AES is a ‘symmetric block cipher’ for encrypting texts which can be decrypted with the original encryption key.
For many purposes, a simpler encryption algorithm such as TEA is perfectly adequate – but if you suspect the world’s best cryptographic minds, and a few million dollars of computing resource, might be attempting to crack your security, then AES, based on the Rijndael algorithm, is the tightest security currently available (approved by the US government for classified information up to ‘Secret’ – and in in 192 or 256 key lengths, up to ‘Top Secret’). AES was adopted by NIST in 2001 as FIPS-197, and is the replacement for DES which was withdrawn in 2005.
This script also includes a wrapper function which implements AES in the ‘Counter’ mode of operation (specified in NIST SP 800-38A) to encrypt arbitrary texts – many descriptions of AES limit themselves to the Cipher routine itself, and don’t consider how it can be used to encrypt texts.
Much of the Rijndael algorithm is based on arithmetic on a finite field, or Galois field (after the mathematician). Regular arithmetic works on an infinite range of numbers – keep doubling a number and it will get ever bigger. Arithmetic in a finite field is limited to numbers within that field. The Rijndael algorithm works in GF(28), in which arithmetic results can always be stored within one byte – which is pretty convenient for computers. I can’t begin to understand the maths (considering that addition and subtraction are the same thing – an xor operation – and multiplication is performed ‘modulo an irreducible polynomial’: doubling 0x80 in GF(28) gives 0x1b).
The Rijndael algorithm lends itself to widely differing implementations, since the maths can be either coded directly, or pre-computed as lookup tables – directly parallel to using log tables for arithmetic. Different implementations can have varying pay-offs between speed, complexity, and storage requirements. Some may barely resemble each other. In this implementation, I have followed the standard closely; as per the standard, I have used a lookup table (‘S-box’) to implement the multiplicative inverse (i.e. 1/x) within a finite field (used for the SubBytes transformation), but other calculations are made directly rather than being pre-computed.
If you want to convince yourself that the Cipher function is working properly internally (and you
should!), NIST provide test vectors for AES (appendix C.1 of the standard). Click
and the cipher output block should be
(In counter mode, a text could decrypt correctly even if the cipher routine was flawed).
The Inverse Cipher is largely a mirror of the Cipher routine, with parallel functions for Cipher, SubBytes and ShiftRows. The MixColumns routine is slightly more complex in the inverse. I have not implemented the inverse cipher here as it is not required in counter mode.
Counter mode of operation: the AES standard concerns itself with numeric or binary data (Rijndael, along with most other encryption algorithms, works on a fixed-size block of numbers – in the case of AES, each block is 128 bits or 16 bytes).
In order to make use of it to encrypt real things (such as texts), it has to be used within a certain ‘mode of operation’. This is the interface between text or files, and the purely numerical encryption algorithm. See NIST Special Publication SP800-38A for more details and test vectors.
The simplest mode of operation (‘electronic codebook’) encrypts a text block-by-block – but since the same block of plaintext will always generate the same block of ciphertext, this can leave too many clues for attackers.
A curious quality of counter mode is that decryption also uses the cipher algorithm rather than the inverse-cipher algorithm. Though simple to implement, it has been established to be very secure.
Encrypting texts or files require not just the mode of operation. When implementing AES, you have to consider
The key in this script is obtained by applying the Cipher routine to encrypt the first
16/24/32 characters of the password (for 128-/192-/256-bit keys) to make the key. This is a
convenient way to obtain a secure key within an entirely self-contained script (in a production
environment, as opposed to this essentially tutorial code, the key might be generated
as a hash, e.g. simply
key = Sha256(password)).
In more detail, the supplied password is converted to to UTF-8 (to be byte-safe), then
the first 16/24/32 characters are converted to bytes. The resulting pwBytes is used as a seed
for the Aes.keyExpansion() which is then used as the key to encrypt pwBytes with Aes.cipher().
Examples of keys generated in this way from (unrealistically) simple passwords:
|‘a’ (U+0061):||pwBytes =||61 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00|
|key =||60 84 dd 49 14 7b 5d 05 7a e3 f8 81 b9 0e e7 dd|
|‘b’ (U+0062):||pwBytes =||62 00 00 00 00 00 00 00 00 00 00 00 00 00 00 00|
|key =||b4 1a 83 4f da 4b aa 41 76 62 be d6 2c 66 83 6d|
|‘☺’ (U+263a):||pwBytes =||e2 98 ba 00 00 00 00 00 00 00 00 00 00 00 00 00|
|key =||d1 0c cd fd 44 45 54 ef 59 aa f8 dc 78 8e 9a 7c|
Even with a single bit difference between two passwords (‘a’ and ‘b’), the key is entirely different.
Usage: this implementation would be invoked as follows:
var password = 'L0ck it up saf3'; var plaintext = 'pssst ... đon’t tell anyøne!'; var ciphertext = Aes.Ctr.encrypt(plaintext, password, 256); var origtext = Aes.Ctr.decrypt(ciphertext, password, 256);
The test vectors have been confirmed in IE 6 & 7 (Win), FF 2 & 3 (Win), Safari 2 (Mac), Opera 9 (Linux), and Konqueror 3 (Linux) (thx Jon Passki, Vincenzo Buttazzo). If you can confirm any other versions (or find any problems), please let me know!
In other languages: I’ve developed a PHP version which directly
and has no unsigned-right-shift operator(!), but is otherwise a straightforward port. In other languages,
be sure to use 64-bit integers/longs, either unsigned or with unsigned right-shift operators; you
may need to take into consideration the way different languages handle bitwise ops, and of course
standard issues such as array handling and strict typing. I’m not aware of any other issues.
I’m not familiar with Python, but there is a Python version available at wiki.birth-online.de/snippets/python/aes-rijndael.
Speed: as mentioned, this is not an optimised implementation – on a 2GHz Intel Core 2 machine, this implementation processes around 6kB/sec using IE7, and 30kB/sec using FF3(!) (one page of text at a standard 250 words is about 1.5kB). The 128-bit version is some 25% faster than the 256-bit version.
For more information, have a look at
For some security applications, a cryptographic hash is more appropriate than encryption – if you are interested in a hash function, see my implementations of SHA-1 and SHA-256.
I offer these formulæ & scripts for free use and adaptation as my contribution to the open-source info-sphere from which I have received so much. You are welcome to re-use these scripts [under a simple attribution license, without any warranty express or implied] provided solely that you retain my copyright notice and a link to this page.
If you would like to show your appreciation and support continued development of these scripts, I would most gratefully accept donations.
Note: this script was revised on 1 August 2008 to use Base64 encoding – the previous version, which used less standard encoding, is still available if you have need to refer back to it.
If you have any queries or find any problems, contact me at ku.oc.epyt-elbavom@cne-stpircs.
© 2005-2012 Chris Veness