Moderately-hard functions are useful for many applications
and there are quite many papers concerning on moderately-hard
functions.
However, the formal model for moderately-hard functions
have not been proposed.
In this paper, first, we propose the formal model for moderately-hard functions.
For this purpose, we construct the computational model and
investigate the properties required for moderately-hard functions.
Then, we propose that some particular functions can be used
as moderately-hard functions.
These functions are based on two ideas: the difficulty of 
factoring $p^r q$ and sequential computation of primitive functions.