Attacking 2-Round AES with 1 Known Plaintext
An implementation of 1 known plaintext 2-round AES attack from a paper by Charles Bouillaguet, et. al. regarding AES attacks.
Introduction
Challenge Description
#!/usr/bin/env python3
"""
This is a modified version of boppreh's AES implementation found at https://github.com/boppreh/AES. Follow the original disclaimer
__________________________________
This is an exercise in secure symmetric-key encryption, implemented in pure
Python (no external libraries needed).
Original AES-128 implementation by Bo Zhu (http://about.bozhu.me) at
https://github.com/bozhu/AES-Python . PKCS#7 padding, CBC mode, PKBDF2, HMAC,
byte array and string support added by me at https://github.com/boppreh/aes.
Other block modes contributed by @righthandabacus.
Although this is an exercise, the `encrypt` and `decrypt` functions should
provide reasonable security to encrypted messages.
"""
s_box = (
# omitted for brevity
)
inv_s_box = (
# omitted for brevity
)
def sub_bytes(s):
for i in range(4):
for j in range(4):
s[i][j] = s_box[s[i][j]]
def inv_sub_bytes(s):
for i in range(4):
for j in range(4):
s[i][j] = inv_s_box[s[i][j]]
def shift_rows(s):
s[0][1], s[1][1], s[2][1], s[3][1] = s[1][1], s[2][1], s[3][1], s[0][1]
s[0][2], s[1][2], s[2][2], s[3][2] = s[2][2], s[3][2], s[0][2], s[1][2]
s[0][3], s[1][3], s[2][3], s[3][3] = s[3][3], s[0][3], s[1][3], s[2][3]
def inv_shift_rows(s):
s[0][1], s[1][1], s[2][1], s[3][1] = s[3][1], s[0][1], s[1][1], s[2][1]
s[0][2], s[1][2], s[2][2], s[3][2] = s[2][2], s[3][2], s[0][2], s[1][2]
s[0][3], s[1][3], s[2][3], s[3][3] = s[1][3], s[2][3], s[3][3], s[0][3]
def add_round_key(s, k):
for i in range(4):
for j in range(4):
s[i][j] ^= k[i][j]
# learned from https://web.archive.org/web/20100626212235/http://cs.ucsb.edu/~koc/cs178/projects/JT/aes.c
def xtime(a): return (((a << 1) ^ 0x1B) & 0xFF) if (a & 0x80) else (a << 1)
def mix_single_column(a):
# see Sec 4.1.2 in The Design of Rijndael
t = a[0] ^ a[1] ^ a[2] ^ a[3]
u = a[0]
a[0] ^= t ^ xtime(a[0] ^ a[1])
a[1] ^= t ^ xtime(a[1] ^ a[2])
a[2] ^= t ^ xtime(a[2] ^ a[3])
a[3] ^= t ^ xtime(a[3] ^ u)
def mix_columns(s):
for i in range(4):
mix_single_column(s[i])
def inv_mix_columns(s):
# see Sec 4.1.3 in The Design of Rijndael
for i in range(4):
u = xtime(xtime(s[i][0] ^ s[i][2]))
v = xtime(xtime(s[i][1] ^ s[i][3]))
s[i][0] ^= u
s[i][1] ^= v
s[i][2] ^= u
s[i][3] ^= v
mix_columns(s)
r_con = (
0x00, 0x01, 0x02, 0x04, 0x08, 0x10, 0x20, 0x40,
0x80, 0x1B, 0x36, 0x6C, 0xD8, 0xAB, 0x4D, 0x9A,
0x2F, 0x5E, 0xBC, 0x63, 0xC6, 0x97, 0x35, 0x6A,
0xD4, 0xB3, 0x7D, 0xFA, 0xEF, 0xC5, 0x91, 0x39,
)
def bytes2matrix(text):
""" Converts a 16-byte array into a 4x4 matrix. """
return [list(text[i:i+4]) for i in range(0, len(text), 4)]
def matrix2bytes(matrix):
""" Converts a 4x4 matrix into a 16-byte array. """
return bytes(sum(matrix, []))
def xor_bytes(a, b):
""" Returns a new byte array with the elements xor'ed. """
return bytes(i ^ j for i, j in zip(a, b))
def inc_bytes(a):
""" Returns a new byte array with the value increment by 1 """
out = list(a)
for i in reversed(range(len(out))):
if out[i] == 0xFF:
out[i] = 0
else:
out[i] += 1
break
return bytes(out)
def pad(plaintext):
"""
Pads the given plaintext with PKCS#7 padding to a multiple of 16 bytes.
Note that if the plaintext size is a multiple of 16,
a whole block will be added.
"""
padding_len = 16 - (len(plaintext) % 16)
padding = bytes([padding_len] * padding_len)
return plaintext + padding
def unpad(plaintext):
"""
Removes a PKCS#7 padding, returning the unpadded text and ensuring the
padding was correct.
"""
padding_len = plaintext[-1]
assert padding_len > 0
message, padding = plaintext[:-padding_len], plaintext[-padding_len:]
assert all(p == padding_len for p in padding)
return message
def split_blocks(message, block_size=16, require_padding=True):
assert len(message) % block_size == 0 or not require_padding
return [message[i:i+16] for i in range(0, len(message), block_size)]
def expand_key(master_key, n_rounds):
"""
Expands and returns a list of key matrices for the given master_key.
"""
# Initialize round keys with raw key material.
key_columns = bytes2matrix(master_key)
iteration_size = len(master_key) // 4
i = 1
while len(key_columns) < (n_rounds + 1) * 4:
# Copy previous word.
word = list(key_columns[-1])
# Perform schedule_core once every "row".
if len(key_columns) % iteration_size == 0:
# Circular shift.
word.append(word.pop(0))
# Map to S-BOX.
word = [s_box[b] for b in word]
# XOR with first byte of R-CON, since the others bytes of R-CON are 0.
word[0] ^= r_con[i]
i += 1
elif len(master_key) == 32 and len(key_columns) % iteration_size == 4:
# Run word through S-box in the fourth iteration when using a
# 256-bit key.
word = [s_box[b] for b in word]
# XOR with equivalent word from previous iteration.
word = xor_bytes(word, key_columns[-iteration_size])
key_columns.append(word)
# Group key words in 4x4 byte matrices.
return [key_columns[4*i: 4*(i+1)] for i in range(len(key_columns) // 4)]
(A Little) Story Time
Where The Paper Comes In
The Attack
Notations
Phase 1
Steps 1 - 4 (Spoiler Alert: It's Not Really Necessary)
Steps 5 - 6
Step 7
References
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