'Euclidean algorithm' presentation slideshows

SYMMETRIC CIPHERS

SYMMETRIC CIPHERS. Contents. Classical encryption techniques Block ciphers and the data encryption standard Basic concepts in number theory and finite fields Advanced encryption standard Block cipher operation Pseudorandom number generation and stream ciphers.

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Session 4

Session 4. Asymmetric ciphers. Contents. Definition of asymmetric (public key) ciphers Applications of asymmetric ciphers The public key encipherment procedure The RSA public key cipher system. KEY. KEY. encipher. Ciphertext. decipher. Plaintext. Plaintext. A. B. Cryptanalysis.

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Cryptography Overview

Cryptography Overview. John Mitchell. Cryptography. Is A tremendous tool The basis for many security mechanisms Is not The solution to all security problems Reliable unless implemented properly Reliable unless used properly Something you should try to invent yourself unless

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Prime Numbers

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RSA

RSA. Slides by Kent Seamons and Tim van der Horst Last Updated : Oct 1, 2013. Recap. Recap. Number theory What is a prime number? What is prime factorization? What is a GCD? What does relatively prime mean? What does co-prime mean? What does congruence mean?

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Euclidean Algorithm

Euclidean Algorithm. Applied Symbolic Computation CS 567 Jeremy Johnson. Greatest Common Divisors. g = gcd ( a,b ) g |a and g|b e|a and e|b ? e|g. Unique Factorization. p |ab ? p|a or p|b a = p 1 ? ? ? p t = q 1 ? ? ? q s ? s = t and ? i ?j: p i = q j

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Section 2.5

Section 2.5. Integers and Algorithms. Euclidean algorithm for finding gcd. Where L is a larger number, and S is a smaller number, to find gcd(L,S): divide L by S to obtain: L = S * c + r where c is some constant and r is the remainder next, find gcd(S,r) using the same method

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Public-Key Cryptography

Public-Key Cryptography. Public-Key Cryptography . Asymmetric encryption is a form of cryptosystem in which encryption and decryption are performed using the different keys. Each individual has two keys: private key (not revealed to anyone) public key (make it known to everyone )

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Chapter 0: Introduction

Chapter 0: Introduction. Computer Science: An Overview Eleventh Edition by J. Glenn Brookshear. Chapter 0: Introduction. 0.1 The Role of Algorithms 0.2 The Origins of Computing Machines 0.3 The Science of Algorithms 0.4 Abstraction 0.5 An Outline of Our Study 0.6 Social Repercussions.

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Greek Mathematics Period ( 6 00 B.C.-A.D. 500)

Greek Mathematics Period ( 6 00 B.C.-A.D. 500). Much of what is considered Greek math may not have come from Greece, but was written in the language. Greek Logic and Philosophy Greek philosophers promote logical, rational explanations of natural phenomena.

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Homework

Homework. Complete Worksheet #3 Test on Real Analysis next time. Homework. Solve the inequality and graph each non-empty solution. 1. ?------ ? -----|----|----|----|----|----|----|----|----|----|----|----|----|----|----|----

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Direct Proof and Counterexample III Part 2

Direct Proof and Counterexample III Part 2. Lecture 16 Section 3.3 Tue, Feb 13, 2007. Example: Direct Proof. Theorem: Let a and b be integers. If a | b and b | a , then a = ?? b . Proof:. Example: Direct Proof.

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Information Security

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The Division Algorithm

The Division Algorithm. In the context of division, 203 is called the dividend, 8 the divisor, 25 the quotient and 3 the remainder. The relationship between these four quantities can also be expressed as. This theorem is referred to as the division algorithm or the division identity.

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New Algorithm for Classical Modular Inverse

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Euclidean Number theory

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Properties of Arithmetic

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CSE 202 - Algorithms

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Greatest Common Divisor

Greatest Common Divisor. Definitions. Let a and b be two non-zero integers. The greatest common divisor of a and b , denoted gcd(a,b) is the largest of all common divisors of a and b . When gcd( a,b ) = 1, we say that a and b are relatively prime. Examples. gcd(10,25) =

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