Types of Ciphers
- Classical Ciphers
- Transposition Ciphers
- Substitution Ciphers
- Monoalphabetic/Polyalphabetic
- Steganography
- Modern Ciphers
- Computation-intensive mathematical ciphers
Practical Applications
- Digital authentication
- Time stamping
- Exchanging digital currency (cryptocurrency)
- Secure network communication
- Disk encryption
Cryptography and Linear Algebra
Cryptography Background
The Information Age
- Math-based cryptography > Linguistic cryptograpy
- Increase in sophistication of both cryptography and cryptanalysis
- Deciphering requires much more effort than enciphering
Alan Turing
- Goal: secure communication
- First used in Egypt
- Message confidentiality
- Linguistic and lexicographic patterns
- Data Encryption
- Mathematics
Definitions
- Cryptography = the study of encoding and decoding messages
- Ciphers = Codes
- Plaintext = Uncoded Messages
- Ciphertext = Coded Messages
Bobby McGrane
Michael Tang
Enciphering with Hill Ciphers
- Lester S. Hill
- Assign Numbers to Characters
- Matrix A
- Pair the Plaintext
- Make the pairs into vectors
- Make the vectors into a matrix
- C=AP
- Make C into vectors
- Convert to letters
Example
Given the start of the plaintext matrix provided by Bobby, decipher the following ciphertext matrix.
Deciphering With Hill Ciphers
- P = CA^-1
- Set up Augmented Matrix
- RREF
- Transpose
Example
Use the 2 x 2 matrix A to encipher the message "Linear Algebra"