'Mod q' presentation slideshows

CSE 321 Discrete Structures

CSE 321 Discrete Structures. Winter 2008 Lecture 8 Number Theory: Modular Arithmetic. Announcements. Readings Today: 3.4 (5 th Edition: 2.4) Monday and Wednesday: 3.5, 3.6, 3.7 (5 th Edition: 2.5, 2.6). Number Theory (and applications to computing).

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Chapter 9: Digital signatures

IV054. Chapter 9: Digital signatures. Digital signatures are one of the most important inventions of modern cryptography.

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CHAPTER 9

CHAPTER 9. Text Searching. Algorithm 9.1.1 Simple Text Search. This algorithm searches for an occurrence of a pattern p in a text t . It returns the smallest index i such that t [ i..i + m- 1] = p , or - 1 if no such index exists. Input Parameters: p , t Output Parameters: None

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Cryptography and Network Security Chapter 10

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Overview of Public-Key Cryptography

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Overview of Public-Key Cryptography

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RSA

RSA. Preliminaries. Division Algorithm. Given integers a and b ?0 , there exist unique Integers q and r such that a = bq +r where 0 ? r < |b| a is the dividend , b is the divisor , and r is the remainder . b divides a or b is a factor of a if r=0.

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Computer Security CS 426 Lecture 35

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Digital Signatures

Digital Signatures. have looked at message authentication but does not address issues of lack of trust digital signatures provide the ability to: verify author, date & time of signature authenticate message contents be verified by third parties to resolve disputes

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String Matching Using the Rabin-Karp Algorithm

String Matching Using the Rabin-Karp Algorithm. Katey Cruz CSC 252: Algorithms Smith College 12.12.2000. Outline. String matching problem Definition of the Rabin-Karp algorithm How Rabin-Karp works A Rabin-Karp example Complexity Real Life applications Acknowledgements.

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String Matching Algorithms

String Matching Algorithms. Topics Basics of Strings Brute-force String Matcher Rabin-Karp String Matching Algorithm KMP Algorithm. In string matching problems, it is required to find the occurrences of a pattern in a text.

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The Rabin-Karp Algorithm

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The Rabin-Karp Algorithm

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Agenda

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Question 13 page 160

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p,q : 2 distinct odd primes n=pq gcd(x,pq) =1

p,q : 2 distinct odd primes n=pq gcd(x,pq) =1. a. Show that x 1/2 ?(n) ?1 (mod p) and x 1/2 ?(n) ?1 (mod q) p = 2k +1 & q = 2l +1 gcd(x,p)=1 & gcd(x,q) =1 x 1/2 ?(n) = x 1/2(p-1)(q-1) = x 1/2 (2k)(2l) = x 2kl .

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