CSE 589 -- Part VIIII

11/29/00


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Table of Contents

CSE 589 -- Part VIIII

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Cryptography

Outline

Cryptography

Security Risks of Internet Communication

Terminology

Cryptography: communication in the presence of adversaries.

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

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Shannon’s Theory

Two approaches to discussing security of a cryptosystem

Unconditional Security

Perfect Secrecy

Realization of Perfect Secrecy: The One-time Pad (1917)

Computational Security: Types of cryptanalytic attack

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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

Extended Euclidean Algorithm

Fermat’s Little Theorem

Euler Totient Function (Euler phi function f(n) )

Multiplicative Inverse

Special case of Chinese Remainder Theorem

Summary of Number-theoretic Preliminaries

Summary, cont.

Summary, cont.:

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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.

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Digital Signatures

Digital Signatures

Signing Documents with Public Key Cryptography

Just to be completely clear… Using RSA...

Digital Signatures

Problem

Digital Signatures + Encryption proof of authorship + privacy

Issues

Digital Signatures useful for

Chosen Ciphertext Attack Against RSA: Scenario 1

Chosen Ciphertext Attack Against RSA: Scenario 2

What’s going on?

Author: Anna Karlin

Email: karlin@cs.washington.edu

Home Page: http://www.cs.washington.edu/education/courses/589

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