On the Use of Financial Data as a Random Beacon

In standard voting procedures, random audits are one method for
increasing election integrity. In the case of cryptographic (or
end-to-end) election verification, random challenges are often used to
establish that the tally was computed correctly. In both cases, a
source of randomness is required. In two recent binding cryptographic
elections, this randomness was drawn from stock market data. This
approach allows anyone with access to financial data to verify the
challenges were generated correctly and, assuming market fluctuations
are unpredictable to some degree, the challenges were generated at the
correct time. However the degree to which these fluctuations are
unpredictable is not known to be sufficient for generating a fair and
unpredictable challenge. In this paper, we use tools from
computational finance to provide an estimate of the amount of entropy
in the closing price of a stock. We estimate that for each of the 30
stocks in the Dow Jones industrial average, the entropy is between 6
and 9 bits per trading day. We then propose a straightforward protocol
for regularly publishing verifiable 128-bit random seeds with entropy
harvested over time from stock prices. These "beacons" can be used as
challenges directly, or as a seed to a deterministic pseudorandom
generator for creating larger challenges.