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 straight-forward 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.

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