Earlier quoted context omitted.
Isn't table lookup constant time?
No. At least not with modern caching (or very old page boundary crossings). A constant time implementation has to avoid tables & compute the values directly (and slowly) or take special care to ensure that all of the table is hit/cached on each access.
> or take special care to ensure that all of the table is hit/cached on each access.
For example, by using an oblivious read: Access each row, AND it with a mask that is either all 1s or all 0s depending on if its the row you want (which you must set without branching) and OR all the results together.
Very slow.