scholarly journals On the Maximum Order Complexity of the Thue-Morse and Rudin-Shapiro Sequence

2019 ◽  
Vol 14 (2) ◽  
pp. 33-42
Author(s):  
Zhimin Sun ◽  
Arne Winterhof
Keyword(s):  
Linear Complexity ◽  
Expected Value ◽  
Quality Measure ◽  
Explicit Formulas ◽  
Maximum Order ◽  
Order Of Magnitude ◽  
Large Maximum ◽  
Maximum Order Complexity

AbstractExpansion complexity and maximum order complexity are both finer measures of pseudorandomness than the linear complexity which is the most prominent quality measure for cryptographic sequences. The expected value of the Nth maximum order complexity is of order of magnitude log N whereas it is easy to find families of sequences with Nth expansion complexity exponential in log N. This might lead to the conjecture that the maximum order complexity is a finer measure than the expansion complexity. However, in this paper we provide two examples, the Thue-Morse sequence and the Rudin-Shapiro sequence with very small expansion complexity but very large maximum order complexity. More precisely, we prove explicit formulas for their N th maximum order complexity which are both of the largest possible order of magnitude N. We present the result on the Rudin-Shapiro sequence in a more general form as a formula for the maximum order complexity of certain pattern sequences.

scholarly journals On the Maximum Order Complexity of Thue–Morse and Rudin–Shapiro Sequences along Polynomial Values

2020 ◽  
Vol 15 (2) ◽  
pp. 9-22
Author(s):  
Pierre Popoli
Keyword(s):  
Open Problem ◽  
General Pattern ◽  
Correlation Measure ◽  
Open Problems ◽  
Maximum Order ◽  
Large Maximum ◽  
Maximum Order Complexity

AbstractBoth the Thue–Morse and Rudin–Shapiro sequences are not suitable sequences for cryptography since their expansion complexity is small and their correlation measure of order 2 is large. These facts imply that these sequences are highly predictable despite the fact that they have a large maximum order complexity. Sun and Winterhof (2019) showed that the Thue–Morse sequence along squares keeps a large maximum order complexity. Since, by Christol’s theorem, the expansion complexity of this rarefied sequence is no longer bounded, this provides a potentially better candidate for cryptographic applications. Similar results are known for the Rudin–Shapiro sequence and more general pattern sequences. In this paper we generalize these results to any polynomial subsequence (instead of squares) and thereby answer an open problem of Sun and Winterhof. We conclude this paper by some open problems.

scholarly journals Maximum order complexity of the sum of digits function in Zeckendorf base and polynomial subsequences

2021 ◽  
Author(s):  
Damien Jamet ◽  
Pierre Popoli ◽  
Thomas Stoll
Keyword(s):  
Natural Generalization ◽  
Correlation Measure ◽  
Pseudorandom Sequences ◽  
Maximum Order ◽  
Automatic Sequences ◽  
Sum Of Digits ◽  
Sum Of Digits Function ◽  
Large Maximum ◽  
Maximum Order Complexity ◽  
Subword Complexity

AbstractAutomatic sequences are not suitable sequences for cryptographic applications since both their subword complexity and their expansion complexity are small, and their correlation measure of order 2 is large. These sequences are highly predictable despite having a large maximum order complexity. However, recent results show that polynomial subsequences of automatic sequences, such as the Thue–Morse sequence, are better candidates for pseudorandom sequences. A natural generalization of automatic sequences are morphic sequences, given by a fixed point of a prolongeable morphism that is not necessarily uniform. In this paper we prove a lower bound for the maximum order complexity of the sum of digits function in Zeckendorf base which is an example of a morphic sequence. We also prove that the polynomial subsequences of this sequence keep large maximum order complexity, such as the Thue–Morse sequence.

scholarly journals Maximum-Order Complexity and Correlation Measures

Cryptography ◽  
2017 ◽  
Vol 1 (1) ◽  
pp. 7 ◽  
Author(s):  
Leyla Işık ◽  
Arne Winterhof
Keyword(s):  
Maximum Order ◽  
Correlation Measures ◽  
Maximum Order Complexity

Hubungan Antara Anemia dan Kebiasaan Merokok pada Ibu Hamil dengan Kejadian BBLR di Rumah Sakit Umum Pusat Dr. Mohammad Hoesin Palembang Tahun 2016

2018 ◽  
Vol 1 (2) ◽  
pp. 89-94
Author(s):  
Intan Sari
Keyword(s):  
Birth Weight ◽  
Low Birth Weight ◽  
General Hospital ◽  
Smoking Habit ◽  
Complete Information ◽  
Developed Countries ◽  
Statistical Test ◽  
Survey Method ◽  
Bivariate Analysis ◽  
Cross Sectional

Low Birth Weight (LBW) is an infant born with a birth weight of less than 2500 grams regardless of gestation. Birth weight is the weight of the baby weighed in 1 hour after birth. (Depkes RI, 2009). Based on WHO and UNICEF data, in 2013 about 222 million babies were born in the world, of which 16% were born with low birth weight. The percentage of LBW in developing countries is 16.5% twice that of developed countries (7%) (Scholar Unand, 2014). The purpose of this study was to determine whether there is a relationship between anemia and Smoking Habit in Pregnant Women with LBW occurrence in General Hospital Dr. Mohammad Hoesin Palembang Year 2016. This research use analytical survey method with cross sectional approach. The population in this study were all mothers who gave birth monthly in Midwifery Installation of Dr. General Hospital Mohammad Hoesin Palembang in 2016 as many as 315 respondents. The sample of this research is some of mothers who give birth enough month in Midwifery Installation of Dr. General Hospital Mohammad Hoesin Palembang Year 2016 as many as 315 respondents. ". From the results of bivariate analysis of anemic respondents with the occurrence of LBW obtained statistical test X2 count = 23.22 which means there is a significant relationship between anemia with the incidence of BBLR. Respondents smoking with the occurrence of LBWR obtained statistical test X2 count = 41.20 which means there is a relationship Meaningful between smoking and LBW incidence. From the results of this study is expected that this research can be a reference material and is a complete information and useful for the development of knowledge about LBW.

Pengaruh Kualitas Pelayanan Terhadap Kepuasan Pelanggan di Kantor Perusahaan Umum Badan Urusan Logistik Kota Sampit Kabupaten Kotawaringin Timur

2016 ◽  
Vol 2 (2) ◽  
pp. 1-5
Author(s):  
Masrukin Masrukin ◽  
Hermanto Hermanto
Keyword(s):  
Quality Of Service ◽  
Customer Satisfaction ◽  
Service Quality ◽  
Error Rate ◽  
Research Method ◽  
Statistical Test ◽  
Quality Factors ◽  
Public Companies ◽  
Public Company

Customer satisfaction is influenced by service quality factors, this study aims to find out and analyze how much influence the quality of service on customer satisfaction is felt by customers who use the service of Poor Rice (Raskin) at the Office of Public Companies Logistics Agency (Perum BULOG) in Sampit City Regency East Kotawaringin. The research method used in this study is the method of observation, questionnaire/questionnaire and documentation using a Likert scale and the method of determining the sample used is the error rate of 5% as many as 213 samples. Testing the hypothesis used is a statistical test with the formula "Product moment person". The results showed that there was a very strong correlation between Service Quality and Customer Satisfaction of the Office of Public Company of the Logistics Affairs Agency (Perum BULOG) in the District of East Kotawaringin. As much as 0.9968514278 based on the calculation of Pearson Product Moment value.

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