Question

Hybrid encryption combines the convenience of a public-key cryptosystem with the efficiency of a symmetric-key cryptosystem and it is used in both TLS and SSL. Say we have the secured RSA and AES available, show how to use hybrid encryption to encrypt a message m= m₁m₂m₃m₄m₅ with 640 bits without a pre-shared secret between Jane and Karl.

Answer 1

Solution:

• The message m which is being transmitted between Jane and Karl is represented by ‘m’.
• But between Jane and Karl, there is no secret between them which is being shared.
• The secured RSA and AES is there between them.
• The hybrid encryption can be done in two ways, one in which is the public key cryptosystem and the other one is the symmetric key cryptosystem.

The steps are as follows:

Step 1:

• For exchanging the key between Jane and Karl, first use the RSA.
• The two different large prime numbers are selected which are represented by p and q.
• Multiply the two prime numbers and store it in n = pq.
• Identify an integer, say k > 0 which is able to satisfy the condition gcd (k, φ(n)) = 1.
• Place (n, k) in the public so that the messages could be sent to the persons.
• Between Jane and Karl the symmetric key is being passed.
• The key of 128 bit is being shared between Jane and Karl, since the bit commonly used by AES is of 128 bits.

Step 2:

• For symmetric key encryption, use AES.
• The AES is a kind of block cipher. And having the common block size of 128 bits.
• The data/message m is of 640 bits. Therefore, the number of blocks are as follows:

Number of blocks = 640 / 128

= 5 blocks

• Now, on the computed blocks, it performs the AES encryption technique to transfer the data between Jane and Karl.