# Computational Complexity of SHA-3 (SHAKE128)

Please, I got the question "what is the computational complexity of SHA-3 (SHAKE128)"?

What does that mean and how can I calculate that??

*I am using SHA-3 (SHAKE128) in my mechanism to hash fix input (100-bits).

• What is the source of that sentence? – kelalaka Dec 10 '18 at 8:20
• I am a degree student and I proposed a mechanism using SHA-3 (SHAKE128) to hash 100-bits. When I submit my paper to a journal I got this question: "So what is the computational complexity proposed methodology using SHAKE128?" – Al-Ani Dec 10 '18 at 8:22
• I think the answer requires your mechanism, too. – kelalaka Dec 10 '18 at 8:36
• Since SHAKE128 allows an arbitrary output length, this obviously cannot be answered without knowing the output size. – gammatester Dec 10 '18 at 8:43
• SHA3 and SHAKE128 are related but not the same. – WDS Dec 10 '18 at 8:45

Strictly speaking, computational complexity is certainly not the right term. It is an asymptotic notion, describing the approximate behaviour of the cost for "large enough" inputs. SHAKE is an "extensible output function" (XOF) and its computational complexity is $$O(m + n)$$ where $$m$$ is the size of the input, and $$n$$ the size of the output. I.e., it's "linear". However, this does not apply to your case, where the input size is fixed (100 bits) and I suspect that your output size is also fixed. The "complexity" is when the input size "tends towards infinity", and 100 will never go toward infinity; it's fixed.