After multiplying two shares, the result is a correct share of the
product, but a share from a polynomial of degree 2t. We therefore
normally reshare to get a polynomial of degree t.

But for doing addition these degree 2t shares are fine, so we could
wait with the resharing until it is surely needed.

Let [a]_t denote a share of a using a degree t polynomial and let
[a]_2t -> [a]_t denote a resharing going from degree 2t to t.

We could then calculate

  sum([a_i]_t * [b_i]_t) = sum([a_i b_i]_2t)
                         = [sum(a_i b_i)]_2t -> [sum(a_i b_i)]_t

using only one resharing at the end, saving network traffic. There
does not seem to be many places where we do stuff like that, though.
So the overhead of keeping track of when resharing is needed might be
too big for this to be an improvement.