# Lecture: Polyalphabetic Substitution Cyphers

### Background Material

- Lecture on monoalphabetic
substitution cyphers
- Elementary discrete probability

### Reading

### Topics

- Review frequency analysis and the limitation of monoalphabetic
substitution cyphers.
- Homophones
- Polyalphabetic substitution cyphers
- Index of coincidence
- Comparing two texts - e.g. prob A = .75, B = .25.
Probability of coincidence = .625. If A and B are swapped
in both texts, the probability remains the same; however, if
A and B are swapped in only one of the texts the probability
of coincidence drops to .375.
- Can use the same concept to a single text.
- IC = sum((n[i]*(n[i]-1))/(N*(N-1)/c),i=1..c), c = size of alphabet, N = length of text, n[i] = number of occurrences of ith letter in test.
- IC_E = sum(f[i]^2/(1/c),i=1..c), f[i] = frequency of ith letter.
- IC_E = 1.73 for English.
- Can use IC to detect monoalphabetic substitution cyphers.

- Vigenere cypher
- Cryptanalysis of the Vigenere cypher - determining the code length
followed by frequency analysis of the subtext obtained from letters
separated by the code length.

### Resources

### Assignments

This assignment is a practice assignment not intended to be handed in.
- Calculate the expected IC using the frequencies of letters in English.
- Calcuate IC for a given plaintext and the corresponding cypher texts
using monoalphabetic and polyalphabetic substitution cyphers.
- Install Maple on your computer.
- Download and study the worksheet (sub.mw).
- Implement a Maple function to determine the shift in a shift cipher

Created: April 1, 2009 (revised Sept. 23, 2016) by jjohnson AT cs DOT drexel DOT edu