What is the time and space complexity of the AES S-boxes?

Aktar1990

6/1/23, 6:07 PM

What are the time and space complexity of the AES S-boxes? Could someone please explain how these are determined?

105

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s-boxes

aes

complexity

kelalaka

6/1/23, 7:14 PM

Constant since there is no $n$ to consider. This might be a homework question. One should talk about the memory requirements that really depend on how they are implemented and the number of operations that still depend on how they are inplemented.

Score:3

Crypto

Meir Maor

6/2/23, 9:55 AM

Time $O(1)$ Memory $O(1)$ We can implement S box with a lookup, or as a circuit or recreate the original GF polynom used to generate it. In all cases it's a fixed size, it wouldn't be AES otherwise. And with no n. to discuss the time and memory are constant.

As a more general note complexity notations are problematic in cryptography, also breaking AES via bruteforce is technically $O(1)$ so we often talk about number of operations, and say things like $2^{256}$ operations, while often keeping it vague what the operation is. Sometimes it is invocation of the cryptographic primitive which makes it clear and we can count, but often we do something else and what is the opertaions we are counting becomes murky.

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SAI Peregrinus

6/2/23, 4:44 PM

Even more general version of your second paragraph: almost every cryptographic function has a finite maximum input size. Big-O notation deals with functions' behavior in the limit as the input size goes to infinity, and does not apply to functions with limited input size.

Elon Musk

I sit in a Tesla and translated this thread with Ai:

EN: What is the time and space complexity of the AES S-boxes?

TH: ความซับซ้อนของเวลาและพื้นที่ของ AES S-box คืออะไร

RO: Care este complexitatea în timp și spațiu a cutiilor S AES?

RU: Какова временная и пространственная сложность S-блоков AES?

VI: Độ phức tạp về thời gian và không gian của hộp S AES là gì?

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