Digital Signatures

• Expected question: Suppose Bobby has got message M. private key sk1 and public key pk1 and Bob has got private key sk2 and publick key pk2. Bobby computes $X = E_{sk1(M)}$, $Y = E_{pk1(H(M))}$ where E is encryption and H is hash. Now she sends this (x, Y) to Bob. State the security goals achieved and not achieved.

• It involves the standard process of encryption and decryption.

• Working: Let the sender be A and the receiver be B.

1. A encryption the plaintext to ciphertext using the public key of B.

   

2. Now A does not directly send the ciphertext to B. It first creates a message digest is encrypted with A's private key. this is called the digital signature.

1. Now A concatenates the ciphertext (CT1) and the digital signture (DS!) and sends it to B. B receives the message as CT2 and DS2.

1. B decrypts ciphertext CT2 into plaintext PT2 using its private key.

1. Now to check if the message actually came from A, B does the following: B decrypts A's digital signature using A's public key. This gives B the message digest. Let us call the message digest as MD2.

   

2. B applied the Hash Function to PT2 to get Message Digest MD3. Now B checks if MD3 and MD2 are the same. If yes then the message was actually sent by A.