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Consider two ciphers, Cipher A and Cipher B, and suppose that Cipher A has a 64-bit key, while Cipher B has a 128-bit key

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Consider two ciphers, Cipher A and Cipher B, and suppose that Cipher

A has a 64-bit key, while Cipher B has 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. Assuming that no shortcut attack is available for either cipher, is Alice's approach sound? Justify your answer.