Table of Contents
CSE 589 -- Part VIIII
PPT Slide
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 SecurityAll security in key; alg can be published
Protocol for communicating using symmetric cryptography
Problems
PPT Slide
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
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
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.:
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
Digital Signatures
Signing Documents with Public Key Cryptography
Just to be completely clear…Using RSA...
Digital Signatures
Problem
Digital Signatures + Encryptionproof 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?
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