Course Objectives:

This course covers the basic concepts in Cryptography, the basic cryptographic algorithms and protocols, including the classical cryptosystems, the block cryptosystems, the public-key cryptosystems, Hash functions, digital signature schemes. This course will provide students with a fundamental support for doing further academic research and engineering practice in Cryptography.

Course Requirements:

1. To master the basic concepts and related theorems in Number Theory, Algebra, Probability and Information Theory;

2. To grasp the basics of the cryptosystems and crypt-analysis;

3. To master some classical cryptosystems, such as the Affine Cipher, the Substitution Cipher, the Permutation Cipher and the Stream Cipher;

4. To master two block cryptosystems: the DES and AES;

5. To grasp the basics of Hash functions, the security and Random Oracle Model, the famous SHA algorithm;

6. To master the basics of the public-key cryptosystems, including:

a. The RSA encryption;

b. The ElGamal encryption;

c. The digital (RSA and ElGamal) Signature Schemes.

Course Contents:

1) Chapter 1-Classical Cryptography: The Shift Cipher, The Substitution Cipher, The Affine Cipher, The Permutation Cipher, Stream Ciphers;

2) Chapter 2-Shannon’s Theory: Elementary of Probability Theory and Entropy, Perfect Secrecy;

3) Chapter 3-Block Ciphers: Basics of the Substitution-Permutation Network, the Data Encryption Standard (DES), the Advanced Encryption Standard (AES);

4) Chapter 4-Hash Functions: Basics and Security of Hash Functions, Iterated Hash Functions and the Secure Hash Algorithm (SHA-1), the Message Authentication Code (MAC);

5) Chapter 5-The RSA Cryptosystem: Introduction to the Public-key Cryptography, The RSA Cryptosystem, Factoring Integers, Factoring Algorithms and other attacks on RSA, the Rabin Cryptosystem, Semantic Security of RSA;

6) Chapter 6-The ElGamal Cryptosystem: the Discrete Logarithm Problem (DLP) and Algorithms, Finite Field and Elliptic Curves, Security of ElGamal Systems;

7) Chapter 7-Signature Schemes: Basics of and Security Requirements for Signature Schemes, the RSA signature scheme, the ElGamal signature scheme, the Digital Signature Standard (DSS);

8) Some Research Topics in Cryptography.

Credits: 2