🔐 AES S-box Substitution Tool

The AES S-box (Substitution box) is a key component of the AES encryption algorithm. It provides non-linearity to the cipher by substituting each byte with another according to a fixed lookup table. This substitution is a crucial part of the SubBytes operation in AES.

The S-box is carefully designed to have specific mathematical properties that make the cipher resistant to various cryptanalytic attacks:

• It has no fixed points (no byte maps to itself)
• It has high non-linearity
• It provides good diffusion properties
• It is resistant to differential and linear cryptanalysis

The AES S-box is not randomly generated but is constructed using a specific mathematical process:

1. Multiplicative Inverse: Each byte is replaced with its multiplicative inverse in the finite field GF(2⁸). The value 0x00, which has no multiplicative inverse, is mapped to itself.
2. Affine Transformation: An affine transformation is applied to the result, which consists of:
   • A bitwise matrix multiplication
   • XOR with the constant 0x63

This construction gives the S-box its strong cryptographic properties while being efficiently implementable in both hardware and software.

In the AES encryption process, the S-box is used in two main operations:

1. SubBytes: Each byte in the state matrix is replaced with its corresponding value in the S-box.
2. Key Expansion: The S-box is used in the key schedule to introduce non-linearity when generating round keys.

For decryption, an inverse S-box is used, which performs the reverse substitution.