53) Ceasar Cipher is one of the earliest classical substitution ciphers. It invo
ID: 3746645 • Letter: 5
Question
53) Ceasar Cipher is one of the earliest classical substitution ciphers. It involves replacing each letter in the plaintext by a shifted 1) letter in the alphabet used.
Mathematically it can be expressed as follows:
c = E(p) = (p + k) mod (26)
p = D(c) = (c – k) mod (26)
where p and c refer to the plaintext and ciphertext, respectively; E(p) and D(C) are the encryption and decryption functions, respectively; and k is the secret key.
a) Show the encryption and decryption processes of the plaintext “Attack at dawn” using a key value of 4;
b) Explain how a brute force attack can break this simple cryptosystem;
c) Use a brute force attack to decrypt (decipher) the following message “TEBKFKQEBZLROPBLCERJXKBSBKQP”.
What is the original plaintext and the encryption key used?
Explanation / Answer
In a Ceaser substitution cipher each letter of a given text is replaced by a letter some fixed number of positions down the alphabet.
a)
A substitution cipher works like this, you start with the alphabet on one line and then add a second line with the alphabet shifted along a bit.
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In this case key is 4, because the second line alphabets are shifted a position of 4 to the right.
Now if we want to encrypt the word “attack at dawn” then you take the first letter ‘a’, and look at the letter below it, that gives us ‘e’. Then‘t’ gives ‘x’ and so on.
Hence the encrypted form of ‘attack at dawn’ is ‘exxego ex hear’.
To decrypt ‘exxego ex hear we look up ‘e’ on the bottom row and see ‘a’ above, then the ‘x’ on the bottom to get the ‘t’ above it and so on. Complete this process and we get ‘attack at dawn’.
b)
In a brute force attack, 2.an attacker knows that a Caesar cipher text, but does not know the shift value. Here breaking the scheme is straightforward. Since there are only a limited number of possible shifts (26 in English), they can each be tested in turn in a brute force attack.One way to do this is to write out a snippet of the ciphertext in a table of all possible shifts.
Example
The example given is for the ciphertext "EXXEGOEXSRGI"; the plaintext is recognizable by at a shift of four.
Decryption
shift
Candidate plaintext
0
exxegoexsrgi
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dwwdfndwrqfh
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cvvcemcvqpeg
3
buubdlbupodf
4
attackatonce
5
zsszbjzsnmbd
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yrryaiyrmlac
...
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haahjrhavujl
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gzzgiqgzutik
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fyyfhpfytshj
c)
For each shift the substitution letters are as follws
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Here the cipher text is “TEBKFKQEBZLROPBLCERJXKBSBKQP”
Now, using this table to find the correspondences for each letter of the ciphertext with the plaintext we can decipher the message. For example T in the ciphertext is q in plaintext. By doing the same with each letter we have:
TEBKFKQEBZLROPBLCERJXKBSBKQP
wheninthecourseofhumanevents
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Inserting spaces in all the appropriate places we have the final plaintext “When in the course of human events”
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