CumulativeSums Reverse Test

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Contents 1 Cumulative Sums (Cusum) Reverse Test 1.1 The Test 1.2 NIST Special Publication 800-22 2 References

Cumulative Sums (Cusum) Reverse Test

Bit stream Random Test.

The Test

The focus of this test is the maximal excursion (from zero) of the random walk defined by the cumulative sum of adjusted (-1, +1) digits in the sequence. The purpose of the test is to determine whether the cumulative sum of the partial sequences occurring in the tested sequence is too large or too small relative to the expected behavior of that cumulative sum for random sequences. This cumulative sum may be considered as a random walk. For a random sequence, the excursions of the random walk should be near zero. For certain types of non-random sequences, the excursions of this random walk from zero will be large.

NIST Special Publication 800-22

The Special Publication 800-22, titled "A Statistical Test Suite for the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications" has been developed by NIST - Computer Security Division - Computer Security Resource Center - Random Number Generation Technical Working Group (RNG-TWG).

The paper provides aspects of selecting and testing random and pseudorandom number generators.

You can find in the book:

- Test Purpose
- Function Call
- Test Statistic and Reference Distribution
- Test Description
- Decision Rule (at the 1 % Level)
- Conclusion and Interpretation of Test Results
- Input Size Recommendations
- Example
- Technical description of the test
- Testing strategy and result interpretation

Please refer to the book for original information.

References

[NIST] National Institute of Standards and Technology.

[NIST RNGT] NIST Random Number Generation and Testing.

[NIST RNGT Special Publication 800-22] Revised NIST Special Publication 800-22, " A Statistical Test Suite for the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications.

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