Tag: modern

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:

Overview of the complete simplified AES algorithm
Simplified AES Algorithm taken &
modified from [1]

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. [2]. 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 [1]. This design allows cryptography enthusiasts to grasp the core concepts without the overwhelming complexity of AES.

[1] Holden Joshua, Rose Hulman Institute of Technology ” A Simplified AES Algorithm “. 2010 (Figures by Holden)
[2] 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.

2. AddRoundKey Operation

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:

AddRoundKey operation

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:

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:

SubstituteNibbles operation

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:

Example S-box lookup for a specific value

The corresponding S-box table is defined as follows:

S-AES s-box table

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:

ShiftRows operation

An example computation of ShiftRows looks like:

Example computation of ShiftRows

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:

MixColumns operation

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

The matrix to mix the columns is is:

MixColumns matrix

An example computation of both state bytes looks like:

Example computation of a single byte

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:

KeyExpansion scheme

And the g function is defined as follows:

KeyExpansion g function

7. YouTube Video

If you want some more explanations and details, please have a look at my YouTube video about S-AES, where I explain each step in more detail:

The Simplified Advanced Encryption Standard (S-AES) Explained

Cryptography for everybody: I Created a Text-Based AES-Like Cipher – A Cipher Built Using Only Classical Ciphers

Can you build a cipher with the structure of the Advanced Encryption Standard (AES), our current standard modern symmetric cipher, but only use classical ciphers? I asked myself this question when I implemented AES in C# as a preparation for my upcoming AES videos on my YouTube channel in 2021.

AES’ structure (10 rounds for AES-128) consists of 4 different building blocks:
1) AddRoundKey,
2) SubBytes,
3) ShiftRows, and
4) MixColumns:

AES structure

The AddRoundKey building block adds a round key to the state array of 16 bytes (or plain and/or ciphertext) using XOR. The SubBytes building block substitutes each byte using AES’ S-Box, the ShiftRows building block performs a shift of the rows of the state array, and the MixColumns building block mixes the columns of the state array by multiplying each “vector” with an invertible matrix in the finite field GF(2^8).

When I implemented each of these four steps, I was reminded of some classical ciphers: AddRoundKey reminded me of an additive cipher, SubBytes reminded me of a simple substitution cipher, MixColumns reminded me of a transposition cipher, and the matrix multiplication finally reminded me of a Hill cipher.

Thus, I changed the inputs (plaintext and key) and the output (ciphertext) of the AES to simple text (just letters from A to Z), exchanged AddRoundKey with an additive cipher (using MOD 26), exchanged SubBytes by SubBigrams (a bigram substitution cipher), I kept ShiftRows as it was, and exchanged MixColumns with a 4×4 Hillcipher (also using MOD 26). The “TextAES” was born :-).

To also allow decryption, I computed the inverse S-Box (an inverse lookup table for the bigram substitution cipher) and an inverse matrix for the Hill cipher.

I kept the key expansion more or less as it was, but with text, and also used the bigram substitution and replaced its round constants by “AAAA”,”BAAA”,”CAAA”, etc.

Finally, I was convinced that you can create an AES-like cipher using only classical ciphers :-).

If you are interested in details of this self-made crazy cipher, have a look at the video I made about it:

I Created a Text-Based AES-Like Cipher

If you are interested in details of the real AES, you may also have a look at my other two videos about AES and AES key schedule:

AES – The Advanced Encryption Standard Explained
AES – Key Schedule/Key Expansion Explained

Also, if you want to play with my source code in C# of AES and TextAES, you can find it freely available on GitHub: https://github.com/n1k0m0/AES-and-Text-Based-AES

Finally, here is the original publication of AES:
Daemen, Joan, and Vincent Rijmen. The design of Rijndael. Vol. 2. New York: Springer-verlag, 2002.

Nils