Suppose that Alice and Bob have access to two secure block ciphers, say, Cipher A and Cipher B, where Cipher A uses a 64-bit key, while Cipher B uses a 128-bit key. Alice prefers Cipher A, while Bob...

Suppose that Alice and Bob have access to two secure block ciphers, say, Cipher A and Cipher B, where Cipher A uses a 64-bit key, while Cipher B uses a 128-bit key. Alice prefers Cipher A, while Bob wants the additional security provided by a 128-bit key, so he insists on Cipher B. As a compromise, Alice proposes that they use Cipher A, but they encrypt each message twice, using two independent 64-bit keys. Assume that no shortcut attack is available for either cipher. Is Alice's approach as secure as Bob's?