Comp 3704
Introduction to Cryptography
Homework 1
Due Tuesday, January 14, 2003
  1. Cryptanalyze the following text, which was encrypted with a shift cipher. 
        Iq uzfqzp fa nqsuz gzdqefduofqp egnymduzq imdrmdq az ftq rudef
    ar Rqndgmdk.
    (This text is the first line of the infamous "Zimmerman telegram", sent by German's Foriegn Minister to the Mexican president via the German ambassador to Mexico in 1917. It announced Germany's intention to wage war against the United States. This telegram was intercepted and decrypted by British intelligence.)
  2. Choose a passage of text, and encrypt it with a (nontrivial) affine cipher. Give me the plaintext, the values of the keys a and b, and the ciphertext. Also turn in a separate piece of paper that has nothing but another copy of the ciphertext written on it. Next week someone in the class will do a cryptanalysis of your ciphertext.
  3. Show that in a cryptosystem, ek is an injective function for every key k.
  4. Use the Euclidean algorithm to find the greatest common divisor of 1326 and 252.
  5. Find 17-1 mod 449, if it exists. What about 148-1mod 717?