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A Universal Statistical Test for Random Bit Generators

Ueli Maurer

A new statistical test for random bit generators is presented that is universal in the sense that any significant deviation of the output statistics from the statistics of a perfect random bit generator is detected with high probability when the defective generator can be modeled as an ergodic stationary source with finite memory. This is in contrast to most presently used statistical tests which can detect only one type of non-randomness, for example, a bias in the distribution of 0's and 1's or a correlation between consecutive bits. Moreover, the new test, whose formulation was motivated by considering the universal data compression algorithms of Elias and of Willems, measures the entropy per output bit of a generator. This is shown to be the correct quality measure for a random bit generator in cryptographic applications. A generator is thus rejected with high probability if and only if the cryptographic significance of a statistical defect is above a specified threshold. The test is easy to implement and very fast and thus well-suited for practical applications.