A sequence can be completely deterministic and yet pass all randomness tests. For instance, if I tell you I randomly chose numbers between 0 and 16, inclusive,

A sequence can be completely deterministic and yet pass all randomness tests. For instance, if I tell you I randomly chose numbers between 0 and 16, inclusive, and got 14, 13, 10, 1, 6, 5, 2, 9, in that order, as far as you can tell it looks random. However, x_{n+1} was generated by taking (3 * x_n + 3) % 16, and hence I can predict the next random number in the sequence trivially. [This is a bad random number generator for other reasons --- see Wikipedia on LCGs for more --- but a good demonstration of how random numbers can appear random but be usable by $attacker.]