Advanced method of factorization of multi-bit numbers based on Fermat's theorem in the system of residual classes

Karpinski, Mikolaj; Ivasiev, Stepan; Yakymenko, Igor; Kasianchuk, Mykhajlo; Gancarczyk, Tomasz

doi:10.1109/iccas.2016.7832500

Cited by 40 publications

(4 citation statements)

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“…Cybersecurity breaches, a notorious issue, can compromise user data, eroding the trust that takes years to build. Here, the proposed CRT-based NPNS demonstrate superiority by providing a framework that inherently disperses information, making it less susceptible to traditional hacking methods [34,35].…”

Section: Fault Tolerance In E-commerce: Defining the Need And Scopementioning

confidence: 99%

“…Furthermore, the CRT finds profound utility in cryptographic communications, an integral element of secure digital transactions [34,60]. It undergirds several cryptographic protocols by enabling secure information transmission over public channels and plays a significant role in algorithms for public key cryptography, such as RSA [35,60].…”

Section: Crt Explanation: Theoretical Insights Into the Chinese Remai...mentioning

confidence: 99%

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Integrating Non-Positional Numbering Systems into E-Commerce Platforms: A Novel Approach to Enhance System Fault Tolerance

Krasnobayev,

Kuznetsov

2023

JTAER

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In the dynamic landscape of electronic commerce, the robustness of platforms is a critical determinant of operational continuity and trustworthiness, necessitating innovative approaches to fault tolerance. This study pioneers an advanced strategy for enhancing fault tolerance in e-commerce systems, utilizing non-positional numbering systems (NPNS) inspired by the mathematical robustness of the Chinese Remainder Theorem (CRT). Traditional systems rely heavily on positional numbering, which, despite its ubiquity, harbors limitations in flexibility and resilience against computational errors and system faults. In contrast, NPNS, characterized by their independence, equitability, and residue independence, introduce a transformative potential for system architecture, significantly increasing resistance to disruptions and computational inaccuracies. Our discourse extends beyond theoretical implications, delving into practical applications within contemporary e-commerce platforms. We introduce and elaborate on new terminologies, concepts, and a sophisticated classification system for fault-tolerance mechanisms within the framework of NPNS. This nuanced approach not only consolidates understanding but also identifies underexplored pathways for resilience in digital commerce infrastructure. Furthermore, this research highlights the empirical significance of adopting NPNS, offering a methodologically sound and innovative avenue to safeguard against system vulnerabilities. By integrating NPNS, platforms can achieve enhanced levels of redundancy and fault tolerance, essential for maintaining operational integrity in the face of unforeseen system failures. This integration signals a paradigm shift, emphasizing proactive fault mitigation strategies over reactive measures. Conclusively, this study serves as a seminal reference point for subsequent scholarly endeavors, advocating for a shift towards NPNS in e-commerce platforms. The practical adaptations suggested herein are poised to redefine stakeholders’ approach to system reliability, instigating a new era of confidence in e-commerce engagements.

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Section: Fault Tolerance In E-commerce: Defining the Need And Scopementioning

confidence: 99%

Section: Crt Explanation: Theoretical Insights Into the Chinese Remai...mentioning

confidence: 99%

Integrating Non-Positional Numbering Systems into E-Commerce Platforms: A Novel Approach to Enhance System Fault Tolerance

Krasnobayev,

Kuznetsov

2023

JTAER

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“…At this level the data collected at the previous two level are grouped and summarized [9]. Decision making frequently require using mathematical models for prediction different characteristics [10][11][12][13][14][15]. In case of uncertain conditions, data-driven models, built on interval approach, are used [16][17][18][19][20][21][22][23][24].…”

Section: Rector Of West Ukrainian National Universitymentioning

confidence: 99%

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Sysoieva

Pukas

Pushkar

et al. 2022

2022 12th International Conference on Advanced Computer Information Technologies (ACIT)

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by the by our partner -Catholic University in Ru omberok. We hope that the spirit of the ACIT'2022 International Conference will be present at the plenary and sectional meetings and will ensure a high level of scientific discussions.Dear participants! We wish you to have productive discussions and hope that the conference will give you good inspiration for further developments in the field of Advanced Computer and Information Technologies!

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“…На сьогоднішній день криптосистема Рабіна є однією з найбільш ефективних [1], оскільки для шифрування потрібна лише операція піднесення до квадрату за модулем, а не модулярне експоненціювання, як в асиметричних криптосистемах RSA та Ель-Гамаля [2]. Крім того, її стійкість ґрунтується на проблемі факторизації [3,4] та пошуку квадратичного лишку [5]. Дана операція має субекспоненційну складність [6], тому для забезпечення достатньої стійкості при сьогоднішніх обчислювальних потужностях розрядність числових полів повинна бути більшою 1024 біт [7].…”

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Rabin's Crypto System on the Basis of the Addition Operation

Yakymenko¹,

Kasianchuk²,

Ivasiev³

2019

MCM-TECH

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І. З. Якименко, канд. техн. наук, М. М. Касянчук, канд. фіз.-мат. наук, С. В. Івасьєв, канд. техн. наук Тернопільський національний економічний університет, м. Тернопіль КРИПТОСИСТЕМА РАБІНА НА ОСНОВІ ОПЕРАЦІЇ ДОДАВАННЯ У роботі наведено теоретичні основи криптосистеми Рабіна з використанням тільки операції додавання, завдяки чому досягається зменшення часової складності процесу шифрування / дешифрування інформаційних потоків. Запропонований підхід дозволяє збільшувати розмірності вхідних параметрів для підвищення стійкості без втрати швидкодії. Представлено приклад застосування запропонованої реалізації криптосистеми Рабіна. Ключові слова: криптосистема Рабіна, векторно-модульний метод модулярного множення, квадратичний лишок, операція додавання, часова складність.

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Advanced method of factorization of multi-bit numbers based on Fermat's theorem in the system of residual classes

Cited by 40 publications

References 2 publications

Integrating Non-Positional Numbering Systems into E-Commerce Platforms: A Novel Approach to Enhance System Fault Tolerance

Integrating Non-Positional Numbering Systems into E-Commerce Platforms: A Novel Approach to Enhance System Fault Tolerance

Information Support of Social Audit

Rabin's Crypto System on the Basis of the Addition Operation

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