- [20 Points] Please evaluate the following being sure to show all calculations:
(a) [5 Points] 7503 mod 81
(b) 5 Points mod 81
(c) [5 Points] 81 mod 7503
(d) 5 Points mod 7503 - [10 Points] Use an exhaustive key search to decrypt the following ciphertext, which was
encrypted using the Shift Cipher. Please submit your supporting code or work, including all
“decrypted” output.
RZGXJHZOJECPXMTKOJGJBTGZONCVQZAPI - (a) [10 Points] Suppose that π is the following permutation of {1, . . . , 8}.
x 1 2 3 4 5 6 7 8
π(x) 4 1 6 2 7 3 8 5
Compute the permutation π
−1
(b) [10 Points] Decrypt the following ciphertext, for the following Permutation Cipher
with m = 8, which was encrypted using the key π
PTRHPEOUFSOEMOPCNUITSIIGGNTSNIOHMTENRUSB - [10 Points] Recall from pg 39, that with a chosen-plaintext attack (CPA) an adversary
has obtained temporary access to the encryption machinery. Hence, they can choose a
plaintext string, x, and obtain the corresponding ciphertext string, y.
Show that the shift, substitution, and Vigen`ere ciphers are all trivial to break using a chosenplaintext attack. - [10 Points] The index of coincidence method relies on a known value for the sum of the
squares of plaintext-letter frequencies. Why would it not work using the following: P
i
pi? - [30 Points] Determine the plaintext associated with this Vigen`ere encrypted ciphertext.
You may find Example 2.12 (pg 46-48) helpful. Stinson-Paterson use subscript notation,
fi
, in their formulas. You may find it more convenient to use array notation, f[i]. In this
case, f[i], 0 ≤ i ≤ 25, represents the count of the number of the i-th characters in the given
substring. So f[0] = the number of As, f[1] = the number of Bs, f[25] = the number of Zs.
In particular, we can rewrite fi + g as f[i + g] where i + g is calculated mod 26.
Please see the supplied spreadsheet for sample calculations of Mg for the first
substring from Example 2.12
QHYXEFMGJRFXGOXZXHJXKESJOAGKASJPEMHQHYXEFHRGCUHRIIUMXCIEESJOAGKW
EUDAVVVLWJCGNLVZWMSOVMLXOLSMXCIVHXNAAEPNSEXLJAUHRIIUMMICGNVAYLNV
ZCGNGVRLCYNXSLOXYKMSHIJLACELMLZCOTROEFWXCIFMVTXGZMQILAEOXGMLZQTR
XCILBQZCGNKZXAMFPMDMXCIQEPREFMWJQWMLDRYGIRMEVSIZAGGZHLAEOETHYOLS
EJJJOAEOWWIEMELXWOLWLYXGWLWAYDXROVWIVZRWNVNJJHQOLWGSIWMVGZWKYYGS
FXWDWHNVZTWKWZZWKEIGW
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An exhaustive key search to decrypt the following ciphertext
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