We will give a simple example at a medium level of detail to illustrate the basic operation of the computation. We will not describe the lower level details of secure distributed computation. Let c=2 (the radix), and d=3 (the number of digits). This will allow for 8 bidding points, say . With base c=2, one polynomial is sufficient to represent each digit of the bid. This means that l=1 for all polynomials, so we will omit the l subscript. We will use p=7, m=3, t=1, and for this example. Note that these parameters are chosen strictly for simplicity of the example; they are not secure.
Suppose three bidders , , and have bids , , and respectively. In this case, the winner should be and the selling price should be the second highest bid, .
We use the symbols and to denote the values of polynomials' free coefficients. We will use the notation `` '' to mean that `` '' and `` '' to mean that .
During the bid submission step, each bidder selects the polynomials ( ) to encode the digits of their bids. Each bid is encoded with one polynomial per digit (since c=2). The bids are and similarly and .
The shared polynomials are distributed among the auctioneers, after which the auctioneers compute the result without further involvement from the bidders.
For example, the polynomials for could be , , and , and then bidder would share her polynomials by
Given the points of the shared polynomials, each auctioneer computes at round by . Table 1 shows how the polynomials are assigned through k = 1, 2, 3. The starting (i.e. k=1) values are . As stated in the description, the values for the are just for consistency, they are known values and are only in the useless operations of multiplication by 1 ( ) or addition to 0 ( ).
: Computation of polynomials for example auction