Question

Please concur with, dispute, or qualify the following statement. Performing a frequency analysis would be a good starting point for cracking an RSA-encrypted message.

 

 

Answer 1

WHAT IS FREQUENCY ANALYSIS?

Frequency analysis means looking at how many times each letter appears in the encrypted message, and using this information to crack the message. A letter that appears many times in a message is far more likely to be “T” than “Z”!

RSA AND FREQUENCY ANALYSIS?

Simple frequency analysis would be possible since textbook RSA encryption is deterministic.The encryption and decryption that was described on the previous page. Type a short sentence in the input field and then press enter; you will see the  hash code  in the window below it. This gives an integer representation of each character of the word. We are using a hash code with only the numbers 1 through 29 in this simple example. Letters are represented by numbers 1 through 26 independently of the case (that is 'A' and 'a' are represented by 1, and so on), space is represented by the number 27, period by 28, and all the other symbols by 29.

Pressing the  Encrypt next character  button will give you the encryption for each of the successive integers in the hash code, computed via the formula  y = x r (mod n) , where  n  and  r  are from the previous page, namely  y = x 25  (mod 1073) . Pressing the  Decrypt next character  button will, on the other hand, compute y s  (mod n) , which in this case is  y 121  (mod 1073)  for each of these encrypted integers; you can check that these are the original integers back again!

FREQUENCY ANALYSIS CAN BE USED TO DECRYPT

You may have noticed that the letter A corresponds to 1 in a hash code. Hence, it is always encrypted as 1. In real RSA systems we never encrypt letter by letter, we encrypt the large block of several letters at once. The reason we want large blocks is that encrypting letter by letter we have the same encryption for the same letter (this is called a substitution cipher),  hence we can use frequency analysis to decrypt. The larger the blocks the fewer patterns will be kept in the result.

USES OF FREQUENCY ANALYSIS.

f requency analysis approach, it is not critical to the use of this approach. When the world was new to this subject--when it had just discovered ciphers and keys and cryptanalysis--all of the knowledge was completely new. It was the cutting edge, so not many people understood it yet. It was essential to attain a high level of education to comprehend the mysteries of cryptology.

the mysteries of cryptology.