If c>2, then the method of representing bids allows a bidder to
submit a bid which does not correspond to a single value. This is due
to the unary-style representation of the individual digits. We are
unaware of any advantage that could be derived from using such
malformed bids, but they could be easily prevented (if desired) as
follows. After all bids are received, the auctioneers select a random
number . The
should then be recomputed in order
of descending l by
For the base case, l=c-1, the polynomial remains
unchanged. Since r is a scalar rather than polynomial, all these
computations can be performed without any communication (other than
agreeing upon r).