8. An apparatus according to claim 1 , wherein condition (a) is satisfied.
8. An apparatus according to claim 1 , wherein condition (a) is satisfied. 13. An apparatus according to claim 8 , wherein the algorithm different from the first random number algorithm is selected such that if two different apparatuses repeatedly execute the algorithm different from the first random number algorithm, each apparatus obtains a set of numerical values from the algorithm different from the first random number algorithm that matches in whole or in part a set of numerical values from the algorithm different from the first random number algorithm obtained by the other of the two different apparatuses.