Generalization of Rijndael, an introduction

Long time a go I have received a request to prepare a system to encode some data in barcodes. I thought in two options: symmetric cryptography or hash algorithm. But, there where two requirements: "non collision (in between the same key)" and "recover information from the code". Then the choose is made, they can only complained by the symmetric algorithms.

The first symmetric algorithm was to simply operate with an xor operation. But this, as a Vernam type algorithm, is more to a stream ciphering or a one-time pad. Basically means is not the correct algorithm if a key is used more than one time.

To think in the block symmetric algorithms, the old DES, the new AES or any of the finalists in the trial are candidates. I have decided for the Rijndael, the winner of the AES contest. Usually the input/output size on the symmetric algorithms must be as big as possible because the data to cipher is much bigger. For example, in the implementations of the public key cryptosystems is usual to do a hybrid system, and the data is very big. Usually the problem on the symmetrics is to interlace the blocks to avoid patterns between them.

One of the goodness of the Rijndael is the capacity of extension, bigger of smaller. The state matrix, in the standard is 4x4, but the number of rows and columns can be changed. Even more, they can be different between them. The word size, is 8 bits (having operations in 32 bits because 8 bits * 4 elements in a column), but it's possible to do Rijndael with different word sizes.

In the application about I'm working the block size will be below 128 bits, but is not fix having the idea of 64 bits block size. DES is 64 bits block (54 bits effective key size). But why to use a replaced algorithm having the possibility to adapt the Rijndael? Even more, with Rijndael the key size can be also adapted to the needs. But in crypto, any modification must have a previous process of deep think, and a post-process of forever-think.

The Triple-DES was an extension to make bigger the key sizes like 112 or 168 (56 plus 2 or 3 of the simple-DES), and there is an extension for the AES with the name AESWrap (the rfc3394), what can be thing like a sextuple-AES.

There is a difference between DES and AES, and between Triple-DES and the AESWrap. The Rijndael is not only using the key, is also doing an expansion of this key to have more bits as a key. Furthermore, the AESWrap is doing a key derivation function to introduce more dispersion and confusion.

Lets go in the first step of this project: A Generalization of Rijndael to have the data block size parametrizable, also the key size and the number of rounds.

Lets start from the simplification, how to do an Small Rijndael Variant? I have found two articles very helpful on that task:

• Mini Advanced Encryption Standard (Mini-AES): A Testbed for Cryptanalysis (2002) by Raphael Chung-wei Phan
• Small Scale Variants of the AES (2005) by C. Cid , S. Murphy , M. J. B. Robshaw

One book for cryptography developers:

• Cryptography for Developers by Tom St. Denis

And the mandatory books for Rijndael:

• AES Proposal: Rijndael (v2) by Joan Daemen, Vincent Rijmen
• The Design of Rijndael AES - The Advanced Encryption Standard  by Joan Daemen, Vincent Rijmen