Lecture 2

• 15-827 Security and Cryptography Lecture 2 .
• Outline .
• Cryptosystem Review .
• Public-Key Cryptosystem (pictorially) .
• Applications of Public-Key Cryptography .
• Applications of Public-Key Cryptography ( cont'd ) .
• Public-Key Cryptography History .
• RSA: Intro .
• RSA: How It Works .
• RSA: Why It Works .
• The RSA Problem and Its Relation to Factoring .
• The RSA Problem Cont'd .
• RSA Properties .
• Attacking RSA ( pp . 287-291) .
• Rabin Public-Key Encryption (Section 8.3) .
• Rabin : How It Works .
• Example .
• ElGamal : Intro .
• ElGamal : How It Works .
• ElGamal : Why It Works .
• Example .
• ElGamal Notes .
• ElGamal Digital Signature: How It Works .
• ElGamal Digital Signature: Why It Works .
• Digital Signature Standard (DSA ElGamal ) .
• Elliptic Curves .
• Addition .
• Algebraic Definition .
• Elliptic Curve Cryptography .
• Homework Exercise .
• Other Public-Key Algorithms .
• Diffie - Hellman Key Exchange .
• Man-in-the-Middle Attack (Active Adversary) .
• Station-to-Station (STS) Protocol .
• Secret Sharing .
• Shamir's (t, n) Threshold Scheme .
• Example .
• Key Escrow .
• Remote Coin Flipping .
• Example .
• Remote Coin Flip Protocol .
• Blum Integers .
• Homework Exercise .
• Oblivious Transfer .
• Rabin's Solution .
• Another Solution Using ElGamal (so you get the general idea) .
• Blind Signatures .
• Next lecture .

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Heather L. Marko
Last Modified: September 1998