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# Introduction to number Theory in cryptography and Network Security ppt

### A Course in Number Theory and Cryptograph

1. 1. Cryptography and Network Security Chapter 8 by William Stallings by B . A . Forouzan. 2. Objectives To introduce prime numbers and their applications in cryptography. To discuss some primality test algorithms and their efficiencies. To discuss factorization algorithms and their applications in cryptography. To describe the Chinese.
2. Cryptography and Network Security Chapter 8 Fifth Edition by William Stallings Lecture slides by Lawrie Brown Chapter 8 -Introduction to Number Theory The Devil said to Daniel Webster: Set me a task I can't carry out, and I'll give you anything in the world you ask for. Daniel Webster: Fair enough
3. 1. Network Security and Cryptography By Adam Reagan CIS 504 - Data Communications The College of Saint Rose, Albany NY Spring 2008. 2. A Need For Security <ul><li>Growing computer use implies a need for automated tools for protecting files and other information </li></ul><ul><li>The use of networks and communications facilities for carrying data.
4. Cryptography and Network Security Chapter 8 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 8 - Introduction to Number Theory The Devil said to Daniel Webster: Set me a task I can't carry o ut, and I'll give you anything in the world you ask for. Daniel Webster: Fair enough. Prove that for n greater than 2, t h
5. Cryptography and network security 1. CRYPTOGRAPHY PRATIKSHA PATIL 2. CONTENTS o Introduction o Need of Cryptography o Types of Attacks o Techniques of Cryptography o Encryption Algorithm • Symmetric • Asymmetric o Digital Signature o Visual cryptography 3. INTRODUCTION What is Cryptography? Hidden Writing Mainly used to protect Information. 4

• Classical Cryptography • Shannon's Theory • Block Ciphers -DES, AES, their implementations and their attacks • Stream Ciphers CR • Digital Signatures and Authentication -Hash functions • Public key ciphers -RSA, implementations, and attacks • Side channel analysis • Network Security aspects • Case Studies : Bitcoins 2 In the next sections we will review concepts from Number Theory, the branch of mathematics that deals with integer numbers and their properties. We will be covering the following topics: 1 Divisibility and Modular Arithmetic (applications to hashing functions/tables and simple cryptographic cyphers).Section 3.

Introduction Number theory has its roots in the study of the properties of the natural numbers N = f1,2,3,. . .g and various extensions thereof, beginning with the integers Z = f. . ., 2, 1,0,1,2,. . .g and rationals Q = a b ja,b 2Z, b 6= 0. This leads directly to the ﬁrst two parts of this course, of which the following may serve as a brief outline It is an unbreakable cryptosystem. It represents the message as a sequence of 0s and 1s. this can be accomplished by writing all numbers in binary, for example, or by using ASCII. The key is a random sequence of 0‟s and 1‟s of same length as the message. Once a key is used, it is discarded and never used again To see how this method, known as the RSA algorithm, works, we need to first look at some basic results of number theory, the study of the natural numbers 1, 2, 3, etc. Let's specifically examine the subset of the natural numbers known as the prime numbers. The prime numbers are those natural numbers which have no divisors other than 1 and themselves. For example, 2, 3, and 5 are prime, while 4 and 15 are not prime, since 2 is a divisor of 4 and 3 is a divisor of 15. Here's a. This video covers basic concepts of Prime number, Relative prime number, Modular arithmetic, Congruent modulo, Properties of Modular arithmetic, Properties o.. Cryptography and Network Security by Prof. D. Mukhopadhyay, Department of Computer Science and Engineering, IIT Kharagpur. For more details on NPTEL visit ht..

### Ch08 - SlideShar

Cryptography and Network Security. Introduction. Overview on Modern Cryptography. Introduction to Number Theory. Probability and Information Theory. Classical Cryptosystems. Cryptanalysis of Classical Ciphers. Shannons Theory. Shannons Theory (Contd...1 CSE497b Introduction to Computer and Network Security - Spring 2007 - Professor Jaeger Page Cryptanalysis of DES • DES has an effective 56-bit key length - Wiener: 1,000,000\$ - 3.5 hours (never built) - July 17, 1998, the EFF DES Cracker, which was built for less than \$250,000 < 3 days - January 19, 1999, Distributed.Net (w/EFF), 22 hours an A gentle introduction to the fundamentals of number theory is provided in the opening chapters, paving the way for the student to move on to more complex security and cryptography topics. Difficult math concepts are organized in appendices at the end of each chapter so that students can first learn the principles, then apply the technical background. Hundreds of examples, as well as fully coded programs, round out a practical, hands-on approach which encourages students to test the material.

Introduction to Number Theory Modular Arithmetic. modular arithmetic is 'clock arithmetic' a congruence a = b mod n says when divided by n that a and b have the same remainder 100 = 34 mod 11; usually have 0<=b<=n-1-12mod7 = -5mod7 = 2mod7 = 9mod7 ; b is called the residue of a mod n. can do arithmetic with integers modulo n with all results between 0 and The Basics of Cryptography 12 An Introduction to Cryptography While cryptography is the science of securing data, cryptanalysisis the science of analyzing and breaking secure communication. Classical cryptanalysis involves an interesting combination of analytical reasoning, application o digit) prime numbers is easy, but factoring the product of two such numbers appears computationally infeasible Choose very large prime numbers P and Q - N = P x Q - N is public; P, Q are secret Euler totient: Phi(N) = (P-1)(Q-1) = Number of integers less than N & relatively prime to Units are numbers with inverses. Exponentiation. The behaviour of units when they are exponentiated is difficult to study. Modern cryptography exploits this. Order of a Unit. If we start with a unit and keep multiplying it by itself, we wind up with 1 eventually. The order of a unit is the number of steps this takes. The Miller-Rabin Tes

2.1 Quick & Dirty Introduction to Complexity Theory Deﬁnition 2.1. An algorithm1 is called deterministic if the output only depends on the input. Otherwise we call it probabilistic or randomized. Deﬁnition 2.2. Let f,g: N! R be two functions. We denote f (n) = O (g(n)) for n ! 1 iff there is a constant M 2 R>0 and an N 2 N such that jf (n)j Mjg(n)j for all n N Cryptography and Network Security Chapter 8 Fifth Edition by William Stallings Lecture slides by Lawrie Brown (with edits by RHB) Chapter 8 - Introduction to Number Theory The Devil said to Daniel Webster: Set me a task I can't carry o ut, and I'll give you anything in the world you ask for. Daniel Webster: Fair enough. Prove that for n greater than 2, t he equation a n + + bn = cn has no. Introduction to Number Theory and its Applications Lucia Moura Winter 2010 \Mathematics is the queen of sciences and the theory of numbers is the queen of mathematics. (Karl Friedrich Gauss) CSI2101 Discrete Structures Winter 2010: Intro to Number TheoryLucia Moura. The Integers and Division Primes and Greatest Common Divisor Applications The Integers and Division Introduction In the next.

• Authentication: An Introduction to Cryptography, in Proc. IEEE, vol. 67, no.3, pp. 397 - 427, 1979 Fundamentals of Wired and Wireless Networks, Kameswari Chebrolu and Bhaskaran Raman, 09­13 May 200
• e (in breadth) a few.
• An Introduction to Elliptic Curve Cryptography. Application of Elliptic Curves to Cryptography. Implementation of Elliptic Curve Cryptography. Secret Sharing Schemes. A Tutorial on Network Protocols. System Security. Firewalls and Intrusion Detection Systems. Side Channel Analysis of Cryptographic Implementations
• What is the foundation of internet security? algorithms, data structures, database, parallel computing, distributed systems, cryptography, computer networks Logic, number theory, counting, graph theory

### Network Security and Cryptography - SlideShar

of 'provable security'. No longer does a cryptographer informally argue why his new algorithm is secure, there is now a framework within which one can demonstrate the security relative to other well-studied notions. Cryptography courses are now taught at all major universities, sometimes these are taught in the context of a Mathematics degree, sometimes in the context of a Computer Science. Class lectures on Network Security covering Course Introduction, Security Overview, Classical Encryption Techniques, Block Ciphers and DES, Basic Concepts in Number Theory and Finite Fields, Advanced Encryption Standard (AES), Block Cipher Operations, Pseudo Random Number Generation and Stream Ciphers, Number Theory, Public Key Cryptography, Other Public Key Cryptosystems, Cryptographic Hash.

### Cryptography and network security - SlideShar

• cryptography, you will not be able to understand the workings of several modern protocols (like the SSH protocol you use everyday for logging into other computers) for secure 3. Computer and Network Security by Avi Kak Lecture4 communications over networks. You will also not be able to understand what has become so important in computer security — user and document authentication with.
• Theorem 1.2 Any natural number greater than 1 can be written as a product of prime numbers, and this expression is unique apart from re-ordering the factors. Proof We show the existence of a factorisation into primes by induction. Given a natural number n, if n is prime, then it is the product of just one prime. (Thi
• An Introduction to Cryptography 8 Network security Books • Building Internet Firewalls, Elizabeth D. Zwicky, D. Brent Chapman, Simon Cooper, and Deborah Russell (Editor), O'Reilly & Associates, Inc., 2000; ISBN: 1565928717. This book is a practical guide to designing, building, and maintain-ing firewalls
• g exercises and term projects, you can utilize open source security.

key cryptography, attacks on public-key systems, and playing a central role in Andrew Wiles' resolution of Fermat's Last Theorem. Today, pure and applied number theory is an exciting mix of simultane-ously broad and deep theory, which is constantly informed and motivated by algorithms and explicit computation. Active research is underway that promises to resolve the congruent number. Introduction to Cryptography Winter 2021. Cryptography is an indispensable tool for protecting information in computer systems. This course explains the inner workings of cryptographic primitives and how to use them correctly. Administrative . Course syllabus (and readings) Course overview (grading, textbooks, coursework, exams) Course staff and office hours. Lectures: Monday, Wednesday, 2:30. network like the Internet. The most basic goal of cryptography is to provide such parties with a means to imbue their communications with security properties akin to those provided by the ideal channel. At this point we should introduce the third member of our cast. This is our adversary,de-noted A. An adversary models the source of all.

This text is an introduction to number theory and abstract algebra; based on its presentation, it appears appropriate for students coming from computer science. The book starts with basic properties of integers (e.g., divisibility, unique factorization), and touches on topics in elementary number theory (e.g., arithmetic modulo n, the distribution of primes, discrete logarithms, primality. ematics, ranging from number theory to complex analysis, and from cryptography to mathematical physics. An Introduction to the Theory of Elliptic Curves { 5{Elliptic Curves Points on Elliptic Curves † Elliptic curves can have points with coordinates in any ﬂeld, such as Fp, Q, R, or C. † Elliptic curves with points in Fp are ﬂnite groups. † Elliptic Curve Discrete Logarithm Prob-lem. Cryptography Tutorial. This tutorial covers the basics of the science of cryptography. It explains how programmers and network professionals can use cryptography to maintain the privacy of computer data. Starting with the origins of cryptography, it moves on to explain cryptosystems, various traditional and modern ciphers, public key encryption.

### Cryptography and Number Theory Science4Al

Foreword This is a set of lecture notes on cryptography compiled for 6.87s, a one week long course on cryptography taught at MIT by Shaﬂ Goldwasser and Mihir Bellare in the summers of 1996{2002, 2004, 2005 and 2008 [R3] Bernard Menezes: Network Security & Cryptography, 1st Edition, Cengage Learning, Delhi, 2011. Note: In this course, I will follow [T1] as textbook. However, the students are suggested to consult with the books [R1] - [R3] for Modern Cryptography and Network Security. Lecture Plan Lecture # Topics to be covered Reading Section A: Cryptographic Techniques and Algorithms 1 Course. 4.4. ( 31) Here you can download the free lecture Notes of Cryptography and Network Security Pdf Notes - CNS Notes pdf materials with multiple file links to download. The CNS Pdf Notes book starts with the topics covering Information Transferring, Interruption, Interception, Services and Mechanisms, Network Security Model, Security, History, Etc First, the basic issues to be addressed by a network security capability are explored through a tutorial and survey of cryptography and network security technology. Then, the practice of network security is explored via practical applications that have been implemented and are in use today. An unparalleled support package for instructors and students ensures a successful teaching and learning.

Introduction to Cryptography: Provides a Web-based introduction to cryptography for non-CS majors. Although elementary, it provides a useful feel for some key concepts. Originally appeared in the on-line Journal on Educational Resources in Computing, September 2002. Security Cartoon: A cartoon-based approach aimed at improving the understanding of security risk among typical Internet users. Cryptography Seminar and PPT with pdf report: Cryptography is the practice and the study of concealing the information and it furnishes confidentiality, integrity, and exactness. Cryptography is used to defend the data and to defend the data and to define it in the simple and easy words, it is an art of writing and solving the codes Search within a range of numbers Put. between two numbers. For example, camera \$50..\$100. Combine searches Put OR between each search query. For example, marathon OR race. Home » Courses » Electrical Engineering and Computer Science » Network and Computer Security » Lecture Notes and Readings Lecture Notes and Readings Course Home Syllabus Calendar Lecture Notes and Readings. Connections between graph theory and cryptography Sparse graphs, social networks and mobile security systems Asparsegraphisagraphinwhichthenumberofedgesismuc

### NETWORK SECURITY- INTRODUCTION TO NUMBER THOERY - YouTub

Cryptography is the study and practice of techniques for secure communication in the presence of third parties called adversaries. It deals with developing and analyzing protocols which prevents malicious third parties from retrieving information being shared between two entities thereby following the various aspects of information security As long as all of the networks in the internet have unique network numbers, combining the network number and host number will give unique global names. Therefore from the outside an internet looks like a single network! A router: A device that appears simultaneously on two or more networks. (Usually this is a computer or device with two or more network interface cards, or NICs.) The Internet.

### Introduction to Number Theory - YouTub

freely. Cryptography is the branch of information security which covers the study of algorithms and protocols that secure data. It is a diverse ﬂeld, taking in elements of electronic engineering, computer science and mathematics, including computational and algebraic number theory, combinatorics, group theory, and complexity theory Introduction to Cryptography and Security Mechanisms: Introduction to Network Security: Theory and Practice. Wiley and HEP, 2015 * J. Wang and Z. Kissel. | PowerPoint PPT presentation | free to view . PRNG, Block and Stream Cipher - RBG: a device or algorithm which outputs a sequence of generating random bit sequence of length lg n 1, Test: comparing with expected | PowerPoint. Introduction to Crypto-terminologies. Cryptography is an important aspect when we deal with network security. 'Crypto' means secret or hidden. Cryptography is the science of secret writing with the intention of keeping the data secret. Cryptanalysis, on the other hand, is the science or sometimes the art of breaking cryptosystems and network professionals can use cryptography to maintain the privacy of computer data. Starting with the origins of cryptography, it moves on to explain cryptosystems, various traditional and modern ciphers, public key encryption, data integration, message authentication, and digital signatures. Audience This tutorial is meant for students of computer science who aspire to learn the basics.

1. Computer and Network Security Concepts . 2. Introduction to Number Theory . 3. Classical Encryption Techniques . 4. Block Ciphers and the Data Encryption Standard . 5. Finite Fields . 6. Advanced Encryption Standard . 7. Block Cipher Operation . 8. Random Bit Generation and Stream Ciphers . 9. Public-Key Cryptography and RSA . 10. Other. Introduction. This book constitutes the proceedings of the 15 th International Conference on Applied Cryptology and Network Security, ACNS 2017, held in Kanazawa, Japan, in July 2017. The 34 papers presented in this volume were carefully reviewed and selected from 149 submissions. The topics focus on innovative research and current developments. Since we will be focusing on computer cryptography and as each datum is a series of bytes, we are only interested in Galois Field of order 2 and 28 in this paper. Because computer stores data in bytes, each binary number must be 8 bits long. For number that is less than 8 bits long, leading zeros are added Theory of codes and cryptography are two more recent fields of application. This book tells about CRT, its background and philosophy, history, generalizations and, most importantly, its applications. The book is self-contained. This means that no factual knowledge is assumed on the part of the reader. We even provide brief tutorials on relevant subjects, algebra and information theory. However.

### Cryptography and Network Security - NPTE

Departamento de Informática e Estatístic It all depends on the security of the network itself in such a case. If the network is secure, the information can be shared. In case not, I will probably wait for the Cryptography tool to be active. This is because any information without proper encryption can easily be leaked. 9) What exactly do you know about RSA? It is basically a public key cryptography approach that is based on. Contents 1 Introduction 27 1.1 Public Key Cryptography . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.2 The Textbook RSA Cryptosystem. This self-contained introduction to modern cryptography emphasizes the mathematics behind the theory of public key cryptosystems and digital signature schemes. The book focuses on these key topics while developing the mathematical tools needed for the construction and security analysis of diverse cryptosystems. Only basic linear algebra is required of the reader; techniques from algebra. Cryptography and Information Security. Cryptography strives to achieve the following four key objectives of information security, both in the storage and communication of information and data: . Confidentiality. . Integrity. . Authentication. . Non-repudiation. Confidentiality. Sometimes also known as privacy or secrecy, confidentiality is ensuring that data and information are.

6 Number Theory II: Modular Arithmetic, Cryptography, and Randomness For hundreds of years, number theory was among the least practical of math- ematical disciplines. In contrast to subjects such as arithmetic and geometry, which proved useful in everyday problems in commerce and architecture, as-tronomy, mechanics, and countless other areas, number theory studies very ab-stract ideas called. Elementary Number Theory A revision by Jim Hefferon, St Michael's College, 2003-Dec of notes by W. Edwin Clark, University of South Florida, 2002-Dec. LATEX source compiled on January 5, 2004 by Jim Hefferon, jim@joshua.smcvt.edu. License restriction claimed by W. Edwin Clark. Copyleft 2002: Copyleft means that unrestricted redistribution and modiﬁcation are permitted, provided that all.

Intro to number theory. Public-Key cryptography and RSA. Other public-key cryptosystems. Exercises 3. Week 4 Hash functions. Message authentication codes. Digital signatures. Exercises 4. Week 5 Keywrapping, SHA-3, etc. Quantum cryptography. Exercises 5. Overall Course Assessment. Exam: 50%, Exercises 1-5: 50% Course Slides Course Slides (.pdf) General Resources COMP61411 Exercises (.pdf. Let's say that C is a product of two prime numbers P and Q. While encrypting, say, your credit card details, the number C is used to generate the public key. This key, as its name suggests, is available to the public, meaning that it can be intercepted and read by anyone in the network. Banks are known to use public keys that are 617. If you're working in the cybersecurity field, or are interested in getting a foot in the door, it's crucial that you understand how cyberattacks are perpetrated and the best practices for preventing and responding to them. This short, free, non-credit course is the perfect way to get started on building this knowledge. In this course, you'll learn from experts in the field about the. Cyber Security is the process and techniques involved in protecting sensitive data, computer systems, networks and software applications from cyber attacks. The cyber attacks are general terminology which covers a large number of topics, but some of the popular are: Tampering systems and data stored within. Exploitation of resources Cryptography and Network Security 7 Introduction - Overall Trends in the Research In reviewing the research that has already been published with regard to cryptography and network security since the 1970s, some noteworthy trends have emerged. There is a prevailing myth that secrecy is good for security, and since cryptography is based on secrets, it may not be good for security in a practical.

Number theory is the branch of mathematics that deals with different types of numbers that we use in calculations and everyday life. Number theory is the study of integers and their properties Most if not all universities worldwide offer introductory courses in number theory for math majors and in many cases as an elective course. The notes contain a useful introduction to important topics that need to be ad- dressed in a course in number theory. Proofs of basic theorems are presented in an interesting and comprehensive way that can be read and understood even by non-majors with the. Number Theory Web. Aims; New Listings; Number theorists' Home Pages/Departmental listings; Things of Interest to Number Theorists; Search the Number Theory Web Pages. The Italian mirror site is at Università di Roma Tre, Rome, Italy The Japanese mirror site is at Toyama University. Created and maintained by Keith Matthews, Brisbane, Australia, who acknowledges the support of the School of. Introduction to Cryptography. Cryptography, or the art and science of encrypting sensitive information, was once exclusive to the realms of government, academia, and the military. However, with recent technological advancements, cryptography has begun to permeate all facets of everyday life. Everything from your smartphone to your banking relies heavily on cryptography to keep your information. Cryptography studies ways to share secrets securely, so that even eavesdroppers can't extract any information from what they hear or network traffic they intercept. One of the most popular cryptographic algorithms called RSA is based on unique integer factorization, Chinese Remainder Theorem and fast modular exponentiation. In this module, we are going to study these properties and algorithms. World's Best PowerPoint Templates - CrystalGraphics offers more PowerPoint templates than anyone else in the world, with over 4 million to choose from. Winner of the Standing Ovation Award for Best PowerPoint Templates from Presentations Magazine. They'll give your presentations a professional, memorable appearance - the kind of sophisticated look that today's audiences expect

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