## Simplified AES (S-AES) Cipher Explained: Understanding Cryptographic Essentials

In the world of cryptography, security and simplicity are often at odds. But what if there were a way to bridge the gap between understanding and robust encryption? Enter Simplified AES (S-AES), a fascinating cryptographic cipher designed as an educational tool, analogous to Simplified DES (S-DES) for DES. This blog article will take you through the key components of S-AES, breaking down its two rounds and demonstrating its fundamental operations.

The following figure shows an overview of the complete algorithm:

The block cipher has a keysize of 16 bit and a blocksize of 16 bit. It consists of two rounds and a key expansion, which generates two additional round keys based on the provided 16-bit key. The first round consists of four building blocks, while the last round only uses three of these. In the following, we first shortly discuss the history of the S-AES cipher and after that each of the building blocks. Finally, we have a look at the key scheduling.

### 1. The S-AES Cipher

Simplified AES, or S-AES, made its debut in 2003 thanks to the work of Musa et al. . Just like its more complex counterpart, the Advanced Encryption Standard (AES), S-AES is a block cipher. However, it is designed primarily for educational purposes, making it a learning tool for the classroom. While AES operates on 128-bit blocks and employs 128, 192, or 256-bit keys, S-AES works with 16-bit blocks and 16-bit keys. Furthermore, S-AES comprises only two rounds, as opposed to AES, which has 10, 12, or 14 rounds depending on the key length . This design allows cryptography enthusiasts to grasp the core concepts without the overwhelming complexity of AES.

 Holden Joshua, Rose Hulman Institute of Technology ” A Simplified AES Algorithm “. 2010 (Figures by Holden)
 Musa, Mohammad A., Edward F. Schaefer, and Stephen Wedig. “A Simplified AES Algorithm and its Linear and Differential Cryptanalyses“. Cryptologia 27.2 (2003): 148 177.

The first step in an S-AES round is AddRoundKey. This operation involves XORing a 16-bit round key onto the 16-bit state. The state is shown here always as 4×4-table, each cell contains a nibble and the first column is the first byte and the second column is the second byte. XORing is a bitwise operation that combines the bits of two inputs, returning a new value based on their differences. Consider the following example:

In this case, each corresponding bit of the state and the round key is XORed together, producing the result 4E 52. Example XORing of a single state nibble:

### 3. SubstituteNibbles Operation

Next up is SubstituteNibbles, which applies a 4-bit S-box to the 16-bit state. The S-box is a lookup table that replaces each 4-bit input with a corresponding 4-bit output. For instance:

The S-AES 4-bit S-box is a key element of this operation, performing a specific substitution for each possible 4-bit input value. An example S-box lookup for a specific value looks like:

The corresponding S-box table is defined as follows:

### 4. ShiftRows Operation

ShiftRows involves exchanging the last two nibbles of the 16-bit state. It’s important to note that this operation is self-inverse, meaning it can be reversed to decrypt the data. For example:

An example computation of ShiftRows looks like:

This is the only primitive, which is self inverse. All other primitives have an inverse which is used for decryption instead of the encryption primitive.

### 5. MixColumns Operation

MixColumns applies a matrix operation on the 16-bit state within the Galois field GF(16). This operation can be quite complex, but it’s essential for ensuring strong encryption. For example:

It uses the reducible polynomial 𝑥^4+𝑥+1 for GF(16).

The matrix to mix the columns is is:

An example computation of both state bytes looks like:

The matrix multiplication is performed within GF(16). Best is to use a precomputed lookup table for the multiplication. To see how computing in finite fields works, have a look at https://en.wikipedia.org/wiki/Finite_field.

### 6. KeyExpansion

Inspired by the AES key expansion algorithm, S-AES’s ExpandKey operation computes round keys for each round. It employs a round constant array (Rcon) to generate the necessary keys. For instance, roundKey1 and roundKey2 can be computed using this scheme:

And the g function is defined as follows: