Introduction to the Mathematics of Cybersecurity

• Lab 3 : Division Algorithms
  • 1 Preliminaries
  • 2 Implementing the book proof
  • 3 Printing a run of div_alg
  • 4 Inefficiency of div_alg
  • 5 Long Division
• Lab 4 : Extended Euclidean algorithm and the sieve of Eratosthenes
  • 1 Preliminaries
  • 2 Extended Euclidean algorithm
  • 2 The sieve of Eratosthenes
• Lab 5 : Additive Ciphers
  • 0 Preliminaries
  • 1 From the alphabet to \(\mathbb{Z}_{26}\)
  • 2 Encrypting a message
  • 3 Decrypting a message
• Lab 6 : Keyword ciphers
  • 0 Preliminaries
  • 1 From the alphabet to \(\mathbb{Z}_{26}\)
  • 2 Remove duplicates
  • 3 Extending the list
  • 4 Cycling the list
  • 5 Mapping from plaintext to ciphertext
  • 6 Encryption and decryption of a number
  • 7 Encryption and decryption of a message
  • 8 Put everything together
• Lab 7 : Let’s be clever and crack the ciphers
  • 0 Preliminaries
  • 1 Introduction
  • 2 Convert between the alphabet and \(\mathbb{Z}_{26}\)
  • 2 Additive cipher
  • 3 Frequency analysis
  • 4 Crack the additive cipher
  • 5 Affine cipher
  • 6 Crack the affine cipher
• Lab 8 : Permutations and Combinations
  • 0 Preliminaries
  • 1 Counting permutations and combinations
  • 2 Listing combinations
  • 3 Listing permutations
• Lab 9 : Cryptanalysis of the Vigenère cipher
  • 0 Preliminaries
  • 1 Vigenère cipher
  • 2 Guessing keys
  • 4 Index of Coincidence
  • 5 Kasiski test
• Lab 10 : Basic matrix operations
  • 0 Preliminaries
  • 1 Matrix shape
  • 2 Matrix Addition
  • 3 Matrix Multiplication
  • 4 Transpose
  • 5 Identity matrix
  • 6 Pretty-printing
• Lab 11 : Matrix Inverses
  • 0 Preliminaries
  • 1 Warm up
  • 2 Matrix Inverse
  • 3 Checking the inverse
  • 4 Modular arithmetic
  • 5 Modular inverse
  • 6 Matrix inverse modulo n
  • 7 Checking the matrix inverse mod n
• Lab 12 : Hill’s System
  • 0 Preliminaries
  • 1 Matrix times a vector
  • 2 Encryption in Hill’s system
  • 3 Decryption in Hill’s system
• Lab 13 : Modular Exponentiation
  • 0 Preliminaries
  • 1 Slow exponentiation
  • 2 Binary representation
  • 3 Square and multiply
  • 4 Modular square and multiply
  • 5 Brute force modular root finding
• Lab 14 : Plain RSA
  • 0 Preliminaries
  • 1 Random prime generation
  • 2 Key generation
  • 3 Encryption and decryption