Cryptography - from A to Omega
Duration: 5 days

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Synopsis This course undertakes to lay the foundations of both classic and modern-day cryptography over the span of 5 days. No mere feat!

The first day begins with the basic principles. By day II, it quickly moves on to discussion of modern ciphers such as RC4, DES and the present-day standard of AES (Rijndael). PKI methods such as Diffie-Hellman, RSA and ECC (Elliptic Curves) are explained in mathematical detail. Digital signature techniques and principles, including hash functions such as the (insecure) MD5 and SHA-1/SHA-256 are discussed as well. Finally, the course concludes by taking the algorithms discussed and showing their incorporation in protocols - both secure (TLS, IPSec, Kerberos) and insecure (NTLM, WEP). The course concludes with a deep discussion on the algorithms driving Cryptocurrency - from BTC to ETH and the myriad "alt-coins" which surface every day.

The course is highly theoretical, but laced with plentiful examples of real world applications and implementations in today's computing environments
Target Audience Developers, security analysts
Prerequisites
  • Mathematics background - basic algebra at a minimum - vital
  • Linear Algebra/Matrix operations - highly recommended
Objectives
  • Understand the principles behind public key cryptography
  • Understand symmetric algorithms, primarily AES
  • Explain the relatively simple mathemtical ideas behind PKI algorithms of DSA and Diffie Hellman
  • Define the principles of Elliptic Curve Cryptography
  • Understand hash functions, in particular SHA-1 and SHA-256
  • Analyze cryptographic foundations of common protocols
  • Explain the principles of cryptocurrency driving BitCoin
Exercises Course presents and solves mathematical problems step by step, but due to packed syllabus no time is allotted for free exercises
Modules
Day 1
1. Mission Statements
1 hours
This module deals explains the basic ideas and tenets of cryptography. Goals and mission statements
  • Principles
    • Terminology
      • Encryption
        • Authentication
          • Attestation
            2. Simple Ciphers
            3 hours
            		Putting the principles and nomenclature into practice with historical ciphers that (at least at one time) were considered state of the art..
            • Monoalphabetic Ciphers (example: Caesar)
              • Polyalphabetic Ciphers (examples: Vigenere, Hill)
                • Transposition Ciphers
                  • Basic Cryptanalysis and Statistics
                    3. Information Theory basics
                    2-3 hours
                    		Exploring Claude Shannon's landmarks principles of entropy and cryptanalysis
                    • Entropy
                      • Redundancy and Unicity Distance
                        • Chosen/Known Plaintext/Ciphertext attacks
                          • Complexity Theory
                            • P, NP, NP-Complete
                              Day 2
                              5. Prelude: Randomness
                              2 hours
                              		Explaining the importance of random number generation in cryptography
                              • Randomness and pseudo-randomness
                                • PRNG algorithms
                                  • Phase space analysis and attractors/fractals
                                    • Case study: TCP sequence numbers
                                      • Stream Ciphers - LSFR
                                        • Case Study: RC4
                                          • Block Cipher modes (ECB, CBC, Counter)
                                            6. The (former) Data Encryption Standard
                                            2 hours
                                            		Taking DES as a case study of one of the world's most popular algorithms, having survived for over two decades but now deemed entirely insecure.
                                            • DES
                                              • FIPS 46
                                                • Differential cryptanalysis attacks
                                                  • Triple DES
                                                    7. The Advanced Encryption Standard
                                                    3 hours
                                                    		Taking AES as a case study of the current standard, and a modern (1990-2000) algorithm
                                                    • Rijndael
                                                      • FIPS 197
                                                        • S Boxes and P Boxes
                                                          • Hardware implementations and chip-level acceleration
                                                            • Application: Disk encryption (AES-XTS in Linux DM-Crypt and certain filesystems)
                                                              Day 3
                                                              8. Number Theory, in a nutshell
                                                              2 hours
                                                              		This module deals with the basic concepts of number theory and advanced algebra which drive public key algorithms
                                                              • Modular Arithmetic
                                                                • Prime Numbers and Primality Testing
                                                                  • Sets and Fields
                                                                    • Chinese Remainder Theorem
                                                                      • Fermat's Little Theorem
                                                                        9. Diffie Hellman
                                                                        1 hours
                                                                        		Explicating the principles of Diffie-Hellman Key Exchange (agreement) algorithm
                                                                        • Basic ideas of key exchange
                                                                          • Inefficient - the three way handshake
                                                                            • Diffie Hellman-Merkle
                                                                              10. RSA
                                                                              1 hours
                                                                              		Rivest Shamir Adleman Algorithm
                                                                              • Algorithm
                                                                                • Attacks/Cryptanalysis
                                                                                  • PKCS
                                                                                    • Variants (elGamal, etc)
                                                                                      • Blum Blum Shub as a secure PRNG
                                                                                        11. ECC
                                                                                        2 hours
                                                                                        		An introduction to Elliptic Curve Cryptosystems, which provide an alternative substrate to PKI , particularly in embedded systems
                                                                                        • Elliptic Curves
                                                                                          • Applications as fields
                                                                                            • Applying Diffie Hellman over ECC
                                                                                              Day 4
                                                                                              12. Hash Functions
                                                                                              2 hours
                                                                                              		Basic theory of hash functions, with applications
                                                                                              • What makes for a good hash?
                                                                                                • Hash Collisions
                                                                                                  • Second Preimage attacks
                                                                                                    • The Birthday Paradox
                                                                                                      • Case Study (insecure): MD5
                                                                                                        • Case Study (more secure): SHA-1
                                                                                                          • Case Study (standard): SHA-256
                                                                                                            • The road ahead: SHA-ng
                                                                                                              • Application: Merkle Trees and Linux DM-Verity (used for disk authentication)
                                                                                                                • Application: FS-Verity (Filesystem authenticaiton in Android)
                                                                                                                  13. Digital Signatures and certificates
                                                                                                                  2 hours
                                                                                                                  		Applying PKI + Hash functions for digital signatures and certificates
                                                                                                                  • Constructing a digital signature
                                                                                                                    • RSA, DSA and ElGamal signing
                                                                                                                      • Subliminal channels and key leaks
                                                                                                                        14. Zero Knowledge Proofs
                                                                                                                        2 hours
                                                                                                                        		How do you prove you know something, without revealing what that 'something' is?
                                                                                                                        • Harnessing probability
                                                                                                                          • Guillou-Quisquater
                                                                                                                            • Zero Knowledge Proofs
                                                                                                                              • Feige-Fiat-Shamir
                                                                                                                                • Blind Signatures
                                                                                                                                  • Playing poker without a deck of cards (but with a LOT of math..)
                                                                                                                                    15. Advanced Topics
                                                                                                                                    2 hours
                                                                                                                                    		A brief tour of topics at the forefront of cryptography
                                                                                                                                    • Visual Secret Sharing
                                                                                                                                      • Steganography
                                                                                                                                        • Secret Sharing
                                                                                                                                          • Anonymous Broadcasts
                                                                                                                                            • Unbreakable channels: Quantum Cryptography
                                                                                                                                              • The threat to modern day algorithms: Quantum Computing
                                                                                                                                                Day 5
                                                                                                                                                16. Real World Applications
                                                                                                                                                4 hours
                                                                                                                                                		A discussion putting the four days of theory into real-world practice. Topics include:
                                                                                                                                                • Networking Protocol: SSL/TLS
                                                                                                                                                  • Networking Protocol: IPSec (AH, ESP, IKEv2)
                                                                                                                                                    • Application: PGP, S/MIME
                                                                                                                                                      17. Cryptocurrency
                                                                                                                                                      3 hours
                                                                                                                                                      		A discussion of the theory and practice of cryptocurrency, inspired by Satoshi Nakamoto's seminal work
                                                                                                                                                      • The original White Paper
                                                                                                                                                        • Block Chaining
                                                                                                                                                          • Ethereum as an improvement over the original BTC
                                                                                                                                                            • Proofs of stake vs. Proofs of ownership
                                                                                                                                                              • Evaluating alt-coins