CSCI 587 - Solution to Assignment 3 Text Encryption


Date: Jan 30, 1997
Date Due: Feb 11, 1997
  1. Encode the following sentence using the simple polyalphabetic code of period three using ROT3, ROT13, ROT7.
    Carolina beat Vanderbilt.
    I was expected three separate encodings, but accepted the polyalphabetic solution.
    ROT3 FDUROLQD
    ROT 7 JHYVSPUH
    ROT 13 PNEWYVAN
    Polyalphabetic: ROT3 first, ROT13 second, ROT7 next ... FNYRYPQN
    
  2. Decode the text below which was encoded with a simple substitution, (not necessarily a rotation). Implemented by Substitution.c.

    mqphbeapkhqqpybstaeubpbuzpieugpkhopheghpwsbeiqX mekhpatobapzqltketupsqvqvxqseugpkhqpzboX mhqupwstjzaopmqpitjghkpkhqqpkhopyheazsqupktpxqX hqsq*ipbphqbakhpybstaeubpftsqlqspktpkhqqX

    Hint '*' is an apostrophe and '\n' is mapped to "X ", only lower case characters and a space.

    we hail thee carolina and sing thy high praise
    with loyal devotion remembering the day
    when proudly we sought thee thy children to be
    here's a health carolina forever to thee
    
  3. Design an homophonic encryption code based on the frequencies of characters in English (from the handout for assignment 2). This code should be designed so that all output codes are roughly equally likely: The letters should "ZJQXK" have one code "33" of frequency .78% Every other character should have at least one output code and the number of codes should be such that the frequency was roughly 1.0%.
    Space needs 18 codes
    T needs 8
    AIORSN each needs 6
    H needs 4
    CLD each needs 3
    MUPFG each needs 2
    BWYV each needs only one
    
  4. Finalize the computations on the number of initial states of:
    Write the answer in terms of combinations and powers then expand using a calculator.
  5. Given p = 101 and q = 113 Compute n, phi(n), choose b = 3533, show that b and phi(n) are relatively prime.
    Compute the private key.
    p = 101 q = 113
    n = 11413
    phi(n) = 100*112 = 11200
    e = 3533
    6579 calculated with extEuclidean 
    
  6. Using the square and multiply algorithm to encode the plaintext 9726.
    Check your answer by using the private key to decode the message.