Question

1. Suppose the following:
   • James’ public key = K_j, James’ private key = K_j^-1
   • Randy’s public key = K_r, Randy’s private key = K_r^-1
   • Each person’s public key is known to others; Each one’s private key is only known to the owner

1. Explain how Randy can send a plaintext P to James secretly

2. Explain how James can verify if a plaintext P is sent from Randy

3. Explain how Randy can verify if a plaintext P is sent from James and at the same time P is sent secretly from James to Randy.

Answer 1

Each person's public key is known to others; Each one's private key is only known to the owner.

a. Randy sends a Plaintext P to James secretly.

Randy, first encrypts the Plain text using his private key K_r^-1 , then the encrypted ciphertext is again encrypted using James' Public key K_j. Now only James can decrypt the text using his(James') private key K_j^-1.

b. James verify if a Plaintext P is sent from Randy

When James receives a message, first it should be decrypted using James' private key K_j^-1. To verify the received text was sent by Randy, James should again decrypt using Randy's public key K_r.

c. Randy verify if a plaintext P is sent from James and at the same time P is sent secretly from James to Randy

When James sends plaintext P to Randy, first he encrypts using his(James') private key K_j^-1. Then he again encrypts using Randy's Public key K_r.

When Randy receives a message, he first decrypts using his private key K_r^-1. Then to verify it was sent from James he again decrypts using James public key K_j.