LS-14 test suite for long sequences

Ziya Akcengiz; Melis Aslan; Ali Doğanaksoy; Fatih Sulak; Muhiddin Uğuz

Makale detayları

LS-14 test suite for long sequences

Yazarlar:

Ziya Akcengiz | Melis Aslan | Ali Doğanaksoy | Fatih Sulak | Muhiddin Uğuz

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 1, pp.230-250

Belge Tipi:

Makale

Yayın Tarihi:

2/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001312250

pISSN:

2651-477X

Anahtar kelimeler:

Özet:

 Random number sequences are used in many branches of science. Because of many techni- cal reasons and their practicality, pseudo random sequences are usually employed in place of true number sequences. Whether a sequence generated through a deterministic process is a pseudo random, in other words, random-looking sequence or it contains certain pat- terns, can be determined with the help of statistics and mathematics. Although, in the literature there are many statistical randomness tests for this purpose, there is no much work on test suites specialized for long sequences, that is sequences of length 1,000,000 bits or more. Most of the randomness tests for long sequences use some mathematical approximations to compute expected values of the random variables and hence their results contain some errors. Another approach to evaluate randomness criteria of long sequences is to partition the long sequence into a collection short sequences and evaluate the collection for the ran- domness using statistical goodness of fit tests. The main advantage of this approach is, as the individual sequences are short, there is no need to use mathematical approximations. On the other hand when the second approach is preferred, partition the long sequence into a collection of fixed length subsequences and this approach causes a loss of information in some cases. Hence the idea of dynamic partition should be included to perform a more reliable test suite. In this paper, we propose three new tests, namely the entire R2 run, dynamic saturation point, and dynamic run tests. Moreover, we introduce a new test suite, called LS-14, consisting of 14 tests to evaluate randomness of long sequences. As LS-14 employs all three approaches: testing the entire long sequence, testing the collection of fixed length partitions of it, and finally, testing the collection obtained by the dynamic partitions of it, the proposed LS-14 test suit differs from all existing suites. Mutual comparisons of all 14 tests in the LS-14 suite, with each other are computed. Moreover, results obtained from the proposed test suite and NIST SP800-22 suite are compared. Examples of sequences with certain patterns which are not observed by NIST SP800-22 suite but detected by the proposed test suite are given.

 Random number sequences are used in many branches of science. Because of many techni- cal reasons and their practicality, pseudo random sequences are usually employed in place of true number sequences. Whether a sequence generated through a deterministic process is a pseudo random, in other words, random-looking sequence or it contains certain pat- terns, can be determined with the help of statistics and mathematics. Although, in the literature there are many statistical randomness tests for this purpose, there is no much work on test suites specialized for long sequences, that is sequences of length 1,000,000 bits or more. Most of the randomness tests for long sequences use some mathematical approximations to compute expected values of the random variables and hence their results contain some errors. Another approach to evaluate randomness criteria of long sequences is to partition the long sequence into a collection short sequences and evaluate the collection for the ran- domness using statistical goodness of fit tests. The main advantage of this approach is, as the individual sequences are short, there is no need to use mathematical approximations. On the other hand when the second approach is preferred, partition the long sequence into a collection of fixed length subsequences and this approach causes a loss of information in some cases. Hence the idea of dynamic partition should be included to perform a more reliable test suite. In this paper, we propose three new tests, namely the entire R2 run, dynamic saturation point, and dynamic run tests. Moreover, we introduce a new test suite, called LS-14, consisting of 14 tests to evaluate randomness of long sequences. As LS-14 employs all three approaches: testing the entire long sequence, testing the collection of fixed length partitions of it, and finally, testing the collection obtained by the dynamic partitions of it, the proposed LS-14 test suit differs from all existing suites. Mutual comparisons of all 14 tests in the LS-14 suite, with each other are computed. Moreover, results obtained from the proposed test suite and NIST SP800-22 suite are compared. Examples of sequences with certain patterns which are not observed by NIST SP800-22 suite but detected by the proposed test suite are given.

 Random number sequences are used in many branches of science. Because of many techni- cal reasons and their practicality, pseudo random sequences are usually employed in place of true number sequences. Whether a sequence generated through a deterministic process is a pseudo random, in other words, random-looking sequence or it contains certain pat- terns, can be determined with the help of statistics and mathematics. Although, in the literature there are many statistical randomness tests for this purpose, there is no much work on test suites specialized for long sequences, that is sequences of length 1,000,000 bits or more. Most of the randomness tests for long sequences use some mathematical approximations to compute expected values of the random variables and hence their results contain some errors. Another approach to evaluate randomness criteria of long sequences is to partition the long sequence into a collection short sequences and evaluate the collection for the ran- domness using statistical goodness of fit tests. The main advantage of this approach is, as the individual sequences are short, there is no need to use mathematical approximations. On the other hand when the second approach is preferred, partition the long sequence into a collection of fixed length subsequences and this approach causes a loss of information in some cases. Hence the idea of dynamic partition should be included to perform a more reliable test suite. In this paper, we propose three new tests, namely the entire R2 run, dynamic saturation point, and dynamic run tests. Moreover, we introduce a new test suite, called LS-14, consisting of 14 tests to evaluate randomness of long sequences. As LS-14 employs all three approaches: testing the entire long sequence, testing the collection of fixed length partitions of it, and finally, testing the collection obtained by the dynamic partitions of it, the proposed LS-14 test suit differs from all existing suites. Mutual comparisons of all 14 tests in the LS-14 suite, with each other are computed. Moreover, results obtained from the proposed test suite and NIST SP800-22 suite are compared. Examples of sequences with certain patterns which are not observed by NIST SP800-22 suite but detected by the proposed test suite are given.

 Random number sequences are used in many branches of science. Because of many techni- cal reasons and their practicality, pseudo random sequences are usually employed in place of true number sequences. Whether a sequence generated through a deterministic process is a pseudo random, in other words, random-looking sequence or it contains certain pat- terns, can be determined with the help of statistics and mathematics. Although, in the literature there are many statistical randomness tests for this purpose, there is no much work on test suites specialized for long sequences, that is sequences of length 1,000,000 bits or more. Most of the randomness tests for long sequences use some mathematical approximations to compute expected values of the random variables and hence their results contain some errors. Another approach to evaluate randomness criteria of long sequences is to partition the long sequence into a collection short sequences and evaluate the collection for the ran- domness using statistical goodness of fit tests. The main advantage of this approach is, as the individual sequences are short, there is no need to use mathematical approximations. On the other hand when the second approach is preferred, partition the long sequence into a collection of fixed length subsequences and this approach causes a loss of information in some cases. Hence the idea of dynamic partition should be included to perform a more reliable test suite. In this paper, we propose three new tests, namely the entire R2 run, dynamic saturation point, and dynamic run tests. Moreover, we introduce a new test suite, called LS-14, consisting of 14 tests to evaluate randomness of long sequences. As LS-14 employs all three approaches: testing the entire long sequence, testing the collection of fixed length partitions of it, and finally, testing the collection obtained by the dynamic partitions of it, the proposed LS-14 test suit differs from all existing suites. Mutual comparisons of all 14 tests in the LS-14 suite, with each other are computed. Moreover, results obtained from the proposed test suite and NIST SP800-22 suite are compared. Examples of sequences with certain patterns which are not observed by NIST SP800-22 suite but detected by the proposed test suite are given.

Makale detayları

LS-14 test suite for long sequences

Yazarlar:

Ziya Akcengiz | Melis Aslan | Ali Doğanaksoy | Fatih Sulak | Muhiddin Uğuz

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 1, pp.230-250

Belge Tipi:

Makale

Yayın Tarihi:

2/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001312250

pISSN:

2651-477X

Randomness

random number

statistical tests

cryptography

NIST SP800-22

dynamic partitioning

Sayı

Makale detayları

LS-14 test suite for long sequences

Yazarlar: Ziya Akcengiz | Melis Aslan | Ali Doğanaksoy | Fatih Sulak | Muhiddin Uğuz

Yayıncı: Hacettepe University

Ana Başlıklar: Statistics

Dergi: Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 1, pp.230-250

Belge Tipi: Makale

Yayın Tarihi: 2/2024

Belge Dili: İngilizce

Document ID (Org No.): 2001312250

pISSN: 2651-477X

Randomness

random number

statistical tests

cryptography

NIST SP800-22

dynamic partitioning

Sayı

Yazarlar:

Ziya Akcengiz | Melis Aslan | Ali Doğanaksoy | Fatih Sulak | Muhiddin Uğuz

Yayıncı:

Hacettepe University

Ana Başlıklar:

Statistics

Dergi:

Hacettepe Journal of Mathematics and Statistics Vol.53 Issue 1, pp.230-250

Belge Tipi:

Makale

Yayın Tarihi:

2/2024

Belge Dili:

İngilizce

Document ID (Org No.):

2001312250

pISSN:

2651-477X