Table of Contents
CSE 589 -- Lecture 9
Plan for Today
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Digital Signatures
Signing Documents with RSA
Forgery
Once again, using RSA...
Digital Signatures + Encryption proof of authorship + privacy
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Problems with signature schemes:
A solution: One-way hash functions.
Signatures and One-way Hash Functions
Issues and Attacks
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Classic Secret Key Exchange Diffie-Hellman
Security Against Eve
Security Against Mallory Man-in-the-Middle Attack
Approach typically taken
Diffie-Hellman with Authentication A and B agree on large prime p and g < p primitive mod p.
Authenticated Key Exchange Private-Key Setting
Kerberos A key(T,A) B key(T,B) t timestamp K session key L lifetime
What’s going on?
Replay Attacks
Authenticated Key Exchange-- Public-Key Setting
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So far
MAC
Some Applications of MACs
Constructing a MAC
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Secure Socket Layer (SSL) used by Navigator/Explorer...
SSL (Step 1)
SSL Step 2
SSL Step 3
SSL Step 4
SSL Step 5
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Secret Splitting
Simplest secret splitting scheme T splits a secret between A and B
Secret Sharing
Shamir -- Interpolating Poly Scheme
Example: M= 11 (3,5) threshold scheme
The beauty of it
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Digital Cash
First Try
Withdrawal Protocol
Payment Protocol
Deposit Protocol
Analysis
Solving anonymity problem
RSA blind signatures
Result
How to avoid fooling bank
How to avoid double-spending.
Off-line solution
Withdrawal Protocol
Payment Protocol
Deposit Protocol
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Bit Commitment
Bit Commitment Using Symmetric Crypto
Bit Commitment Using One-Way Functions
Mental Poker
Alice who can’t read it, decrypts with her private key and sends it back to Bob
Why does it work?
For A and B to play poker by email.
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Zero-knowledge Proofs
Zero-knowledge Proofs
Graph Isomorphism
Interactive Proof of Graph Isomorphism
Application to User Identification
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Electronic Elections
Other Amazing and Fun Stuff
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Pseudo-random number generators.
What is a random number?
Pseudo-random number generators.
Linear Congruential Generator
Linear Congruential Generators
Linear congruential generator have good statistical behavior with respect to most reasonable empirical tests.
Linear Feedback Shift Registers
To be a maximal-period LFSR
Properties of LFSRs
Insecurity of LFSR
Last but not least, the Blum,Blum Shub. First, background.
More background
Last bit
Quadratic Residues Problem
Blum-Blum-Shub Generator
Security of BBS generator
Summary: Security Risks of Internet Communication
Summary
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