Pseudorandom Number Generator - BSI Evaluation Criteria

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 — A sequence of random numbers with a low probability of containing identical consecutive elements.
• K2 — A sequence of numbers which is indistinguishable from 'true 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 BSI2 (AIS 20, v. 1, 1999) and FIPS (140-1, 1994), 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 any attacker (for all practical purposes) to calculate, or otherwise guess, from any given sub-sequence, 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 standard are acceptable.