Discrete Fourier Transform Test

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Contents 1 Discrete Fourier Transform (Spectral) Test 1.1 The Test 1.2 NIST Special Publication 800-22 2 References

Discrete Fourier Transform (Spectral) Test

Bit stream Random Test.

The Test

The focus of this test is the peak heights in the Discrete Fourier Transform of the sequence. The purpose of this test is to detect periodic features (i.e., repetitive patterns that are near each other) in the tested sequence that would indicate a deviation from the assumption of randomness. The intention is to detect whether the number of peaks exceeding the 95 % threshold is significantly different than 5 %.

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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