Due to the use of verifiable secret sharing, no coalition of at most t
auctioneers can determine any information about the bidding from their
shares of the bids. Similarly, the degree reduction steps preserve
secrecy against coalitions of at most t auctioneers. But what about
the polynomials 
which are revealed in the course of
determining the selling price? A single 
is uniformly random
and independent of all other variables except for its free
coefficient. If 
, then 
. If 
, then
is an element uniformly distributed over 
. Note that 
exactly when there are at least two
bids whose value is at least the speculative selling price (the
previously determined digits of 
together with 
digit
l).