scholarly journals A LINEAR COMPLEXITY ANALYSIS OF QUADRATIC RESIDUES AND PRIMITIVE ROOTS SPACINGS

2019 ◽  
Vol 19 (1) ◽  
pp. 27-37
Author(s):  
Mihai Caragiu ◽  
Shannon Tefft ◽  
Aaron Kemats ◽  
Travis Maenle
2021 ◽  
Vol 23 (Supplement_G) ◽  
Author(s):  
Vanessa Pivetti ◽  
Davide Lazzeroni ◽  
Luca Moderato ◽  
Claudio Stefano Centorbi ◽  
Matteo Bini ◽  
...  

Abstract Aims Arterial hypertension (AHT) represents the leading cause of cardiovascular disease (CVD) and premature death worldwide. Essential AHT accounts for 95% of all cases of hypertension; although the aetiology of essential AHT is still largely unknown, a pivotal role of autonomic nervous system has been proposed and demonstrated. Both excessive sympathetic tone and vagal withdrawal, that define autonomic dysfunction, has been associated with essential AHT. The aim of our study was to investigate the relationship between blood pressure and autonomic function in essential hypertension; this was done comparing 24 h heart rate variability and 24 h blood pressure data, simultaneously collected, in a population of essential AHT subjects. Methods A prospective registry of 179 consecutive not selected essential AHT patients were considered in the present study. All patients underwent cardiac evaluation at the Primary and Secondary Cardiovascular Prevention Unit of the Don Gnocchi Foundation of Parma. All subjects underwent 24 h ECG monitoring, and 24 h Ambulatory Blood Pressure Monitoring, during the same day. Twenty-four hours Heart Rate variability analysis included: Time-domain, frequency-domain and non-linear domain. Results Mean age was 60 0a11.7 years, male gender was prevalent (68.4%). Among the population 26 (14.7%) subjects had diabetes; the prevalence of family history of CVD was 61.7% and 66.5% had dyslipidaemia; body mass index mean values were 27.6 7.4.3. In the whole population, the prevalence of uncontrolled AHT was 80.5%, divided into: 53.1% systo-diastolic, 17.9% isolated systolic, and 9.5% isolated diastolic. The prevalence of untreated AHT (recent diagnosis) was 40.2%, while treated AHT was 59.8% and only 19.6% had controlled blood pressure values (AHT at target). 12.3% of patients were treated with Beta Blockers. A significant correlations between diastolic blood pressure (DBP) values (24 h and day-time), LF/HF ratio (24 h) (r = 0.200; P = 007) and DFA alfa1 (24 h) (r = 0.325; P = 0.000), two know markers of sympathetic tone, were found. A higher sympathetic tone, expressed as high LF/HF, was found in isolated diastolic AHT compared to other types of AHT and the lowest sympathetic tone was found in isolated systolic AHT. Considering non-linear (complexity) analysis, DFA alfa1 (24 h) showed a significant correlation with DBP values that remained independent even after multiple adjustment for BMI, age, gender and Beta Blockers (β = 0.218; P = 0.011). Moreover, the lack of DBP control was associated with high sympathetic tone (LF/HF 3.8 112.3 vs 5.5 .33.3; P < 0.0001). On the other hand, no significant correlations between all DBP data and vagal markers, such as SDNN index, RMSSD and HF, were found. Again, no significant correlations between 24 h, daytime, night-time SBP and time or frequency HRV data as well as with non-linear (complexity) analysis were found. Finally, considering ‘autonomic dipping’, expressed as changes in HRV data between day and night, a strong inverse correlation between vagal markers and Heart Rate Dipping (r = −0.297; P < 0.0001) was found; correlation that remain independent even adjusted for age, gender, BMI, and BB. On the other hand, no association between blood pressure dipping and autonomic dipping was found. Conclusion Diastolic blood pressure and uncontrolled diastolic AHT, rather than systolic AHT, are associated with a hyper-sympathetic tone rather than with blunted vagal tone. The lack of heart rate dipping during night-time in AHT is associated with blunted vagal activation rather than a persistent night-time hyper-adrenergic tone.


1982 ◽  
Vol 98 (1) ◽  
pp. 123-137 ◽  
Author(s):  
Daniel Madden ◽  
William Vélez

2019 ◽  
Vol 100 (3) ◽  
pp. 362-371
Author(s):  
LI-YUAN WANG ◽  
HAI-LIANG WU

Let $n$ be a positive integer and $a$ an integer prime to $n$. Multiplication by $a$ induces a permutation over $\mathbb{Z}/n\mathbb{Z}=\{\overline{0},\overline{1},\ldots ,\overline{n-1}\}$. Lerch’s theorem gives the sign of this permutation. We explore some applications of Lerch’s result to permutation problems involving quadratic residues modulo $p$ and confirm some conjectures posed by Sun [‘Quadratic residues and related permutations and identities’, Preprint, 2018, arXiv:1809.07766]. We also study permutations involving arbitrary $k$th power residues modulo $p$ and primitive roots modulo a power of $p$.


Author(s):  
Rafael Arce-Nazario ◽  
Francis Castro ◽  
Domingo Gomez-Perez ◽  
Oscar Moreno ◽  
José Ortiz-Ubarri ◽  
...  

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
Jilna Payingat ◽  
Deepthi P. Pattathil

This paper proposes a pseudorandom sequence generator for stream ciphers based on elliptic curves (EC). A detailed analysis of various EC based random number generators available in the literature is done and a new method is proposed such that it addresses the drawbacks of these schemes. Statistical analysis of the proposed method is carried out using the NIST (National Institute of Standards and Technology) test suite and it is seen that the sequence exhibits good randomness properties. The linear complexity analysis shows that the system has a linear complexity equal to the period of the sequence which is highly desirable. The statistical complexity and security against known plain text attack are also analysed. A comparison of the proposed method with other EC based schemes is done in terms of throughput, periodicity, and security, and the proposed method outperforms the methods in the literature. For resource constrained applications where a highly secure key exchange is essential, the proposed method provides a good option for encryption by time sharing the point multiplication unit for EC based key exchange. The algorithm and architecture for implementation are developed in such a way that the hardware consumed in addition to point multiplication unit is much less.


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