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 Alice and Bob.

Answer 1

Solution:

Given that the following information about,

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.

Here the message “m” needs to be transmitted between Alice and Bob but there is no shared secret between them.

There are secured RSA and AES are available.

We can use the hybrid encryption in two ways, either we can use public key crypto system first or symmetric key crypto system first.

Step 1:

       First use RSA for a key exchange between Alice and Bob

• The users select two large distinct prime numbers p and q.
• Two number p and q multiplies to form n = pq
• Next find a integer k>0 that satisfies the condition gcd(k, φ (n))=1.
• Now (n, k) placed as public and so the users can send messages to that person.
• The private key (p) can be computed only by knowing the primes p and q.
• Now the symmetric secret key can be passed between Bob and Alice.
• A 128 bit key is used commonly by AES so 128 symmetric key (s) is shared between Alice and Bob.

Step 2:

       Use AES to perform symmetric encryption

• AES is a block cipher and common block size is 128 bits.
• Here the data, “m” is 640 bits, so divide into 640/128= 5 blocks.
• Now perform AES encryption on the blocks to transfer the data between Alice and Bob