Algorithm to generate a (pseudo-) random high-dimensional function

I don't mean a function that generates random numbers, but an algorithm to generate a random function

"High dimension" means the function is multi-variable, e.g. a 100-dim function has 100 different variables.

Let's say the domain is [0,1], we need to generate a function f:[0,1]^n->[0,1]. This function is chosen from a certain class of functions, so that the probability of choosing any of these functions is the same. (This class of functions can be either all continuous, or K-order derivative, whichever is convenient for the algorithm.)

Since the functions on a closed interval domain are uncountable infinite, we only require the algorithm to be pseudo-random.

Is there a polynomial time algorithm to solve this problem?