MA 479 / CSSE 490: Cryptography
Homework 1 problems inspired by Mathematics

Rose-Hulman Institute of Technology
A joint effort of the
Department of Mathematics
and the Department of Computer Science & Software Engineering
Spring term, 2002-2003

All these problems are paper-and-pencil problems, but writing a small computer program to do some of the grunt work for you is okay if you want. If you do write a computer program, please print out the code and include it with your homework.
  1. [1 point.]
    The following text has been encoded using an additive cipher. Break the cipher and find the key. Show all your work, including guesses, errors, and dead ends. (This includes a frequency table if you make one, or part of one.) You do not need to finish deciphering the message if you are sure of your key.

    Warning: this plaintext is unusually rich in t's and o's, in addition to e's.

    Hint: recall that we claimed in class that you only need to get one letter right in order to find the key. 

    KVSMOGKCLOQSXXSXQDYQODFOB
IDSBONYPCSDDSXQLIROBCSCDOBYXDROLKXU
KXNYPRKFSXQXYDRSXQDYNYYXMOYBDG
SMOCRORKNZOOZONSXDYDROLYYUROB
CSCDOBGKCBOKNSXQLEDSDRKNXYZSMD
EBOCYBMYXFOBCKDSYXCSXSDKXN
GRKDSCDROECOYPKLYYUDRYEQRDKVSMO
GSDRYEDZSMDEBOCYB
MYXFOBCKDSYX

  2. [1 point.]
    The following text has been encoded using the affine cipher with key "7x+1". (That is, multiply by 7 and add 1 to encode.) Decipher the text. Show all your work, including guesses, errors, and dead ends. (Note that finding the first couple of words of plaintext and then looking on line for the rest is cheating!) 
    LQTBRCBUKXJKJYJWTKELUXTBRFHUKKELUZ
BQKEJKELUXDTBRCBUKXJK
KEHKTBRCBUKFHUKBDVHWFLGCJ
  3. [1 point.]
    The following text has been encoded using an affine cipher. Break the cipher and find the key. Show all your work, including guesses, errors, and dead ends. (This includes a frequency table if you make one, or part of one.) You do not need to finish deciphering the message if you are sure of your key.

    Hint: to find the key, look at the ciphertext letters corresponding to plaintext letters that are early in the alphabet, such as a and e. 

    FWWOTRWOZLOXIZCFPDMXRZBCTSWXW
OZFTMFSUPFNZEIVTSJUXLSBCXSOZM
ROZJFGZFITWWIZRPMZFNOFIEXEEMT
JOWFSUOFIEXEFSJZMFSUWMTZUWX
KZFWWOZNXEEFSUEXBSUOZMRZIEIV
TSJXSWOZKFSDLTWOOZMOZFUTSWOZ
IFCXEOZMRTRWZMLOXLFRJZSWIVKMB
ROTSJFLFVRXNZUZFUIZFGZRWOFWOFU
EIBWWZMZUUXLSEMXNWOZWMZZRBCXSOZMEFPZ

    The following problems are from pages 51 � 53 of your textbook.

  4. [1 point.] Problem 2.1. Show all your work, including guesses, errors, and dead ends. (Note that finding the first couple of words of plaintext and then looking on line for the rest is cheating!)

  5. [1 point.] Problem 2.7. Be very complete in your description.

  6. [1 point.] How many possible different blocks of 10 letters are there? Express your answer as an approximate power of two.

  7. [2 points.] How many different keys are there for a 2 by 2 Hill cipher? Remember that the determinant has to be relatively prime to 26. How many have determinant 1?

  8. [2 points (but harder than the previous problem!)] Repeat the previous question for an n by n Hill cipher.