Homework 1: Substitution Ciphers

Purpose

This homework is designed to do several things:

• The proficiency problems may become part of your portfolio that demonstrates meeting the content objectives of the course.

• Doing challenge problems and submitting them (and their revised version(s)) demonstrates some of our overall objectives.

• Submitting your check in memo and homework problems are an opportunity to get feedback from Dr. Bolkema.

Instructions

Do as many of the proficiency problems as you feel necessary to meet the objectives. The challenge problems are optional but encouraged. Recall that you can submit up to three problems per week for direct feedback from Dr. Bolkema.

Submit a check-in memo by Friday at noon (under the check in memos tab on Blackboard) by Friday at noon that describes your progress on these problems (and some other things). There are specific questions to answer there. This goes privately to Dr. B who will then give you feedback.

Content Objectives – Module 1

By doing this homework you will demonstrate that you are able to

1. Encrypt strings of information using simple substitution ciphers.

2. Use frequency analysis to decrypt simple substitution ciphertexts.

3. Encrypt (and decrypt) strings of information using Vigene?re ciphers.

Proficiency Problems

1. (Objective 1) Use a Caesar cipher with shift length 23 to encrypt the plaintext “Chicago style hot dogs do not include ketchup”

2. (Objective 1) Use a simple substitution of your choosing to encrypt the plaintext “Sphinx of black quartz judge my vow”

3. (Objective 2) Decrypt each of the following Caesar encryptions.

(a) LWKLQNWKDWLVKDOOQHYHUVHHDELOOERDUGORYHOBDVDWUHH

(b) UXENRBWXCUXENFQRLQJUCNABFQNWRCJUCNAJCRXWORWMB

(c) BGUTBMBGZTFHNLXMKTIPBMAVAXXLXTEPTRLEXTOXKHHFYHKMAXFHNLX

4. (Objective 2) Decrypt the following ciphertext which was encrypted using a simple substitution cipher.

JNRZR BNIGI BJRGZ IZLQR OTDNJ GRIHT

USDKR ZZWLG OIBTM NRGJN IJTZJ LZISJ

NRSBL QVRSI ORIQT QDEKJ JNRQW GLOFN

IJTZX QLFQL WBIMJ ITQXT HHTBL KUHQL

JZKMM LZRNT OBIMI EURLW BLQZJ GKBJT

QDIQS LWJNR OLGRI EZJGK ZRBGS MJLDG

IMNZT OIHRK MOSOT QHIJL QBRJN IJJNT

ZFIZL WIZTO MURZM RBTRZ ZKBNN LFRVR

GIZFL KUHIM MRIGJ LJNRB GKHRT QJRUU

RBJLW JNRZI TULGI EZLUK JRUST QZLUK

EURFT JNLKJ JNRXR S

• The ciphertext contains 316 letters. Here is a frequency table: R J I L Z T N Q B G K U M O S H W F E D X V

Freq 33 30 27 25 24 20 19 16 15 15 13 12 12 10 9 8 7 6 5 5 3 2

• The most frequent bigrams are: JN (11 times), NR (8 times), TQ (6 times), and LW, RB, RZ, and JL (5 times each).

5. (Objective 3) Encrypt each of the following Vigene?re plaintexts using the given keyword.

(a) Keyword: hamlet Plaintext: To be, or not to be, that is the question.

(b) Keyword: fortune Plaintext: The treasure is buried under the big W.

6. (Objective 3) Decrypt each of the following Vigene?re ciphertexts using the given keyword.

(a) Keyword: condiment Ciphertext: r s g h z b m c x t d v f s q h n i g q x r n b m p d n s q s m b t r k u

(b) Keyword: rabbithole Ciphertext: k h f e q y m s c i e t c s i g j v p w f f b s q m o a p x z c s f x e p s o x y e n p k d a i c x c e b s m t t p t x z o o e q l a f l g k i p o c z s w q m t a u j w g h b o h v r j t q h u

Challenge Problems

Justify your answers with complete sentences explaining your reasoning.

7. Suppose that you have an alphabet of 26 letters.

(a) How many possible simple substitution ciphers are there?

(b) A letter in the alphabet is said to be fixed if the encryption of the letter is the letter itself. How many simple substitution ciphers are there that leave:

• No letters fixed? • At least one letter fixed? • Exactly one letter fixed? • At least two letters fixed?

8. Re-encrypting a Vigene?re cipher with another Vigene?re cipher results in a Vigene?re cipher, but the key is likely to be a random string of letters. Vigene?re

(a) A message is encrypted with a Vigene?re cipher using the keyword Ultra and then encrypted again with a Vigene?re cipher using keyphrase Bletchley Park. What is the key to the re-encrypted message?

(b) A message is encrypted with a Vigene?re cipher using the keyword having length 6 and then encrypted again with a Vigene?re cipher using keyword having length 9. What is the length of the key to the re-encrypted message?

(c) A message is encrypted with a Vigene?re cipher using the keyword having length 7 and then encrypted again with a Vigene?re cipher using keyword having length 8. What is the length of the key to the re-encrypted message?

(d) It is possible, by remembering several short keywords, to effectively encipher with a long key. Consider the following encryption. The plaintext was first encrypted with a Vigene?re cipher with keyword history and then encrypted again with a Vigene?re cipher with keyword Enigma and then encrypted again with a Vigene?re cipher with keyword black. What is the length of the keyword for the resulting Vigene?re cipher?