'Little theorem' presentation slideshows

TEST OF FUNDAMENTALS

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Number Theory Algorithms and Cryptography Algorithms

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Primality Test

Lecture 26. Primality Test. Professor Sin-Min Lee Department of Computer Science San Jose State University. Primality Testing A Classical Number Theoretic Problem: . Definition: A positive integer n is prime iff its only divisors are 1 and n .

986 views • 37 slides

22C:19 Discrete Math Integers and Modular Arithmetic

22C:19 Discrete Math Integers and Modular Arithmetic . Fall 2011 Sukumar Ghosh. Preamble. Historically, number theory has been a beautiful area of study in pure mathematics . However, in modern times, number theory is very important in the area of security .

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CPSC 490 Number Theory Primes, Factoring and Euler Phi-function

CPSC 490 Number Theory Primes, Factoring and Euler Phi-function. Mar.31 st , 2006 Sam Chan. Clarifications. The Euclidean Algorithm runs in logarithmic time. Finding modular inverses can be done using the extended Euclidean algorithm.

659 views • 36 slides

Public-Key Cryptography

Public-Key Cryptography. Dr. Ron Rymon Efi Arazi School of Computer Science IDC, Herzliya. 2010/11. Pre-Requisites: Conventional Cryptography. Overview. Public Key Cryptography Crossword puzzles Diffie-Hellman RSA Elliptic Curves Digital Signatures

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Prime Numbers

Prime Numbers. -Timothy Goodman -Tyson Slater. Sieve of Eratosthenes. Background Ancient Algorithm attributed to Eratosthenes Predecessor to the Sieve of Atkin Used to find primes up to n Wheel Factorization Speed increase. Seive of Eratosthenes. Algorithm

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Chapter 3

Chapter 3. 3.7 Applications of Number Theory Some U seful Results Linear C ongruences The C hinese Remainder T heorem Computer Arithmetic with L arge Integers Pseudoprimes Public Key Cryptography. Some Useful Results.

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The AKS Primality Test

The AKS Primality Test. Ilse Haim Directed Reading Program Mentor: Jon Huang University of Maryland, College Park May 2, 2013. Introduction to Primality Testing. Goal: given an integer n > 1, determine whether n is prime Most people know the smallest primes

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PRIMES is in P

PRIMES is in P. Agrawal-Kayal-Saxena Presented by: Xiaosi Zhou. Outline. Introduction 1. What is PRIMES 2. Algorithms for PRIMES before AKS AKS algorithm 1 . Basic idea 2. Notation and Preliminaries 3. The algorithm and its correctness 4. Time complexity analysis

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PRIMES is in P

PRIMES is in P. Agrawal-Kayal-Saxena Presented by: Xiaosi Zhou. Outline. Introduction 1. What is PRIMES 2. Algorithms for PRIMES before AKS AKS algorithm 1 . Basic idea 2. Notation and Preliminaries 3. The algorithm and its correctness 4. Time complexity analysis

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Cryptography and Network Security Chapter 8

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RSA Encryption

RSA Encryption. William Lu. RSA Background. Basic technique first discovered in 1973 by Clifford Cocks of CESG (part of British GCHQ) Invented in 1977 by Ron Rivest, Adi Shamir and Len Adleman. RSA Uses. Public key encryption Digital signatures. RSA Algorithm.

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CMSC 203 / 0201 Fall 2002

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Numerical Algorithms

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NASH EQUILIBRIUM

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Prime Algorithms

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Chapter 8

Chapter 8. More Number Theory. Prime Numbers. Prime numbers only have divisors of 1 and itself They cannot be written as a product of other numbers Prime numbers are central to number theory Any integer a > 1 can be factored in a unique way as a = p1 a1 * p 2 a2 * . . . * p p1 a1

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Modular Arithmetic

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Mathematics

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