(str.strip, f.readlines())
        samples = [binascii.unhexlify(s) for s in samples]

    # correct ciphertext
    correct = binascii.unhexlify(sys.argv[2])

    # optional threshold
    try:
        threshold = int(sys.argv[3])
    except IndexError:
        threshold = None

    # group ciphertext by faulty indexes
    Is = [tuple([shift_rows[v] for v in col]) for col in cols]
    groups = { I: [] for I in Is}
    for sample in samples:
        df = diff(sample, correct)
        for I in Is:
            if all([i in df for i in I]):
                groups[I].append(sample)

    # extract from every group of faulty indexes
    KEY = [None] * 16
    for I in Is:
        print('I : %14s, ciphertexts: %d' % (I, len(groups[I])))

        # find the most seen 32-bit key candidates
        K = collections.Counter()
        for i, sample in enumerate(groups[I]):
            recover(correct, sample, I, K)

            # print status
            show = ''.join(['%02x' % v if v else '??' for v in KEY])
            print('Key: %s, Sample %d / %d, Cand: %d, Top: %s' % (show, i, len(groups[I]), len(K), K.most_common(2)))

            # check optional threshold
            try:
                _, cnt = K.most_common(1)[0]
                if cnt >= threshold:
                    break
            except:
                pass

        # fill in the full round key with the recovered 32-bits
        key, _ = K.most_common(1)[0]
        for j, i in enumerate(I):
            assert KEY[i] is None
            KEY[i] = key[j]

    print('KEY:', bytes(KEY).hex())