Witness Scheduler RNG

The witness scheduler RNG is a random number generator which uses the blockchain random number generator state as its seed.

The witness scheduler RNG creates an infinite stream of random bytes by computing sha256( sha256( seed ) + little_endian_64bit(i) ), increasing i from 0 to 1 to 2, etc. The RNG only runs during a scheduling block, and i starts from 0 in each scheduling block (relying on different seeds to produce different results).

This infinite stream of random bytes is equivalent to an infinite stream of random bits in little bit-endian order. Given a bound B, the bitstream can be used to produce a random number uniformly distributed in the range [0, B) using a sample-and-reject algorithm:

• Let n be the smallest integer such that 2^n >= B.

• Let x be the next n bits from the bitstream, interpreted as an integer in little bit-endian order.

• If x <= B, return x. Otherwise, throw x away and repeat.

The worst-case running time is unbounded, but each iteration has a termination probability greater than one half. Thus the average-case running time is 2 iterations, and a running time of more than N iterations will occur (on average) at most once every 2^N RNG queries (assuming a worst-case choice of e.g. B = 2^63+1 for all queries). Since each RNG query schedules a witness, the query rate is (over the long term) equal to the block production rate (although in practice many queries are all performed at once in scheduling blocks). So while it is, in theory, possible for the algorithm to require more than 1000 iterations, in practice this will occur on average only once every 2^1000 blocks (again assuming all queries have worst-case B).

The sample-and-reject algorithm is totally unbiased; every x value has equal probability.