How to determine cryptographic properties of AES S-Box?

Cat Dragon

5/17/24, 4:52 PM

In the book The Design by Rijndael states that the design criteria for the S-box are nonlinearity and algebraic complexity. Can these two criteria be considered as two specific cryptographic properties of the AES S-box? if not is there any way to determine the cryptographic properties of AES S-Box ?

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kodlu

5/17/24, 5:41 PM

There are a number of different aspects to this, for example one can determine the nonliearity of the AES Sbox as a vectorial boolean function see here

The correlation immunity of the AES Sbox can also be determined, see here

These two properties are conflicting and there is a tradeoff. From the point of view of the designer lower nonlinearity (bad) means higher correlation immunity (good) and the two need to be balanced.

The answer below looks at linear cryptanalysis resistance properties in more detail:

For more mathematical background on AES see Lenstra's short document Rijndael for Algebraists:

https://math.berkeley.edu/~hwl/papers/rijndael0.pdf

as well as the following answer:

any-good-links-to-learn-the-maths-behind-aes/76792#76792

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Elon Musk

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EN: How to determine cryptographic properties of AES S-Box?

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