  Random beacons-information sources that broadcast a stream of random digits
unknown by anyone beforehand-are useful for various cryptographic purposes. But
such beacons can be easily and undetectably sabotaged, so that their output is
known beforehand by a dishonest party, who can use this information to defeat
the cryptographic protocols supposedly protected by the beacon. We explore a
strategy to reduce this hazard by combining the outputs from several
noninteracting (eg spacelike-separated) beacons by XORing them together to
produce a single digit stream which is more trustworthy than any individual
beacon, being random and unpredictable if at least one of the contributing
beacons is honest. If the contributing beacons are not spacelike separated, so
that a dishonest beacon can overhear and adapt to earlier outputs of other
beacons, the beacons' trustworthiness can still be enhanced to a lesser extent
by a time sharing strategy. We point out some disadvantages of alternative
trust amplification methods based on one-way hash functions.
