Core Module 1: Introduction to Modern Cryptography

Unit 1: Mathematical Basics
1.1 Divisibility
1.2 Primes, Primality Testing, and Induction
1.3 An Introduction to Congruences
1.4 Euler, Fermat, and Wilson Theorems
1.5 Primitive Roots
1.6 The Index Calculus and Power Residues
1.7 Legendre, Jacobi, & Quadratic Reciprocity
1.8 Complexity

Unit 2: Cryptographic Basics
2.1 The Objectives of Cryptography
2.2 Classic Ciphers
2.3 Stream Ciphers
2.4 Linear Feedback Shift Registers
2.5 Cryptographic Protocols
2.6 Provable Security
2.7 Attacks

Unit 3: Symmetric-Key Encryption
3.1 Stream Ciphers
3.2 Symmetric Block Ciphers
3.2.1 Data Encryption Standard (DES)
3.2.2 Tripple DES
3.2.3 Blowfish
3.2.4 AES (Rijndael)
3.2.5 RC

Unit 4: Hash Function, Message Digest and Message Authentication Code
4.1 DES-like Message Digest Computation (DMAC)
4.2 MD5
4.3 Secure Hash Algorithm (SHA-1)
4.4 Hashed Message Authentication Codes (HMAC)

Unit 5: Public-Key Cryptography
5.1 The Concept of Public-Key Cryptography
5.2 Diffie–Hellman Exponential Key Exchange
5.3 RSA
5.4 ElGamal
5.5 Schnorr’s Public-key Cryptosystem
5.6 Digital Signature Algorithm

Unit 6: Public-key Infrastructure
6.1 What Is PKI?
6.2 Components of PKI
6.2.1 Digital signatures.
6.2.2 Digitial Certificates.
6.2.3 Key Management
6.2.4 Certifying Authority
6.2.5 Different trust Models Hierarchical/Mesh/Bridge
• Certification authorities/Parameters/Certificate chain
6.2.6 Certificate management
• Registration & Initialization
• Certification
• Expiration and Revocations – CRL (Certification Revocation List)
6.2.7 Directory services such as X.500 and LDAP.
• X.500 for publication of PKC &CRL
• X.509 version 3 certificates
6.2.8 Certificate Validation methods
6.2.9 Time Stamps
6.2.10 Certificate Lifecycle Management
6.2.11 Cross certification
6.3 PKI Architecture and its working

Reference Books:

1) An INTRODUCTION to CRYPTOGRAPHY, Second Edition
Author: RICHARD A. MOLLIN
2) Introduction to Cryptography: Principles and Applications, Second Edition
Author: Hans Delfs, Helmut Knebl
3) Internet Security Cryptographic Principles, Algorithms and Protocols
Author: Man Young Rhee