2. Review thedefinition of permutation ciphers (a.k.a. transposition ciphers). 2

Question

2. Review thedefinition of permutation ciphers (a.k.a. transposition ciphers).

2.1 How many different permutation keys exist for permuting n positions (where n is any positive integer)?

2.2 Let n = 160. How many keys are there (in scientific notation with 2 decimals of precision)? Use the Stirling formula. (This is very large; nevertheless, permutation ciphers are not secure cryptosystems.)

2.3 Show a way to break any permutation cipher, using a known plaintext attack.

2.4 Show a way to break any permutation cipher, using a known ciphertext attack.

Explanation / Answer

Answer 2:

Transportation chipper:- A transposition cipher is a method of encryption by which the positions held by units of plaintext (which are commonly characters or groups of characters) are shifted according to a regular system, so that the ciphertext constitutes a permutation of the plaintext

Answer 2.1.

Different permutation keys exist for permuting n positions – n! = n. (n-1).(n-2).(n-3)……3.2.1

Answer 2.2

For n=160. keys are there Use the Stirling formula:

Stirling formula – n!=(2 n)(n/e)n

160!= (2*3.14*160)(160/e)160

= 4.71(approx.)    Full calculated answer is 4.712268E284.

Answer 2.3:

Known plain text Attack: During known-plaintext attacks, the attacker has an access to the ciphertext and its corresponding plaintext. His goal is to guess the secret key (or a number of secret keys) or to develop an algorithm which would allow him to decrypt any further messages.

Attackers perspective to break permutation chipper:

Suppose the attacker knows that the plaintext is meet me later, and wants to learn about the key. Because learning the key will provide the attacker the capability to learn the encryption, and the decryption mappings, for the future plaintext and ciphertext The attacker, knowing that the key length is four, can construct the same matrix using the known plaintext, meet me later. And now observe where each of the column occurs. For example, focusing on the first row on the left,

the attacker can locate where the alphabet sequence, MMT, occur in the plaintext. The alphabet sequence MMT occurs at the last segment in the ciphertext. That is, suppose the ciphertext is divided into four segments, or divided by the length of the key. Then MMT occurs in the fourth segment. And therefore, the attacker knows that the first element of the key is 4. Similarly, the attacker can locate where the sequence EEE occur, and learn that it is occurring in the third segment of the ciphertext. Therefore, the second element to the key, which corresponds to the permutation of the second row in the matrix, is 3.Following the same logic, the attacker can further learn that the rest of the elements in the key are 1 and 2

Answer 2.4:

The known ciphertext attack, or ciphertext only attack (COA) is an attack method used in cryptanalysis when the attacker has access to a given set of ciphertext(s). The attacker does not have access to corresponding cleartext in this method; however, COA is successful when correspdonding plaintext can be determined from a given set of ciphertext. Occasionally, the key used to encrypt the ciphertext can be determined from this attack. To break permutation chipper just try out different permutations until you find a first block that makes sense. Once you have worked out the permutation, you can then use this to decrypt the rest of the intercept easily.

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