The Distribution of the Spectrum for the Discrete Fourier Transform Test Included in SP800-22

Kenji HAMANO

doi:10.1093/ietfec/e88-a.1.67

The Distribution of the Spectrum for the Discrete Fourier Transform Test Included in SP800-22

Kenji HAMANO

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In this paper, the problem in the distribution of the test statistic of the Discrete Fourier Transform (DFT) test included in SP800-22 released by the National Institute of Standards and Technology (NIST), which causes a very high rate of rejection compared with the significance level, is considered on the basis of the distribution of the spectrum. The statistic of the DFT test, which was supposed to follow the standard normal distribution N(0, 1) according to the central limit theorem, seems to follow the normal distribution N(0.691, 0.5) approximately. The author derived the distribution function of the spectrum, and changed the threshold value from the default value of to the value of 1.7308 , where n is the length of a random number sequence. By this modification, the test statistic becomes to follow the normal distribution N(0, 0.5) approximately. The disagreement between this variance (= 0.5) and that of the standard normal distribution (= 1) can be considered to originate in the dependence of the spectrum. The evidences of the dependence are shown.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E88-A No.1 pp.67-73

Publication Date: 2005/01/01

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DOI: 10.1093/ietfec/e88-a.1.67

Type of Manuscript: Special Section PAPER (Special Section on Cryptography and Information Security)

Category: Symmetric Key Cryptography

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Kenji HAMANO, "The Distribution of the Spectrum for the Discrete Fourier Transform Test Included in SP800-22" in IEICE TRANSACTIONS on Fundamentals, vol. E88-A, no. 1, pp. 67-73, January 2005, doi: 10.1093/ietfec/e88-a.1.67.
Abstract: In this paper, the problem in the distribution of the test statistic of the Discrete Fourier Transform (DFT) test included in SP800-22 released by the National Institute of Standards and Technology (NIST), which causes a very high rate of rejection compared with the significance level, is considered on the basis of the distribution of the spectrum. The statistic of the DFT test, which was supposed to follow the standard normal distribution N(0, 1) according to the central limit theorem, seems to follow the normal distribution N(0.691, 0.5) approximately. The author derived the distribution function of the spectrum, and changed the threshold value from the default value of to the value of 1.7308 , where n is the length of a random number sequence. By this modification, the test statistic becomes to follow the normal distribution N(0, 0.5) approximately. The disagreement between this variance (= 0.5) and that of the standard normal distribution (= 1) can be considered to originate in the dependence of the spectrum. The evidences of the dependence are shown.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e88-a.1.67/_p

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@ARTICLE{e88-a_1_67,
author={Kenji HAMANO, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={The Distribution of the Spectrum for the Discrete Fourier Transform Test Included in SP800-22},
year={2005},
volume={E88-A},
number={1},
pages={67-73},
abstract={In this paper, the problem in the distribution of the test statistic of the Discrete Fourier Transform (DFT) test included in SP800-22 released by the National Institute of Standards and Technology (NIST), which causes a very high rate of rejection compared with the significance level, is considered on the basis of the distribution of the spectrum. The statistic of the DFT test, which was supposed to follow the standard normal distribution N(0, 1) according to the central limit theorem, seems to follow the normal distribution N(0.691, 0.5) approximately. The author derived the distribution function of the spectrum, and changed the threshold value from the default value of to the value of 1.7308 , where n is the length of a random number sequence. By this modification, the test statistic becomes to follow the normal distribution N(0, 0.5) approximately. The disagreement between this variance (= 0.5) and that of the standard normal distribution (= 1) can be considered to originate in the dependence of the spectrum. The evidences of the dependence are shown.},
keywords={},
doi={10.1093/ietfec/e88-a.1.67},
ISSN={},
month={January},}

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TY - JOUR
TI - The Distribution of the Spectrum for the Discrete Fourier Transform Test Included in SP800-22
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 67
EP - 73
AU - Kenji HAMANO
PY - 2005
DO - 10.1093/ietfec/e88-a.1.67
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E88-A
IS - 1
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - January 2005
AB - In this paper, the problem in the distribution of the test statistic of the Discrete Fourier Transform (DFT) test included in SP800-22 released by the National Institute of Standards and Technology (NIST), which causes a very high rate of rejection compared with the significance level, is considered on the basis of the distribution of the spectrum. The statistic of the DFT test, which was supposed to follow the standard normal distribution N(0, 1) according to the central limit theorem, seems to follow the normal distribution N(0.691, 0.5) approximately. The author derived the distribution function of the spectrum, and changed the threshold value from the default value of to the value of 1.7308 , where n is the length of a random number sequence. By this modification, the test statistic becomes to follow the normal distribution N(0, 0.5) approximately. The disagreement between this variance (= 0.5) and that of the standard normal distribution (= 1) can be considered to originate in the dependence of the spectrum. The evidences of the dependence are shown.
ER -