 # Problem 1 (1 point). Given a ciphertext JSSXFEPP encrypted by Shift...

## Question

Problem 1 (1 point). Given a ciphertext JSSXFEPP encrypted by Shift Cipher, compute the key of shift cipher and the original message using brute-force attacks. In this problem, we assume the original message is English and is human-readable. The message space includes all the lower case characters, i.e., M = {a, b, ..., z}, key space is K = {0, 1, ..., 25} and ciphertext space is C = {A, B, ..., Z}.

Problem 2 (1 point). (a) Given an encryption key (i.e., a permutation) of Substitution Cipher presented below
a b c d e f   g h i   j k l m n o p q r s t u v w x y z
E X A U N D K B M V O R Q C S F H Y G W Z L J I T P
(b) If the message space of Substitution Cipher has a number of 50 unique characters/symbols, what is the size of the key space? In other words, how many permutations in total?

Problem 3 (1 point). Assume the key of Vigenere Cipher is cats, what is the ciphertext of a message data security encrypted by this key using Vigenere Cipher? What is the size of the key space for Vigenere Cipher if each key is a string of 4 characters? For easy calculation, a mapping table between characters (a,..., z) and integers (0, ..., 25) is listed below.
a b c d e f g h i j   k    l   m n   o   p   q    r   s   t    u   v   w   x   y z
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25

Problem 4 (1 point). Assume we have a sequence of 100 characters, the frequency distribution of different characters is listed below, compute the (approximate) index of coincidence (IC) of this sequence.
char            a b c d e f g h i j k l m n o p q r s   t    u    v w x y z
frequency   1 1 1 1 1 1 1 1 1 1 5 5 5 5 5 5 5 5 10 10 10 10 10 0 0 0

Problem 5 (1 point). An adversary analyzes a sequence of (ciphertext) characters, which is encrypted by Vigenere Cipher, using Kasishi’s method. In addition, it knows the key length is at least 2. If it can find a sub-string “edlt”, which is repeated twice in the sequence, and the distance of the two repeated sub-strings is 12, what are the possible key length of this Vigenere Cipher?

Problem 6 (1 point). Assume an attacker knows the index of coincidence in plaintext is ICplain = 0.234. Given a long sequence of (ciphertext) characters, e.g., c1c2c3c4c5c6c7c8c9......... which is encrypted by Vigenere Cipher, explain how to calculate/estimate the key length by using the index of coincidence.

## Solution Preview

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Problem 1:
Ciphertext: JSSXFEPP
Shift by: 1 irrwedoo
Shift by: 2 hqqvdcnn
Shift by: 3 gppucbmm
Shift by: 4 football...

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