Multi-Base Chains for Faster Elliptic Curve Cryptography

This research addresses a multi-base number system (MBNS) for faster elliptic curve cryptography (ECC). The emphasis is on speeding up the main operation of ECC: scalar multiplication (tP). Mainly, it addresses the two issues of using the MBNS with ECC: deriving optimized formulas and choosing fast methods. To address the first issue, this research studies the optimized formulas (e.g., 3P, 5P) in different elliptic curve coordinate systems over prime and binary fields. For elliptic curves over prime fields, affine Weierstrass, Jacobian Weierstrass, and standard twisted Edwards coordinate systems are reviewed. For binary elliptic curves, affine, Lambda-projective, and twisted mu4-normal coordinate systems are reviewed. Additionally, whenever possible, this research derives several optimized formulas for these coordinate systems. To address the second issue, this research theoretically and experimentally studies the MBNS methods with respect to the average chain length, the average chain cost, and the average conversion cost. The reviewed MBNS methods are greedy, ternary/binary, multi-base NAF, tree-based, and rDAG-based. The emphasis is on these methods\u27 techniques to convert integer t to multi-base chains. Additionally, this research develops bucket methods that advance the MBNS methods. The experimental results show that the MBNS methods with the optimized formulas, in general, have good improvements on the performance of scalar multiplication, compared to the single-base number system methods

Fast Scalar Multiplication for Elliptic Curves over Binary Fields by Efficiently Computable Formulas

This paper considers efficient scalar multiplication of elliptic curves over binary fields with a twofold purpose. Firstly, we derive the most efficient $3P$ formula in $\lambda$-projective coordinates and $5P$ formula in both affine and $\lambda$-projective coordinates. Secondly, extensive experiments have been conducted to test various multi-base scalar multiplication methods (e.g., greedy, ternary/binary, multi-base NAF, and tree-based) by integrating our fast formulas. The experiments show that our $3P$ and $5P$ formulas had an important role in speeding up the greedy, the ternary/binary, the multi-base NAF, and the tree-based methods over the NAF method. We also establish an efficient $3P$ formula for Koblitz curves and use it to construct an improved set for the optimal pre-computation of window TNAF

Fast Scalar Multiplication for Elliptic Curves over Prime Fields by Efficiently Computable Formulas

This paper addresses fast scalar multiplication for elliptic curves over finite fields. In the first part of the paper, we obtain several efficiently computable formulas for basic elliptic curves arithmetic in the family of twisted Edwards curves over prime fields. Our $2Q+P$ formula saves about $2.8$ field multiplications, and our $5P$ formula saves about $4.2$ field multiplications in standard projective coordinate systems, compared to the latest existing results. In the second part of the paper, we formulate bucket methods for the DAG-based and the tree-based abstract ideas. We propose systematically finding a near optimal chain for multi-base number systems (MBNS). These proposed bucket methods take significantly less time to find a near optimal chain, compared to an optimal chain. We conducted extensive experiments to compare the performance of the MBNS methods (e.g., greedy, ternary/binary, multi-base NAF, tree-based, rDAG-based, and bucket). Our proposed formulas were integrated in these methods. Our results show our work had an important role in advancing the efficiency of scalar multiplication

Double-Base Chains for Scalar Multiplications on Elliptic Curves

Double-base chains (DBCs) are widely used to speed up scalar multiplications on elliptic curves. We present three results of DBCs. First, we display a structure of the set containing all DBCs and propose an iterative algorithm to compute the number of DBCs for a positive integer. This is the first polynomial time algorithm to compute the number of DBCs for positive integers. Secondly, we present an asymptotic lower bound on average Hamming weights of DBCs $\frac{\log n}{8.25}$ for a positive integer $n$. This result answers an open question about the Hamming weights of DBCs. Thirdly, we propose a new algorithm to generate an optimal DBC for any positive integer. The time complexity of this algorithm is $\mathcal{O}\left(\left(\log n\right)^2 \log\log n\right)$ bit operations and the space complexity is $\mathcal{O}\left(\left(\log n\right)^{2}\right)$ bits of memory. This algorithm accelerates the recoding procedure by more than $6$ times compared to the state-of-the-art Bernstein, Chuengsatiansup, and Lange\u27s work. The Hamming weights of optimal DBCs are over $60$\% smaller than those of NAFs. Scalar multiplication using our optimal DBC is about $13$\% faster than that using non-adjacent form on elliptic curves over large prime fields

A Novel Pre-Computation Scheme of Window τ\tauNAF for Koblitz Curves

Let $E_a: y^2+xy=x^3+ax^2+1/ \mathbb{F}_{2^m}$ be a Koblitz curve. The window $\tau$-adic nonadjacent-form (window $\tau$NAF) is currently the standard representation system to perform scalar multiplications on $E_a$ by utilizing the Frobenius map $\tau$. Pre-computation is an important part for the window $\tau$NAF. In this paper, we first introduce $\mu\bar{\tau}$-operations in lambda coordinates ($\mu=(-1)^{1-a}$ and $\bar{\tau}$ is the complex conjugate of the complex representation of $\tau$). Efficient formulas of $\mu\bar{\tau}$-operations are then derived and used in a novel pre-computation scheme to improve the efficiency of scalar multiplications using window $\tau$NAF. Our pre-computation scheme costs $7$M$+5$S, $26$M$+16$S, and $66$M$+36$S for window $\tau$NAF with width $4$, $5$, and $6$ respectively whereas the pre-computation with the state-of-the-art technique costs $11$M$+8$S, $43$M$+18$S, and $107$M$+36$S. Experimental results show that our pre-computation is about $60\%$ faster, compared to the best pre-computation in the literature. It also shows that we can save from $2.5\%$ to $4.9\%$ on the scalar multiplications using window $\tau$NAF with our pre-computation

The Effect of Training and Development Effectiveness on Jordanian Municipalities

Purpose: This study investigates the impact of training and development effectiveness on Jordanian municipality's performance. It aims to understand the relationship between training programs and municipal outcomes, with a focus on employee performance and organizational effectiveness.   Theoretical framework: The study employs a descriptive analysis approach to explore its objectives. It relies on a questionnaire-based data collection method, targeting all workers in Jordanian municipalities and the Greater Amman Municipality. The research uses statistical analysis software SPSS for data analysis and hypothesis testing.   Design, methodology, approach: The study's design involves surveying 7043 employees across various job titles in Jordanian municipalities and the Amman municipality. The questionnaire serves as the primary data collection tool. The research utilizes the SPSS program for statistical analysis and hypothesis validation. Descriptive statistics and analytical methods are employed to assess the effectiveness of training and development programs.   Findings: The study reveals that the majority of employees are male, aged 40 or younger, with less than 15 years of service. Around 78.5% of employees hold a diploma or higher qualification. The research indicates an average level of approval regarding the performance of municipalities and employees. It establishes a significant impact of training and development effectiveness on municipal and employee performance, influenced by factors such as academic qualification and age.   Research, practical & social implications: The findings emphasize the need for tailored training programs, especially for younger employees and newcomers. The study advocates for comprehensive training preparation, evaluation based on predefined criteria, and the allocation of financial resources in municipal budgets for ongoing training and development initiatives. These insights have practical implications for enhancing municipal employee performance and, consequently, the overall functioning of Jordanian municipalities.   Originality: This study contributes original insights by investigating the specific context of Jordanian municipalities. It sheds light on the effectiveness of training and development programs, highlighting their influence on employee and municipal performance. The research provides unique recommendations, emphasizing the importance of targeted training for specific employee groups and the necessity of financial allocation for sustained training efforts

Mapping local patterns of childhood overweight and wasting in low- and middle-income countries between 2000 and 2017

A double burden of malnutrition occurs when individuals, household members or communities experience both undernutrition and overweight. Here, we show geospatial estimates of overweight and wasting prevalence among children under 5 years of age in 105 low- and middle-income countries (LMICs) from 2000 to 2017 and aggregate these to policy-relevant administrative units. Wasting decreased overall across LMICs between 2000 and 2017, from 8.4% (62.3 (55.1–70.8) million) to 6.4% (58.3 (47.6–70.7) million), but is predicted to remain above the World Health Organization’s Global Nutrition Target of <5% in over half of LMICs by 2025. Prevalence of overweight increased from 5.2% (30 (22.8–38.5) million) in 2000 to 6.0% (55.5 (44.8–67.9) million) children aged under 5 years in 2017. Areas most affected by double burden of malnutrition were located in Indonesia, Thailand, southeastern China, Botswana, Cameroon and central Nigeria. Our estimates provide a new perspective to researchers, policy makers and public health agencies in their efforts to address this global childhood syndemic

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

Knowledge and awareness of cancer among Umm Al-Qura University students (Al-Leith Colleges Campus) - Saudi Arabia

Background: Cancer caused over 8 million deaths worldwide in 2013 and has moved from the third leading cause of death in 1990to the second leading cause behind cardiovascular disease in 2013. Cancer can be reduced and controlled by implementing evidencebased strategies for cancer prevention, early detection of cancer and management of patients with cancer. Many cancers have a highchance of cure if detected early and treated adequately. Cancer awareness has been shown to contribute to improvements in theearly detection and management of disease. Objective: The current study aimed to evaluate and assess the level of knowledge andawareness of cancer among Umm Al-Qura University students - Al-Leith colleges campus - Saudi Arabia, the study covered differentcolleges include (health sciences, social, computer, and college of engineering). Methods: This is a descriptive cross-sectional studyconducted in college of health sciences at Al-Leith, Umm Al-Qura University -Kingdom of Saudi Arabia during the period from August2016 to April 2017. Data were collected using a questionnaires, 202 students were randomly selected, 106 (52%) of the students fromhealth sciences college and the remaining 96 (48%) were from other faculties (social sciences, computer, and college of engineering).Results: The education level of students was as follows: 35 (17%) of students in the first level, 28 (14%) of students in the secondlevel, 58 (29%) of students in the third level, and 81(40%) of the fourth level. Most of the students from health sciences college (76%)were answered correctly define cancer, while about half of the students in the other faculties (56% only 58%) gave true definitionof the disease. In terms of knowledge and awareness about risk factors for cancer, the study showed that most students aware bytobacco, alcohol, pesticides, preservative food, radiation, and obesity as cancer risks, but they did not know that viruses, bacteria,fungi, and sports inactivity were classified as risk factors for cancer. Most of the students involved in the current study were awareby lumps pain as cancer signs and symptoms, but at the same time, they do not aware by other signs and symptoms of the disease(skin ulcers, bleeding, low weight, and coughing), they gave low percent of positive results. Conclusion: The study concluded thatstudents’ awareness regarding cancer needs to be raised through educational and awareness programs