An enhancement of the spectral statistical test for randomness

Random numbers play essential roles in cryptography, modeling and simulation applications. NIST statistical test suite for randomness is the most comprehensive set of random tests. It has been popular and used as a benchmark test for randomness. One of the random tests is spectral test. There has been serious problem in spectral test as pointed out by few researchers. In this paper, further theoretical improvement shall be proposed on the spectral test based on computational observation being made on random noise. A recommendation on the spectral test setting for short cryptographic keys shall also be made.