AES Tutorial / Python Implementation June 10th, 2007

Update: 04-Apr-2009

I fixed two bugs in my AES implementation pointed out to me by Josiah Carlson. First, I was failing to pad properly files whose length was an even multiple of the block size. In those cases, bytes would be lost upon decrypting the file. Josiah also pointed out that I was using a static IV, which leaks information about messages which share common prefixes. This is a serious security bug and I was glad to have it pointed out.

Feel free to check out the changes I made or simply download the updated script.

I’ve put together a series of slides as well as a Python implementation of AES, the symmetric-key cryptosystem.

Source: pyAES.py

Sample Usage: (color added for clarity)

[brandon@zodiac pyAES]$ cat > testfile.txt
The sky was the color of television tuned to a dead channel.
[brandon@zodiac pyAES]$ ./pyAES.py -e testfile.txt -o testfile_encrypted.txt
Password:
Encrypting file: testfile.txt
Encryption complete.
[brandon@zodiac pyAES]$ ./pyAES.py -d testfile_encrypted.txt -o testfile_decrypted.txt
Password:
Decrypting file: testfile_encrypted.txt
Decryption complete.
[brandon@zodiac pyAES]$ cat testfile_decrypted.txt
The sky was the color of television tuned to a dead channel.
[brandon@zodiac pyAES]$ md5sum *
19725cef7495fd55540728759a6262c8 pyAES.py
2fffc9072a7c09f4f97862c0bceb6021 testfile_decrypted.txt
3e57070eaf1b4adf7f43b38e1c5ee631 testfile_encrypted.txt
2fffc9072a7c09f4f97862c0bceb6021 testfile.txt

Symmetric Key Cryptography

  • Identical keys used to encrypt/decrypt messages
  • Can be implemented as block ciphers or stream ciphers

Strengths:

  • Speed
  • Much less computationally intensive than public-key crypto
  • Easy to implement in hardware as well as software

Weaknesses:

  • Key Management
  • n users require n(n-1)/2 keys for all to communicate
  • secure key distribution is a challenge
  • Cannot be used (directly) for authentication or non-repudiation


AES – The Advanced Encryption Standard

  • Rijndael algorithm invented by Joan Daemen and Vincent Rijmen and selected as AES winner by NIST in 2001
  • AES uses fixed block size of 128-bits and key sizes of 128, 192 or 256 bits (though Rijndael specification allows for variable block and key sizes)
  • Most of the calculations in AES are performed within a finite field
  • There are a finite number of elements within the field and all operations on those elements result in an element also contained in the field


AES Operations

  • AES operates on a 4×4 matrix referred to as the state
  • 16 bytes == 128 bits == block size
  • All operations in a round of AES are invertible
  • AddRoundKey – each byte of the round key is combined with the corresponding byte in the state using XOR
  • SubBytes – each byte in the state is replaced with a different byte according to the S-Box lookup table
  • ShiftRows – each row in the state table is shifted by a varying number of bytes
  • MixColumns – each column in the state table is multiplied with a fixed polynomial


AES Operation – AddRoundKey

  • Each byte of the round key is XORed with the corresponding byte in the state table
  • Inverse operation is identical since XOR a second time returns the original values
# XOR each byte of the roundKey with the state table
def addRoundKey(state, roundKey):
    for i in range(len(state)):
        state[i] = state[i] ^ roundKey[i]


AES Operation – SubBytes

  • Each byte of the state table is substituted with the value in the S-Box whose index is the value of the state table byte
  • Provides non-linearity (algorithm not equal to the sum of its parts)
  • Inverse operation is performed using the inverted S-Box
# do sbox transform on each of the values in the state table
def subBytes(state):
    for i in range(len(state)):
        state[i] = sbox[state[i]]

# sbox transformations are invertible
>>> sbox[237]
85
>>> sboxInv[85]
237
>>> sbox[55]
154
>>> sbox[154]
184
>>> sboxInv[184]
154
>>> sboxInv[154]
55


AES Operation – ShiftRows

  • Each row in the state table is shifted left by the number of bytes represented by the row number
  • Inverse operation simply shifts each row to the right by the number of bytes as the row number
# returns a copy of the word shifted n bytes (chars) positive
# values for n shift bytes left, negative values shift right
def rotate(word, n):
    return word[n:]+word[0:n]

# iterate over each "virtual" row in the state table
# and shift the bytes to the LEFT by the appropriate
# offset
def shiftRows(state):
    for i in range(4):
        state[i*4:i*4+4] = rotate(state[i*4:i*4+4],i)


AES Operation – MixColumns

  • MixColumns is performed by multiplying each column (within the Galois finite field) by the following matrix:

  • The inverse operation is performed by multiplying each column by the following inverse matrix:

# 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

# mixColumn does Galois multiplication on a state column
def mixColumn(column):
    temp = copy(column)
    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)


AES – Pulling It All Together

The AES Cipher operates using a varying number of rounds, based on the size of the cipher key.

  • A round of AES consists of the four operations performed in succession: AddRoundKey, SubBytes, ShiftRows, and MixColumns (MixColumns is omitted in the final round)
  • 128-bit key → rounds, 192-bit key → 12 rounds, 256-bit key → 14 rounds
  • The AES cipher key is expanded according to the Rijndael key schedule and a different part of the expanded key is used for each round of AES
  • The expanded key will be of length (block size * num rounds+1)
  • 128-bit cipher key expands to 176-byte key
  • 192-bit cipher key expands to 208-byte key
  • 256-bit cipher key expands to 240-byte key


AES – Key Expansion Operations

AES key expansion consists of several primitive operations:

  1. Rotate – takes a 4-byte word and rotates everything one byte to the left, e.g. rotate([1,2,3,4]) → [2, 3, 4, 1]
  2. SubBytes – each byte of a word is substituted with the value in the S-Box whose index is the value of the original byte
  3. Rcon – the first byte of a word is XORed with the round constant. Each value of the Rcon table is a member of the Rinjdael finite field.
# takes 4-byte word and iteration number
def keyScheduleCore(word, i):
    # rotate word 1 byte to the left
    word = rotate(word, 1)
    newWord = []
    # apply sbox substitution on all bytes of word
    for byte in word:
        newWord.append(sbox[byte])
    # XOR the output of the rcon[i] transformation with the first part
    # of the word
    newWord[0] = newWord[0]^rcon[i]
    return newWord

AES – Key Expansion Algorithm (256-bit)

Pseudo-code for AES Key Expansion:

  1. expandedKey[0:32] → cipherKey[0:32] # copy first 32 bytes of cipher key to expanded key
  2. i → 1 # Rcon iterator
  3. temp = byte[4] # 4-byte container for temp storage
  4. while size(expandedKey) < 240
    temp → last 4 bytes of expandedKey

    # every 32 bytes apply core schedule to temp
    if size(expandedKey)%32 == 0
    temp = keyScheduleCore(temp, i)
    ii + 1
    # since 256-bit key -> add an extra sbox transformation to each new byte
    for j in range(4):
    temp[j] = sbox[temp[j]]
    # XOR temp with the 4-byte block 32 bytes before the end of the current expanded key.
    # These 4 bytes become the next bytes in the expanded key
    expandedKey.append( temp XOR expandedKey[size(expandedKey)-32:size(expandedKey)-28]

Another function to note…

# returns a 16-byte round key based on an expanded key and round number
def createRoundKey(expandedKey, n):
    return expandedKey[(n*16):(n*16+16)]


AES – Encrypting a Single Block

  1. state → block of plaintext # 16 bytes of plaintext are copied into the state
  2. expandedKey = expandKey(cipherKey) # create 240-bytes of key material to be used as round keys
  3. roundNum → 0 # counter for which round number we are in
  4. roundKey → createRoundKey(expandedKey, roundNum)
  5. addRoundKey(state, roundKey) # each byte of state is XORed with the present roundKey
  6. while roundNum < 14 # 14 rounds in AES-256
    roundKey → createRoundKey(expandedKey, roundNum)
    # round of AES consists of 1. subBytes, 2. shiftRows, 3. mixColumns, and 4. addRoundKey
    aesRound(state, roundKey)
    roundNumroundNum + 1
  7. # for the last round leave out the mixColumns operation
    roundKey = createRoundKey(expandedKey, roundNum)
    subBytes(state)
    shiftRows(state)
    addRoundKey(state)
  8. return state as block of ciphertext


AES – Encrypting a Single Block (Demo)

>>> key = passwordToKey("s0m3_p@ssw0rD")
>>> key
[62, 142, 78, 2, 164, 231, 18, 196, 148, 177, 82, 186, 240, 44, 136, 242,
23, 13, 20, 169, 248, 69, 163, 79, 13, 155, 97, 200, 241, 15, 76, 15]
>>> plaintext = textToBlock("Hiro Protagonist")
>>> plaintext
[72, 105, 114, 111, 32, 80, 114, 111, 116, 97, 103, 111, 110, 105, 115, 116]
>>> blockToText(plaintext)
'Hiro Protagonist'
>>> ciphertext = aesEncrypt(plaintext, key)

*** aesMain ***
initial state:
[72, 105, 114, 111, 32, 80, 114, 111, 116, 97, 103, 111, 110, 105, 115, 116]
state after adding roundKey0:
[118, 231, 60, 109, 132, 183, 96, 171, 224, 208, 53, 213, 158, 69, 251, 134]

*** AES Round1 ***
state after subBytes:
[56, 148, 235, 60, 95, 169, 208, 98, 225, 112, 150, 3, 11, 110, 15, 68]
state after shiftRows:
[56, 148, 235, 60, 169, 208, 98, 95, 150, 3, 225, 112, 68, 11, 110, 15]
state after mixColumns:
[66, 80, 228, 230, 148, 33, 121, 29, 106, 95, 226, 146, 255, 98, 121, 117]
state after addRoundKey:
[85, 93, 240, 79, 108, 100, 218, 82, 103, 196, 131, 90, 14, 109, 53, 122]

<-- SNIP -->

*** AES Round 14 (final) ***
state after subBytes:
[0, 229, 171, 70, 93, 137, 135, 251, 99, 182, 88, 166, 228, 229, 251, 97]
state after shiftRows:
[0, 229, 171, 70, 137, 135, 251, 93, 88, 166, 99, 182, 97, 228, 229, 251]
state after addRoundKey:
[195, 123, 205, 183, 213, 202, 50, 223, 223, 164, 99, 86, 126, 34, 107, 142]

>>> ciphertext
[195, 123, 205, 183, 213, 202, 50, 223, 223, 164, 99, 86, 126, 34, 107, 142]

>>> blockToText(ciphertext)
'\xc3{\xcd\xb7\xd5\xca2\xdf\xdf\xa4cV~"k\x8e'
>>> cleartext = aesDecrypt(ciphertext, key)

*** aesMainInv ***
initial state:
[195, 123, 205, 183, 213, 202, 50, 223, 223, 164, 99, 86, 126, 34, 107, 142]

*** AES Round 14 ***
state after addRoundKey:
[0, 229, 171, 70, 137, 135, 251, 93, 88, 166, 99, 182, 97, 228, 229, 251]
state after shiftRowsInv:
[0, 229, 171, 70, 93, 137, 135, 251, 99, 182, 88, 166, 228, 229, 251, 97]
state after subBytesInv:
[82, 42, 14, 152, 141, 242, 234, 99, 0, 121, 94, 197, 174, 42, 99, 216]

<-- SNIP -->

*** AES Round 0 (final) ***
state after adding roundKey0:
[72, 105, 114, 111, 32, 80, 114, 111, 116, 97, 103, 111, 110, 105, 115, 116]
>>> cleartext
[72, 105, 114, 111, 32, 80, 114, 111, 116, 97, 103, 111, 110, 105, 115, 116]
>>> blockToText(cleartext)
'Hiro Protagonist'


15 comments on “AES Tutorial / Python Implementation

  1. inedit00 says:

    Hi mate. I’m interested in the source code of Python AES implementation. Maybe you can upload again the file, because the link seems to be broken. Thanks!

  2. bsterne says:

    Thanks for pointing that out. The broken link is fixed now.

  3. inedit00 says:

    Thank you very much.

    Jan.

  4. thanassis says:

    A small bug: in line 360 of the script, change “filename” to “outputfile”.

  5. bsterne says:

    @thanassis,

    Good catch, thank you. The bug is fixed now.

  6. Colombo says:

    Question: suppose AES is used being used a stream cipher and the attacker knows the actual contents of the initial blocks (which is not difficult because, for example, most XMLs begin with DOCTYPE header). Can the attacker get the cipher text and derive the key from the known plaintext from the header?

  7. arun says:

    gud lecturer ..Have worked with Equivalent Inverse Cipher???????
    I need code for it in C

  8. Samee says:

    Interesting, you have separate encrypt and decrypt functions, but they both invoke aesEncrypt. In fact in this implementation, since you are simply XORing plaintext with a key, the encryption is very malleable … I could easily change the ciphertext of “Help him” to “kill him” even if I can never decrypt it. I know it is not supposed to provide authentication, but still.

    So I’m wondering why you chose to implement it like this. Usually people would implement it using one of the standard block cipher modes (http://en.wikipedia.org/wiki/Cipher_modes) to provide non-malleability.

  9. bsterne says:

    Hi Samee,

    Thanks for the comments, though I think you rushed through the reading of my code. First, the encrypt and decrypt functions do call separate methods, so I’m not sure where that comment came from or why it’s relevant. Your example of malleability is extremely contrived. Almost no crypto is going to withstand an attack if you have known plaintext and known ciphertexts, so I don’t think that’s an indictment of my code in particular. I would love to see an example of an 8 byte encrypted message, in plaintext and ciphertext, that can withstand this type of tampering. As far as your comment about not “XORing plaintext with a key”, I have not seen very many cryptosystems that don’t follow this pattern. All of the block cipher modes operate by generating blocks of key material and XORing those with blocks of plaintext to produce blocks of ciphertext. I don’t quite see how to avoid this pattern. Finally, my code does implement AES in Output Feedback Mode, so I am aware of block cipher modes, but I still don’t think these solve your example above. Maybe you can clarify your comments.

    Thanks,
    Brandon

  10. Samee says:

    You know what, you are right. I think I was confused by something else

  11. Josh says:

    Hello. Can you please fix the link to the pyAES.py file, since it is broken.

  12. bsterne says:

    Thanks, Josh. Link is fixed now.

  13. Paladin says:

    1) thanks for tutorial, great work :)
    2) images in section mixColumns do not exist anymore.. :/

  14. Ivan says:

    G’day mate,

    I’ve downloaded and tried yor code, and I get this error (using python 3.3) Python# time ./pyAES.py -e testfile.txt -o testfile_enc.txt
    File “./pyAES.py”, line 352
    print “pyAES: unable to open input file -“, myInput
    ^
    SyntaxError: invalid syntax
    Error in sys.excepthook:
    Traceback (most recent call last):
    File “/usr/lib/python3/dist-packages/apport_python_hook.py”, line 63, in apport_excepthook
    from apport.fileutils import likely_packaged, get_recent_crashes
    File “/usr/lib/python3/dist-packages/apport/__init__.py”, line 5, in
    from apport.report import Report
    File “/usr/lib/python3/dist-packages/apport/report.py”, line 30, in
    import apport.fileutils
    File “/usr/lib/python3/dist-packages/apport/fileutils.py”, line 23, in
    from apport.packaging_impl import impl as packaging
    File “/usr/lib/python3/dist-packages/apport/packaging_impl.py”, line 20, in
    import apt
    File “/usr/lib/python3/dist-packages/apt/__init__.py”, line 23, in
    import apt_pkg
    ImportError: No module named ‘apt_pkg’

    Original exception was:
    File “./pyAES.py”, line 352
    print “pyAES: unable to open input file -“, myInput
    ^
    SyntaxError: invalid syntax

    but when I use python 2 (like the original code) everything works fine.

    My question as I’m newby in python and basically I’m testing some ciphers is, Do you know why this error ocurr and why is linked to the version, obiusly python3 is doing something different that i dont know and/or i cant tell.

    I’ll be nice if you can give me a hand about it.

    Thanks a lot and your code is really nice :D

    take care

    cya

  15. bsterne says:

    In Python 3 print is no longer a statement and has been changed to a proper function. It needs to be called as such, e.g. print("hello"). This code is not valid Python 3.

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