Proof of concept, do not use, just for theory!
With the recent news of SHA1 everybody should be switching to SHA2 or SHA3 by now. I tried turning AES 256 in CTR mode into a 256 bit hash function by XORing the encrypted outputs together. For example, splitting your message into 32 byte blocks and using it as the keys (m0, m1, …, mN):
hash(m) = [AES256(nonce || counter0, m0) || AES256(nonce || counter1, m0)] XOR [AES256(nonce || counter2, m1) || AES256(nonce || counter3, m1)] ... XOR [AES256(nonce || counterN, mN) || AES256(nonce || counterO, mN)]
('test', '8ea2b7ca516745bfeafc49904b496089')
-
('', '09975b45dc8ecebd1519328dbec1c54d66b7fa7a2a4b762368497f81d864819b')
('a', 'c458ace20dc6458d6e589dbf0e560cbcad5b482e5934a86b6e98202a6cd5a6d5')
('abc', '304dfabb945406b40d53160080d078a1a0e5f8330263f578725ecfbccbb2c0ad')
('cba', '76cdfb5e58e06b5bf191656986aa35e405d3f582f307ea3847fe2a48136bf34e')
('the quick brown fox jumps over the lazy dog', '205639b3097f25a1c3a7bee4a3a66c4c3786129dd92c57fdddafc81568ab66f5')
('the quick brown fox jumps over the lazy eog', '3a7a025b5eb99f93caffd09331786cf6a15e1cb5bf41ae68342ea6b2208cf539')
import sys
def subbytes(matrix):
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 range(0, len(matrix)):
matrix[i] = sbox[matrix[i]]
return matrix
def transform(matrix):
t = []
y = 0
for x in range(0, 16):
z = (x % 4)
if ((x > 0) and (z == 0)):
y += 1
t.append(matrix[(z * 4) + y])
return t
def shiftrows(matrix):
val = matrix.pop(4)
matrix.insert(7, val)
# end row 1
val = matrix.pop(8)
matrix.insert(11, val)
val = matrix.pop(8)
matrix.insert(11, val)
# end row 2
val = matrix.pop(15)
matrix.insert(12, val)
# end row 3
return matrix
def gmul(a, b):
p = 0
for c in range(0, 8):
if ((b & 1) != 0):
p = (p ^ a)
hi_bit_set = (a & 0x80)
a = ((a << 1) & 0xff)
if (hi_bit_set != 0):
a = (a ^ 0x1b)
b = (b >> 1)
return p
def mixcols(s):
t = []
for c in range(0, 16):
t.append(0)
for c in range(0, 4):
t[c + 0] = (gmul(0x02, s[c + 0]) ^ gmul(0x03, s[c + 4]) ^ s[c + 8] ^ s[c + 12]);
t[c + 4] = (s[c + 0] ^ gmul(0x02, s[c + 4]) ^ gmul(0x03, s[c + 8]) ^ s[c + 12]);
t[c + 8] = (s[c + 0] ^ s[c + 4] ^ gmul(0x02, s[c + 8]) ^ gmul(0x03, s[c + 12]));
t[c + 12] = (gmul(0x03, s[c + 0]) ^ s[c + 4] ^ s[c + 8] ^ gmul(0x02, s[c + 12]));
return t
def addkey(matrix, keyval):
for i in range(0, 16):
matrix[i] = (matrix[i] ^ keyval[i])
return matrix
def rcon(ind):
c = 1
if (ind == 0):
return 0
while (ind != 1):
c = gmul(c, 2)
ind -= 1
return c
def keycore(subkey, i):
val = subkey.pop(0)
subkey.append(val)
subkey = subbytes(subkey)
subkey[0] = (subkey[0] ^ rcon(i))
return subkey
def keyexp(matrix):
c = 32
i = 1
t = [0, 0, 0, 0]
while (c < 240):
for a in range(0, 4):
t[a] = matrix[a + c - 4]
if ((c % 32) == 0):
t = keycore(t, i)
i += 1
if ((c % 32) == 16):
t = subbytes(t)
for a in range(0, 4):
if (c >= len(matrix)):
matrix.append(0)
matrix[c] = (matrix[c - 32] ^ t[a])
c += 1
return matrix
def hexout(matrix):
o = ""
for d in matrix:
h = hex(d)
h = str(h)
h = h[2:]
if (len(h) < 2):
h = ("0" + h)
o += h
return o
def aescoree(msg, key):
out = []
t = []
i = 0
l = len(key)
for x in range(0, 32):
t.append(0)
if (i < l):
t[x] = ord(key[i])
i += 1
keyval = keyexp(t)
i = 0
l = len(msg)
while (i < l):
input = []
for x in range(0, 16):
input.append(0)
for x in range(0, 16):
if (i < l):
input[x] = ord(msg[i])
i += 1
for r in range(0, 15):
if (r == 0):
input = addkey(input, keyval[r*16:])
if (r > 0):
input = subbytes(input)
input = transform(input)
input = shiftrows(input)
if (r < 14):
input = mixcols(input)
input = transform(input)
if ((r > 0) and (r < 15)):
input = addkey(input, keyval[r*16:])
for o in input:
out.append(o)
return out
def aesctr_hash(message):
x = 0
l = len(message)
n = 0
h = []
c = "aesctrhash31337!"
d = 0
for e in c:
d = ((d << 8) + ord(e))
while ((x == 0) or (x < l)):
u = ((d + n) & 0xffffffffffffffffffffffffffffffff); n += 1
v = ((d + n) & 0xffffffffffffffffffffffffffffffff); n += 1
r = ""
s = ""
while (u > 0):
r = (chr(u & 0xff) + r)
u = (u >> 8)
while (v > 0):
s = (chr(v & 0xff) + s)
v = (v >> 8)
m = message[x:x+32]
a = aescoree(r, m)
b = aescoree(s, m)
t = (a + b)
if (x == 0):
h = t
else:
for i in range(0, 32):
h[i] = (h[i] ^ t[i])
x += 32
print(message, hexout(h))
return h
print("test", hexout(aescoree("\x00\x11\x22\x33\x44\x55\x66\x77\x88\x99\xaa\xbb\xcc\xdd\xee\xff", "\x00\x01\x02\x03\x04\x05\x06\x07\x08\x09\x0a\x0b\x0c\x0d\x0e\x0f\x10\x11\x12\x13\x14\x15\x16\x17\x18\x19\x1a\x1b\x1c\x1d\x1e\x1f")))
print("-")
aesctr_hash("")
aesctr_hash("a")
aesctr_hash("abc")
aesctr_hash("cba")
aesctr_hash("the quick brown fox jumps over the lazy dog")
aesctr_hash("the quick brown fox jumps over the lazy eog")
Jon's FOSS Blog 
Hi,
From the short description at the beginning of the article, it seems to be Merkle-Damgard based, but it lacks the finalization step, so the hash can be easily subject to length extension attack. You would want to add a finalization step, including the size of the data hashed.
Regards.
Hey Yann,
That was quick! Thank you for that tip, I remember now that SHA also does this at the end of their hashing function as well 🙂
This is why one needs a degree in Math and Crypto before making these algorithms!
– Jon C