Cryptography

Most of the notes are directly or indirectly from RPI CSCI 6230.

Number Theory

• 1. Galois Field
• 2. Multiplicative Inverse In GF
• 3. Chinese Reminder Theory
• 4. Miller Rabin Algorithm
• 5. Quadratic Residue Problem
• 6. Legendre Symbol and Jacobi Symbol

Defend Ciphertext Only Attack

• 1. Adversary Model
• 2. RSA
• 3. ElGamal
• 4. Hard-core Bit (Hard-core Prediction)

Defend Chosen Plaintext Attack

• 1. Indistinguishable Chosen Plaintext Attack
• 2. Goldwasser and Micali Algorithm
• 3. Blum and Goldwasser Encryption
• 4. Rabin Encryption Algorithm

Defend Chosen Ciphertext Attack

• 1. Indistinguishable Chosen Ciphertext Attack
• 2. Bellare-Rogaway Plaintext-aware Encryption (OASP)
• 3. Cramer-Shoup Encryption

Homomorphic Encryption

• 1. Homomorphic Encryption
• 2. Pallier PKC

For Fun

• Fiction Characters in Cryptology