# For a given security parameter $\kappa$. what does $poly(\kappa)$ mean?

Let ($$Gen,Enc,Dec$$) be an LHE scheme with security parameter $$\kappa$$ and message space $$M$$. Assume that a multiplication operation exists in $$M$$, i.e., is a finite ring. Let $$F : \{0, 1\}^s × L → M$$ be a pseudo-random function with seed space $$\{0, 1\}^s$$ ( $$s=poly(κ)$$) and the label space $$L$$.

I understand what $$\kappa$$ is as the security parameter of the encryption scheme, but I'm unfamiliar with the notation $$poly()$$.

The only reference I can find to it through Google is as a function in R but the function in R requires more arguments than given and even if it did have enough arguments the documentation says that $$poly()$$ returns all orthogonal polynomials with the given arguments as its attributes.

But this doesn't make sense in this scenario because how can you raise a set to a list of values?

• it means that $s$ is polynomial in the security parameter, i.e., there is some constant $m$ such that $s \le \kappa^m$. Probably they are supposing that we can evaluate the pseudo-random function in time polynomial in $s$, so they also want it to be polynomial in $\kappa$ (poly(s) = poly(poly(k)) = poly(k)...). Jul 15 at 15:52
• I would only add to stress that it means there exists a specific polynomial. I know that's what the other comment meant, but I wanted to stress it. Jul 15 at 18:49
• thanks. so in practice how would I create such a function because as m is arbitrary surely s can be anything Jul 15 at 19:15