Secure Programming Cookbook for C and C++

11.18. Statistically Testing Random Numbers

Problem

You are using a hardware random number generator or some other entropy source that hasn’t been cryptographically postprocessed, and you would like to determine whether it ever stops producing quality data. Alternatively, you want to have your generator be FIPS 140 compliant (perhaps for FIPS certification purposes).

Solution

FIPS 140-2 tests, which are ongoing throughout the life of the generator, are necessary for FIPS 140 compliance. For actual statistical tests of data produced by a source, the full set of tests provided by FIPS 140-1 are much more useful, even though they are now irrelevant to the FIPS certification process.

Discussion

Warning

FIPS 140 tests are useful for proving that a stream of random numbers are weak, but the tests don’t demonstrate at all when the numbers are good. In particular, it is incredibly easy to have a weak generator yet still pass FIPS tests by processing data with a cryptographic primitive like SHA1 before running the tests. FIPS 140 is only useful as a safety net, for when an entropy source you think is strong turns out not to be.

FIPS 140 is a standard authored by the U.S. National Institute of Standards and Technology (NIST; see http://csrc.nist.gov/cryptval/). The standard details general security requirements for cryptographic software deployed in government systems (primarily cryptographic “providers”). There are many aspects to the FIPS 140 standard, one of which is a set of tests that all ...