**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
(2*p* – 1) (2*p* – 3) (2*p* – 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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