Unformatted text preview: Lign 17 Section 2 – Friday, January 21 and Tuesday, January 25 00: A recap – What’s wrong with Monoalphabetic Substitution Ciphers? What kind of mapping does a monoalphabetic substitution cipher give you? Draw an example. What about a monoalphabetic substitution cipher with homophones? What about a polyalphabetic cipher? 01: Mono
alphabetic Substitution Cipher with Homophones: Benford’s law is a terrifying fact about numbers. It states that the probability of first digits in almost any naturally occurring set of measurements (including accounting, election results, growth of trees) is distributed as Where d is a digit from 1
91. This means that the over
all distribution of first
digits is predicted to be as follows: 1 Note that there’s no probability given for 0, since a number can’t properly “begin” with 0; additionally, log10(0) is undefined. d p 1 30.1%
2 17.6%
3 12.5%
4 9.7%
5 7.9%
6 6.7%
7 5.8%
8 5.1%
9 4.6%
This distribution has been used to prove fraud, for instance in the 2009 Iranian elections,
since real data will observe this distribution, but fabricated data will not necessarily.
i  Suppose that for whatever reason, we want to disguise a set of observations that follow
this distribution. We want to use 50 characters to represent the 9 digits from 19. How
many homophones for each character will we need to completely mask this probability
distribution?
d # Homophones
1
2
3
4
5
6
7
8
9
10: Doublets and Nulls: The word bookkeeper is said to have the most sequential double letters in the English language. i
If we were to encrypt this using a simple monoalphabetic substitution cipher, what immediately obvious problem would arise? ii – Suppose the enciphered version of the plaintext bookkeeper turns out to be as follows: viqsqjqsssqwqssqowes What seems off about this encipherment given the plaintext? ____________ What does each character in the ciphertext correspond to? v = i = q = s = j = w = e = 11: Vigenère Cipher Question 1: Let’s say we find a message that has conspicuous repetitions of four characters that start 104, 26, 39 and 65 characters apart. What can we say about the key? What if the first repetition we had found was five characters, starting 17 characters apart? 100: Vigenère Cipher 2: Suppose we want to use a Vigenère cipher to encode the following lyrics: Wake up in the morning feeling like P Diddy
(Hey, what up girl?)
Grab my glasses, I'm out the door, I'm gonna hit this city…. Suppose we want to use the song’s title, Tik Tok, as the key. Provide the cipher
text (use the Tabula Recta below if you need to): 101: Vigenère Cipher 3: Suppose that the plaintext in (1) has been rendered into the cipher
text in (2). (1) Where are my keys? I lost my phone. What's going on on the floor? (2) Yhrkv erh yw mell? Z povf kl dospe. Jarx's jagpo du se mlb ynobk? What key was used? 111: Vigenère Cipher 4: Here’s a climactic quote from one of my favorite Dr Seuss Books. It’s enciphered using the book’s title: Bvbv owsvvwx tfoul hjokj pxbgdsu sf f plbgds yslm hemvj dcnvqsp iav hjo tthqtr'k cp k htcatr sbf dzj dlwqds'u osywko agcfvwx......heml uonv lmwp i zmrfvw uialyw hyowyzb xbgrno tjsqtr fcqndj plbgds rkvizb jnlhno. i
What repetitions do you notice? ii
There’s some extra information in this ciphertext. What wasn’t done? What clues does this give you? iii
How many letters long might the key be? iv
What book is this? ...
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 Winter '08
 Kehler
 Probability distribution, #, Benford

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