Consider the following Double Vigene`re encryption. We choose two random keys K1 and K2 of lengths l and l + 1. To encrypt a message, we first use key K1 to encrypt in the Vigene`re fashion, then use K2 to encrypt.

Describe how to break this encryption scheme under a ciphertext only attack. Does this double encryption offer increased level of security over Vigene`re encryption against a ciphertext only attack? Suppose that we know that 10 l 19. Given a ciphertext of length 50 and its corresponding plaintext, describe how to recover the keys so that any other message encrypted under the same key pair can be decrypted.