Question

Suppose Alice uses the RSA system with a very large modulus n for which the factorization cannot be found in a reasonable amount of time. Suppose Bob sends Alice a message by representing each letter by its ascii value (A->65,B->66, ...) and then encypting each number separately using RSA with the large modulus and some large key e. Is this method secure? If not, describe an efficient attack.

Answer 1

Answer:

Encryption method security:-

• Encryption method representing each alphabetic character as an integer between 0 and 25.
• Now, apply RSA algorithm for each integer is not an efficient secure encryption method.

Explanation:

• Let consider alphabetic characters set {A, B... Z} .
• Each alphabetic character forms a set of message block values M={0,1,2...,25).
• From encryption method the corresponding cipher text block value C = {0e mod n,1e mod n, 2e mod n,..., 25e mod n}.
• Then, compute the cipher text with knowledge of Bob's public key;
• If the public key is generated, then possibility to decrypt the cipher text to plain text.
• The generated public key is easily calculated by everyone and security is lost.
• Therefore, the encryption method is not secure.

Encryption method is not secure, Most efficient attack against this method:-

• Now, compute the encryption message with the function Me mod n for all the possible values of M.
• This is the most efficient attack against the scheme in encryption method.
• Then, create a look-up table with cipher text as an index to the corresponding plain text as a value for appropriate location in the table.