การเปรียบเทียบประสิทธิภาพการแยกตัวประกอบของชุดข้อมูลที่มีเลขประจำหลักเดียวกัน ตั้งแต่ 2 – 20 หลักด้วย Pollard’s rho Algorithm และ Fermat’s Factorization Method

งานวิจัยนี้ได้นำเสนอการเปรียบเทียบประสิทธิภาพการแยกตัวประกอบ เป็นการวิจัยเชิงทดลองด้วยวิธี Pollard's rho Algorithm และ Fermat's Factorization Method ทั้งสองอัลกอริทึมนั้นเป็นอัลกอริทึมที่ได้รับความนิยมในปัจจุบัน หากเปรียบเทียบประสิทธิภาพในการแยกตัวประกอบของตัวเลขทั่วไปแล้วนั้นทั้ง 2 อัลกอริทึม มีประสิทธิภาพในการทำงานแตกต่างกัน โดยทดลองด้วยชุดข้อมูลที่มีค่าข้อมูลเลขประจำหลักเดียวกันทั้งหมด ดังนั้นจึงนำอัลกอริทึมแยกตัวประกอบทั้ง 2 แบบ โดยใช้ชุดข้อมูลตัวเลขทั้งสิ้น 171 ชุด ซึ่งประกอบไปด้วยตัวเลขตั้งแต่ 2 หลัก จนถึง 20 หลัก โดยมีเลขประจำหลักเดียวกัน เริ่มตั้งแต่ 1-9 และเปรียบเทียบว่าทั้งสองอัลกอริทึมนั้นให้ผลลัพธ์ของเวลาและประสิทธิภาพในการแยกตัวประกอบจากชุดข้อมูลแต่ละชุด โดยการแยกตัวประกอบของชุดข้อมูลที่มีเลขประจำหลักเดียวกันทั้งหมด พบว่า การแยกตัวประกอบวิธี Pollard's rho Algorithm มีประสิทธิภาพด้านความเร็วในการแยกตัวประกอบดีกว่าวิธี Fermat's Factorization Methodคำสำคัญ: การแยกตัวประกอบ  อัลกอริทึมพอลลาร์ด โร  อัลกอริทึมทฤษฏีแฟร์มาต์This research showed the factorization to compare the results of the algorithm used to factorization. Experimental research using Pollard's rho algorithm and Fermat's factorization method, both algorithms are currently popular algorithms. Comparing the efficiency of factorization of common numbers, the two algorithms are not very different in their efficiency. Therefore, the two factorial algorithms are used, using 171 numerical data sets, consisting of 2 - 20 digits, with the same numerals from 1 to 9, and comparing the two algorithms. Comparing these two algorithms gives the results of the time and efficiency of the factorization from each set. The results show that the Pollard's rho algorithm is more efficient and faster than the Fermat's factorization method.Keywords: Factorization, Pollard's rho Algorithm, Fermat's Factorization Metho

Pacific Weekly, January 9,1942

https://scholarlycommons.pacific.edu/pacifican/2317/thumbnail.jp

The Security of Elliptic Curve Cryptosystems - A Survey

Elliptic curve cryptography or ECC is a public-key cryptosystem. This paper introduces ECC and describes its present applications. A mathematical background is given initially. Then its’ major cryptographic uses are given. These include its’ use in encryption, key sharing and digital signatures. The security of these ECC-based cryptosystems are discussed. It was found that ECC was well suited for low-power and resource constrained devices because of its’ small key size

An examination of the temperamental and ability characteristics of large animals under open-field and stress conditions

In this study an attempt was made to adapt two tests, developed for use with rats and mice, for work with the larger animals in order to assess their worth for measuring the temperamental and ability characteristics of domestic farm species. To assess the temperamental characteristics an open-field, scaled to 72 feet by 72 feet, was used to score 30 pigs, 30 sheep and 44 cows on three criteria; ambulation, elimination and vocalisation. These scores were correlated with dairymen’s ratings of the cows and plasma cortisol levels in the sheep. It became clear that the open-field test requires further modification before it can provide meaningful results for domestic stock. The closed-field test was used with 63 pigs, 103 sheep, and 73 cows to measure the “intelligence” of normal farm animals. Time and error scores and general behaviour were recorded and analysed, and showed characteristic species differences. In the evaluation of scores from both tests the importance of group effects found in herd animals was considered. A relationship between the closed-field test performance, and the social status of the animals in each test group was considered. Practical problems such as; animal-experimenter interactions; adequate motivation of ruminants; the impossibility of man-handling large animals like cows, and the kind of modifications which must be made to apparatus for this type of work ,are fully discussed. Isolating herd or flock animals appears to cause stress. The results of the closed-field test were compared with similar results from other studies where mice, rats, cats, dogs, ferrets, hens and other species have been tested in smaller versions of the closed-field. The general conclusion is that the potential for training, or utilising in other ways the ability inherent in the farm animal in New Zealand has hardly been touched. Though a number of experimenters have commented on these abilities during trials in research institutions such information has not been fully exploited in normal farm practice

Design and Analysis of Cryptographic Hash Functions

Wydział Matematyki i InformatykiKryptograficzne funkcje haszujące stanowią element składowy wielu algorytmów kryptograficznych. Przykładowymi zastosowaniami kryptograficznych funkcji haszujących są podpisy cyfrowe oraz kody uwierzytelniania wiadomości. Ich własności kryptograficzne mają znaczący wpływ na poziom bezpieczeństwa systemów kryptograficznych wykorzystujących haszowanie. W dysertacji analizowane są kryptograficzne funkcje haszujące oraz omówione główne zasady tworzenia bezpiecznych kryptograficznych funkcji haszujących. Analizujemy bezpieczeństwo dedykowanych funkcji haszujących (BMW, Shabal, SIMD, BLAKE2, Skein) oraz funkcji haszujących zbudowanych z szyfrów blokowych (Crypton, Hierocrypt-3, IDEA, SAFER++, Square). Głównymi metodami kryptoanalizy użytymi są skrócona analiza różnicowa, analiza rotacyjna i przesuwna. Uzyskane wyniki pokazują słabości analizowanych konstrukcji.Cryptographic Hash Functions (CHFs) are building blocks of many cryptographic algorithms. For instance, they are indispensable tools for efficient digital signature and authentication tags. Their security properties have tremendous impact on the security level of systems, which use cryptographic hashing. This thesis analyzes CHFs and studies the design principles for construction of secure and efficient CHFs. The dissertation investigates security of both dedicated hash functions (BMW, Shabal, SIMD, BLAKE2, Skein) and hash functions based on block ciphers (Crypton, Hierocrypt-3, IDEA, SAFER++, Square). The main cryptographic tools applied are truncated differentials, rotational and shift analysis. The findings show weaknesses in the designs

The transformation of the small master economy in the boot and shoe industry 1887-1914 : with special reference to Northampton

The footwear industry is one of the important examples of late industrial transformation in nineteenth century  Britain. The aim here is to investigate shoe manufacturers' reactions to this period of structural and  organisational change. The thesis is in three parts:(I) Chapters One-Three explore the character and scope of industrialisation in the industry. The literature on  British entrepreneurship, evaluates the shifts in attitude and strategy of dominant groups within each industry;  much less attention has been given to the often wide divergence of experience within business communities as a whole. In small master-dominated industries, like shoemaking, there existed a range of business experience  - both business success and failure - which has not been the subject of close empirical study. Here, the  assumption of an orderly, progressive concentration of capital is challenged. The small shoe masters' role  during industrialisation was more complex than the literature allows. Secondly, the chronology and  determinants of change are reappraised. And, finally, the size, character and structure of the Northampton footwear business community is studied.(II) Chapters Four-Six take up this theme of business failure. Little previous systematic, empirical investigation  of patterns of failure has been carried out by historians. Thus, initially, general issues of methodology and theory are broached. The data presented, not only allows failure trends to be analysed, but is also used to explore  small masters' attitudes and reactions to change. Three facets of failure were isolated. Failure linked to  business cycle effects (Chapter Four). The high endemic levels of failure linked to normal trading pressures  with reference particularly to infant firms. Here questions of credit provision, failure causation and small master  motivation are examined (Chapter Five), in addition to normal and hiatus failures amongst mature firms (Chapter Six). Lastly, failures linked to industrialisation are investigated (Chapter Six). There are two features:  the contraction of the small master base and the failure of old established firms.(III) As a counterpoint to Section II, Chapters Seven and Eight study those firms that survive to 1914. These  included a small, dominant elite group of established firms, whose industrial policies, family business  organisation and striving for social acceptance are examined

KOSMOS in John

The purpose of this study is to determine what John aims to say with the word kosmos . What understanding of man underlies John\u27s semantic signal kosmos? Why did John choose this particular word to signal the thought he wanted to convey? What role did this term play in the Umwelt of John? Is the idea behind the term kosmos effectively and accurately signalled by the English term world