**AES may have been broken. Serpent, too. Or maybe
not. In either case, there's no need to panic. Yet. But there might be
soon. Maybe. **

---Bruce Schneier---

**Some words for...**

The Advanced Encryption Standard (AES)

The Advanced Encryption Standard (AES)

The Advanced Encryption Standard (AES) is a new Federal Information
Processing Standard (FIPS) Publication that specifies a cryptographic
algorithm for use by U.S. Government organizations to protect sensitive
(unclassified) information.

So, the AES is really a cryptographic algorithm named **Rijndael**
and was selected during a U.S. Government contest in October 2000 among the
following algorithms : **MARS**, **RC6**, **Rijndael**, **Serpent**,
and **Twofish**.

The AES specifies three key sizes: 128, 192 and 256 bits. In decimal terms, this means that there are approximately:

3.4 x 10possible 128-bit keys;^{38}

6.2 x 10possible 192-bit keys; and^{57}

1.1 x 10possible 256-bit keys.^{77}

In comparison, DES keys are 56 bits long, which means there are approximately
7.2 x 10^{16} possible DES keys. Thus, there are on the order
of 10^{21} times more AES 128-bit keys than DES 56-bit keys.

The numbers above indicate that using brute force to crack something
encrypted with the AES will require *many* times the estimated age of the
universe. And if you knew something so important that someone could wait,
let's say, 5 times the age of universe to decrypt it, you should consider
something better than encrypting it with AES and leaving it in your Palmtop
:-)

**What changed since the contest**

The story goes like this: Nicolas Courtois and Josef Pieprzyk published a paper in which they showed how the Rijndael (AES) algorithm could be written as an overdefined system of multivariate quadratic equations (MQ). And some time ago a paper was published at the Eurocrypt by Shamir (Adi Shamir, the S in the RSA algorithm) in which he described the subexponential way to find a solution for the MQ systems described above. That meant that, **increasing the rounds at the Rijndael algorithm, the security would not grow exponentially**.

Exactly on the XL method of Shamir was based the technique (XSL) that Nicolas Courtois and Josef Pieprzyk described in their paper, which with the help of a cipher called BES, isomorphic to AES for some subsets of plaintexts, is able to launch an attack at AES with a 2^{100} complexity^{1}. And as Bruce Schneier, one of the most famous cryptanalysts today says, "**the attack against AES can only now get better**". And if someone comes up with a 2^{80} complexity attack against the AES... it is only a matter of years...

^{1 }2

^{100}complexity means, that by using brute force, we have to check 2

^{100}possible keys.