1. Encipher the following message using



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Chapter 8
1. Suppose the following was presented as the plaintext/ciphertext generated by an Enigma machine. Could the claim be true? Explain why or why not.
Plaintext: DERNATIONALSOZIALISMUSHATALLEWERTEZERSTOERT

Ciphertext: HEKIFHSLQOOFHECSMZHFVBDUTOPSKEFAJNDLRHEMDFS


2. Express the Atbash substitution cipher below using cyclic permutation notation.
ABCDEFGHIJKLMNOPQRSTUVWXYZ Plaintext

ZYXWVUTSRQPONMLKJIHGFEDCBA Ciphertext


3. Express a Caesar shift of 3 using cyclic permutation notation.
4. For the commercial Enigma, we had
H:

Input ABCDEFGHIJKLMNOPQRSTUVWXYZ

Output JWULCMNOHPQZYXIRADKEGVBTSF
H-1:
Input ABCDEFGHIJKLMNOPQRSTUVWXYZ

Output QWERTZUIOASDFGHJKPYXCVBNML


Express each of these in cycle notation.
5. Find all possible factorizations of

AD = (UMJWBOKNZPVCL)(GFDAERIQSXYHT)


6. Find all possible factorizations of

AD = (UHEBVOKJSX)(QPRLAGDNFZ)(IWY)(MTC)


7. Given the following enciphered session keys, recover the permutations AD, BE, and CF.
ANX GBP JGD JPA SOA RVZ

BRF OXM KZN IUT TDP QQU

CCL DFK LFJ LYH UJZ CTD

DMQ PLY MAT NZE VXY ZAI

EIV FMR NQB SCF WEK BGW

FUE XKG OTM HRJ XYC YSQ

GBS UWL PKR TIS YHW ENV

HPI MDC QLG AON ZWO KEB

ISU VHX RVH WJO

8. In Simon Singh’s The Code Book, he gives an example of what we called the permutation product AD.5 It’s presented in a different format, but is equivalent to



AD = (AFW)(BQZKVELRI)(CHGOYDP)(JMXSTNU). What is wrong with this example?
9. In calculating the number of ways an Enigma plugboard can be wired, the identity

(2p – 1) (2p – 3) (2p – 5)(1) =

was used. Prove that this is true.


10. In some systems, enciphering a message twice with distinct keys is no different than enciphering once with some other (single) key. This is the case for any monoalphabetic substitution ciphers, Vigenere ciphers, matrix encryption, and more. Is it the case for Enigma?
11. Is there a way to distinguish messages that have been enciphered twice with Enigma (using two different keys) from messages that have only been enciphered once?





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