**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:

- 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]
- SubBytes – each byte of a word is substituted with the value in the S-Box whose index is the value of the original byte
- 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:

**expandedKey**[0:32] →**cipherKey**[0:32] # copy first 32 bytes of cipher key to expanded key**i**→ 1 # Rcon iterator**temp**= byte[4] # 4-byte container for temp storage- 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**)

**i**→**i**+ 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

**state**→ block of plaintext # 16 bytes of plaintext are copied into the state**expandedKey**= expandKey(**cipherKey**) # create 240-bytes of key material to be used as round keys**roundNum**→ 0 # counter for which round number we are in**roundKey**→ createRoundKey(**expandedKey**,**roundNum**)- addRoundKey(
**state**,**roundKey**) # each byte of state is XORed with the present roundKey - 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**)

**roundNum**→**roundNum**+ 1 - # for the last round leave out the mixColumns operation

**roundKey**= createRoundKey(**expandedKey**,**roundNum**)

subBytes(**state**)

shiftRows(**state**)

addRoundKey(**state**) - 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'

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!

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

Thank you very much.

Jan.

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

@thanassis,

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

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?

gud lecturer ..Have worked with Equivalent Inverse Cipher???????

I need code for it in C

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.

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

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

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

Thanks, Josh. Link is fixed now.