round of resolution, the auctioneers compute
the 
values
The products 
require a degree reduction step on
all 
products (these can be done simultaneously). This step is
necessary only once one of the first k-1 digits of the bid is
determined to be non-zero. Prior to this point, the value of
is known to be 1 for all j, and the multiplication is
unnecessary (in particular, it will never be necessary in the first
round).