What does the "static" assumption mean?

Question

We can prove the security of a cryptographic scheme in standard model and non-standard model.

Standard models like using some computational assumptions, on the other hand, non-standard models like random oracle, generic group model. Right?

I've seen in a paper [CGKV18 ,page 10] the term $\color{blue}{static}$ computational assumption:

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The question is: What does the adjective static mean in "static computational assumption"? Do we have non-static computational assumptions? like non-static learning with errors (LWE) (if exists)?

Answer 1

Static assumptions are in opposition to "$q$-type" assumptions where the length of the problem can vary independently of the security parameter. An example is the $q$-strong Diffie-Hellman problem introduced by Boneh and Boyen: given $g,g^\alpha, g^{\alpha^2},\dots,g^{\alpha^q}$, compute $g^{\alpha^{q+1}}$. The problem with this type of assumption is that they tend to get stronger as $q$ increases (weaker assumptions are always preferable). This paper has some other references in the introduction if you want to dig deeper.