Предельные совместные распределения статистик четырех критериев пакета NIST

2021 ◽  
Vol 33 (2) ◽  
pp. 141-154
Author(s):  
Максим Павлович Савелов ◽  
M P Savelov
Keyword(s):  
Template Matching ◽  
Test Frequency ◽  
Frequency Test ◽  
Matching Test

Найдено предельное совместное распределение статистик следующих критериев пакета НИСТ: «Monobit Test», «Frequency Test within a Block», «Runs Test» и обобщения критерия шаблонов «Non-overlapping Template Matching Test» в ситуации, когда исследуемая последовательность является бернуллиевской с параметром $p$. Отдельно рассматривается случай $p=\frac12 $. Установлены необходимые и достаточные условия асимптотической некоррелированности, а также необходимые и достаточные условия асимптотической независимости рассматриваемых статистик.

Templates selection in non‐overlapping template matching test

2016 ◽  
Vol 52 (18) ◽  
pp. 1533-1535 ◽  
Author(s):  
Meihui Chen ◽  
Hua Chen ◽  
Limin Fan ◽  
Dengguo Feng
Keyword(s):  
Template Matching ◽  
Matching Test

scholarly journals Một số cải tiến cho các kiểm tra thống kê tính ngẫu nhiên sử dụng so khớp mẫu

2021 ◽  
Vol 1 (13) ◽  
pp. 49-61
Author(s):  
Hoang Dinh Linh ◽  
Trần Thị Lượng
Keyword(s):  
Template Matching ◽  
Test Suite ◽  
Minimum Length ◽  
Number Generator ◽  
Matching Test ◽  
Randomness Tests

Tóm tắt—Các kiểm tra liên quan đến so khớp mẫu chồng lấp đã được đề xuất trong NIST SP 800-22 [1], tuy nhiên các xác suất trong các kiểm tra này chỉ đúng cho các mẫu đặc biệt và cần được tính lại cho các mẫu khác. Trong [2], các tác giả đã đề xuất các tiêu chuẩn thống kê so khớp mẫu mới cho tất cả các mẫu 4 bit. Các kiểm tra mới này áp dụng cho chuỗi bất kỳ có độ dài tối thiểu là 5504 bit, trong khi theo NIST độ dài tối thiểu 106 bit. Trong bài báo này, chúng tôi đã cải tiến và đề xuất các kiểm tra so khớp mẫu 4 bit mới mà có thể áp dụng cho các chuỗi bất kỳ có độ dài nhỏ nhất chỉ là 3726 bit. Hơn nữa, chúng tôi đưa ra 3 kiểm tra thống kê so khớp mẫu 5 bit mới. Kết quả lý thuyết và thực hành cho thấy các đề xuất cải tiến của chúng tôi là rất hiệu quả trong việc đánh giá tính ngẫu nhiên cho các bộ tạo số giả ngẫu nhiên. Abstract—Randomness tests related to overlapping template matching have been proposed in NIST SP 800-22 [1], however the probabilities in these tests are only valid for specific samples and should be recalculated for other samples. In [2], the authors proposed new template matching tests for all 4-bit templates. The new tests can be applied to any sequence of minimum length of 5504 bits whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length of 106 bits. In this paper, we have modified and proposed new 4-bit template matching tests that can be applied to any sequence of minimum length 3726 bits. Furthermore, we proposed three new 5-bit template matching tests. Our theoretical and practical results show that our new proposed tests are very efficient in psedorandom number generator testing.

Предельные совместные распределения статистик трех критериев пакета NIST

2021 ◽  
Vol 33 (3) ◽  
pp. 92-106
Author(s):  
Максим Павлович Савелов ◽  
M P Savelov
Keyword(s):  
Test Frequency ◽  
Frequency Test ◽  
Cumulative Sums

Найдены совместное распределение и предельное совместное распределение статистик следующих критериев пакета NIST: «Monobit Test», «Frequency Test within a Block» и «Cumulative Sums Test» в случае, когда исследуемая последовательность имеет распределение Бернулли. В случае, когда в критерии «Frequency Test within a Block» используются два блока, найдены попарные ковариации данных статистик.

Performance Decrements during a Continuous Discrimination Task

1969 ◽  
Vol 29 (1) ◽  
pp. 43-49
Author(s):  
Alfred G. Klipple ◽  
Lynn M. Scelfo
Keyword(s):  
Task Difficulty ◽  
Discrimination Task ◽  
Vigilance Task ◽  
Test Frequency ◽  
Frequency Test ◽  
Event Frequency ◽  
Over Time

3 experiments involving 48 Ss were conducted to study the effects of four variables (event frequency, test frequency, task difficulty, and mode of responding) on performance in a prolonged discrimination task. As in the typical vigilance study, decrements in performance were observed over time. The variables which generally affect the decrements in the vigilance task, however, did not produce significant effects when continuous discriminations were required.

Parallel implementation of the non-overlapping template matching test using CUDA

2020 ◽  
Vol 17 (8) ◽  
pp. 234-241
Author(s):  
Kaikai Li ◽  
Jianguo Zhang ◽  
Pu Li ◽  
Anbang Wang ◽  
Yuncai Wang
Keyword(s):  
Template Matching ◽  
Parallel Implementation ◽  
Matching Test

scholarly journals Mối liên hệ giữa tính nhận biết tiền ảnh và một số tính chất mật mã khác của hàm băm

2021 ◽  
Vol 1 (13) ◽  
pp. 12-20
Author(s):  
Nguyễn Tuấn Anh ◽  
Triệu Quang Phong
Keyword(s):  
Template Matching ◽  
Test Suite ◽  
Minimum Length ◽  
Number Generator ◽  
Matching Test ◽  
Randomness Tests

Tóm tắt—Các kiểm tra liên quan đến so khớp mẫu chồng lấp đã được đề xuất trong NIST SP 800-22 [1], tuy nhiên các xác suất trong các kiểm tra này chỉ đúng cho các mẫu đặc biệt và cần được tính lại cho các mẫu khác. Trong [2], các tác giả đã đề xuất các tiêu chuẩn thống kê so khớp mẫu mới cho tất cả các mẫu 4 bit. Các kiểm tra mới này áp dụng cho chuỗi bất kỳ có độ dài tối thiểu là 5504 bit, trong khi theo NIST độ dài tối thiểu 106 bit. Trong bài báo này, chúng tôi đã cải tiến và đề xuất các kiểm tra so khớp mẫu 4 bit mới mà có thể áp dụng cho các chuỗi bất kỳ có độ dài nhỏ nhất chỉ là 3726 bit. Hơn nữa, chúng tôi đưa ra 3 kiểm tra thống kê so khớp mẫu 5 bit mới. Kết quả lý thuyết và thực hành cho thấy các đề xuất cải tiến của chúng tôi là rất hiệu quả trong việc đánh giá tính ngẫu nhiên cho các bộ tạo số giả ngẫu nhiên. Abstract—Randomness tests related to overlapping template matching have been proposed in NIST SP 800-22 [1], however the probabilities in these tests are only valid for specific samples and should be recalculated for other samples. In [2], the authors proposed new template matching tests for all 4-bit templates. The new tests can be applied to any sequence of minimum length of 5504 bits whereas the overlapping template matching test in the NIST test suite can only be applied to sequences of minimum length of 106 bits. In this paper, we have modified and proposed new 4-bit template matching tests that can be applied to any sequence of minimum length 3726 bits. Furthermore, we proposed three new 5-bit template matching tests. Our theoretical and practical results show that our new proposed tests are very efficient in psedorandom number generator testing.

scholarly journals AN IMPROVED METHOD FOR IDENTIFICATION OF PATTERNS IN THE NON-OVERLAPPING TEMPLATE MATCHING TEST

2017 ◽  
Vol 30 (1) ◽  
pp. 15-25
Author(s):  
Yuichi Takeda ◽  
Mituaki Huzii ◽  
Norio Watanabe ◽  
Toshinari Kamakura
Keyword(s):  
Template Matching ◽  
Improved Method ◽  
Matching Test

scholarly journals Randomness of Möbius coefficients and Brownian motion: growth of the Mertens function and the Riemann hypothesis

2021 ◽  
Vol 2021 (11) ◽  
pp. 113106
Author(s):  
Giuseppe Mussardo ◽  
André LeClair
Keyword(s):  
Random Walk ◽  
Riemann Hypothesis ◽  
Template Matching ◽  
Statistical Tests ◽  
Probabilistic Approach ◽  
Rank Test ◽  
Binary Matrix ◽  
Matching Test ◽  
Longest Run ◽  
Normal Law

Abstract The validity of the Riemann hypothesis (RH) on the location of the non-trivial zeros of the Riemann ζ-function is directly related to the growth of the Mertens function M ( x ) = ∑ k = 1 x μ ( k ) , where μ(k) is the Möbius coefficient of the integer k; the RH is indeed true if the Mertens function goes asymptotically as M(x) ∼ x 1/2+ϵ , where ϵ is an arbitrary strictly positive quantity. We argue that this behavior can be established on the basis of a new probabilistic approach based on the global properties of the Mertens function, namely, based on reorganizing globally in distinct blocks the terms of its series. With this aim, we focus attention on the square-free numbers and we derive a series of probabilistic results concerning the prime number distribution along the series of square-free numbers, the average number of prime divisors, the Erdős–Kac theorem for square-free numbers, etc. These results point to the conclusion that the Mertens function is subject to a normal distribution as much as any other random walk. We also present an argument in favor of the thesis that the validity of the RH also implies the validity of the generalized RH for the Dirichlet L-functions. Next we study the local properties of the Mertens function, i.e. its variation induced by each Möbius coefficient restricted to the square-free numbers. Motivated by the natural curiosity to see how closely to a purely random walk any sub-sequence is extracted by the sequence of the Möbius coefficients for the square-free numbers, we perform a massive statistical analysis on these coefficients, applying to them a series of randomness tests of increasing precision and complexity; together with several frequency tests within a block, the list of our tests includes those for the longest run of ones in a block, the binary matrix rank test, the discrete Fourier transform test, the non-overlapping template matching test, the entropy test, the cumulative sum test, the random excursion tests, etc, for a total of 18 different tests. The successful outputs of all these tests (each of them with a level of confidence of 99% that all the sub-sequences analyzed are indeed random) can be seen as impressive ‘experimental’ confirmations of the Brownian nature of the restricted Möbius coefficients and the probabilistic normal law distribution of the Mertens function analytically established earlier. In view of the theoretical probabilistic argument and the large battery of statistical tests, we can conclude that while a violation of the RH is strictly speaking not impossible, it is however extremely improbable.

A Developmental Study of Intonation Recognition

1968 ◽  
Vol 11 (4) ◽  
pp. 825-832 ◽  
Author(s):  
Marilyn M. Corlew
Keyword(s):  
Significant Interaction ◽  
Multiple Choice ◽  
Semantic Content ◽  
First Grade ◽  
Choice Test ◽  
Developmental Study ◽  
Multiple Choice Test ◽  
The Third ◽  
Matching Test ◽  
Better Than

Two experiments investigated the information conveyed by intonation from speaker to listener. A multiple-choice test was devised to test the ability of 48 adults to recognize and label intonation when it was separated from all other meaning. Nine intonation contours whose labels were most agreed upon by adults were each matched with two English sentences (one with appropriate and one with inappropriate intonation and semantic content) to make a matching-test for children. The matching-test was tape-recorded and given to children in the first, third, and fifth grades (32 subjects in each grade). The first-grade children matched the intonations with significantly greater agreement than chance; but they agreed upon significantly fewer sentences than either the third or fifth graders. Some intonation contours were matched with significantly greater frequency than others. The performance of the girls was better than that of the boys on an impatient question and a simple command which indicates that there was a significant interaction between sex and intonation.

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