Table of Contents
CSE 589 -- Lecture 6
PPT Slide
Plan for Today
PPT Slide
Local Search Algorithms
Local Search Procedure for TSP
Does Greedy Local Search Lead Eventually To Optimal Tour?
Solution Spaces
Other Types of Local Moves For TSP Used
PPT Slide
Simulated Annealing
Notation
Metropolis Algorithm
What’s going on?
Some Details
Cryptography
Outline
Cryptography
Terminology
Cryptography: communication in the presence of adversaries.
Cryptographic Tools
The cast of characters
Cryptanalysis
Kerckhoff’s Doctrine
Key-Based Security All security in key; alg can be published
Protocol for communicating using symmetric cryptography
Problems
Public key algorithms:
Protocol for communicating using public-key cryptography
Types of cryptanalytic attack
PPT Slide
Shannon’s Theory
Two approaches to discussing security of a cryptosystem
Unconditional Security
Perfect Secrecy
Example: P = {a,b}, K = {k1, k2, k3}, C = {1,2,3,4}
Shannon’s Characterization of Perfect Secrecy
Idea
Realization of Perfect Secrecy: The One-time Pad (1917)
Other important ideas from Shannon’s paper
PPT Slide
Public-Key Cryptography
Public-Key Cryptography
Idea: uses trapdoor one-way function.
One-Way Functions
Number Theoretic Preliminaries
Number-theoretic Preliminaries
Modular Arithmetic
Digression to use modular arithmetic; cryptanalysis
Possible solution: use more keys => Addition Cipher
Known-plaintext attack
Ciphertext-only attack
Modular Arithmetic (cont.)
Prime Numbers and GCD
Inverses Modulo a Number
Euclid’s Algorithm for computing the gcd of two numbers, r0 and r1
Example of Extended Euclidean Algorithm: computing 28-1 mod 75
More precisely
Fermat’s Little Theorem
Euler Totient Function (Euler phi function f(n) )
Multiplicative Inverse
Chinese Remainder Theorem
Example: n= pq
PPT Slide
RSA
Example
Issues
Why does it work? Encryption & decryption inverses
Implementing RSA
Probabilistic Primality Testing
Probabilistic Primality Testing
A few obvious questions….
Implementing RSA, cont.
Security of RSA
Factoring
A bit of factoring history...
General Comments About Public-Key Cryptosystems
Hybrid Cryptosystems
Exercise: Show RSA encryption and decryption inverses.
PPT Slide
Digital Signatures
Signing Documents with Public Key Cryptography
Problem
Summarizing this part..
PPT Slide
Chosen Ciphertext Attack Against RSA: Scenario 1
Chosen Ciphertext Attack Against RSA: Scenario 2
What’s going on?
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