# Course Objective

This is an introductory graduate course on cryptography. This will enable the students to learn fundamental concepts of cryptography, cryptanalysis and utilize these techniques in computing systems.

# Course Contents

Introduction and mathematical foundations:

1. Overview of cryptography (1 lecture)
2. Number Theory: modular arithmetic, extended Euclid’s algorithm, Euler’s theorem, Fermat’s little theorem, examples of easy and hard problems in computational number theory (4 lectures)
3. Discrete Probability: discrete probability spaces and distributions, binomial distribution, birthday paradox (2 lectures)

Symmetric-key Encryption

1. One time pad and stream ciphers: perfect secrecy and the one-time pad, semantic security and stream ciphers. Linear Feedback Shift Registers as a way of implementing stream ciphers, analyze their properties with examples, RC4. (3 lectures)
2. Block Ciphers: feistel networks and iterated Even-Mansour ciphers, examples. Pseudo Random Permutations (PRP), Pseudo Random Functions (PRF), security against chosen plaintext attacks (CPA), Modes of operation: CBC and counter mode (4 lectures)
3. Attacks on block ciphers: exhaustive search, time-space tradeoffs, differential & linear cryptanalysis, meet in the middle, side channels (4 lectures)

Hash Functions

1. Definition of hash functions and properties, Unkeyed hash functions, Keyed hash functions (2 lectures)
2. Message Authentication Codes (MAC), The Random Oracle Model (ROM) (2 lectures)

Public key cryptography

1. Cryptography using arithmetic modulo primes: Diffie-Hellman key exchange, the hardness of discrete-log assumption. (5 lectures)
2. Public key encryption: semantically secure ElGamal encryption, Chosen Ciphertext Attack (CCA) security (3 lectures)
3. Arithmetic modulo composites: RSA and Rabin functions, how to encrypt with trapdoor permutations, RSA OAEP encryption (4 lectures)

Digital signatures

1. Digital signatures: definitions and applications: how to sign using RSA (3 lectures)
2. More signature schemes and applications: hash based signatures, certificates, certificate transparency, certificate revocation (2 lectures)

Special Topic (2 lectures)

# Learning Outcomes:

At the end of the course, the students should have:

• Knowledge in modern cryptosystems, their analysis and applications to other fields
• They will be able to combine these basics with their knowledge of experimental methodologies to identify, formulate, and solve engineering problems

# Text Books

1. A Graduate Course in Applied Cryptography by D. Boneh and V. Shoup.
2. Cryptography and Network security: Principles and Practice, William Stallings, Pearson Education, 2002
1. Introduction to Modern Cryptography by J. Katz and Y. Lindell
2. Cryptography: Theory and Practice, Douglas R. Stinson, CRC Press