only one. BSI evaluation criteria The German Federal Office for Information Security (, BSI) has established four criteria for quality of deterministic random number generators. They are summarized here: K1 – There should be a high probability that generated sequences of random numbers are different from each other. K2 – A sequence of numbers is indistinguishable from "truly random" numbers according to specified statistical tests. The tests are the monobit test (equal numbers of ones and zeros in the sequence), poker test (a special instance of the chi-squared test), runs test (counts the frequency of runs of various lengths), longruns test (checks whether there exists any run of length 34 or greater in 20 000 bits of the sequence)—both from BSI and NIST, and the autocorrelation test. In essence, these requirements are a test of how well a bit sequence: has zeros and ones equally often; after a sequence of n zeros (or ones), the next bit a one (or zero) with probability one-half; and any selected subsequence contains no information about the next element(s) in the sequence. K3 – It should be impossible for an attacker (for all practical purposes) to calculate, or otherwise guess, from any given subsequence, any previous or future values in the sequence, nor any inner state of the generator. K4 – It should be impossible, for all practical purposes, for an attacker to calculate, or guess from an inner state of the generator, any previous numbers in the sequence or any previous inner generator states. For cryptographic applications, only generators meeting the K3 or K4 standards are acceptable. Mathematical definition Given: – a probability distribution on (where is the standard Borel set on the real line) – a non-empty collection of Borel sets , e.g. . If is not specified, it may be either or , depending on context. – a non-empty set (not necessarily a Borel set). Often is a set between 's support and its interior; for instance, if is the uniform distribution on the interval , might be . If is not specified, it is assumed to be some set contained in the support of and containing its interior, depending on context. We call a function (where is the set of positive integers) a pseudo-random number generator for given taking values in if and only if: ( denotes the number of elements in the finite set .) It can be shown