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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, whilecipher b uses a 128-bit key. alice prefers cipher a, while bob wants theadditional security provided by a 128-bit key, so he insists on cipher b. as a compromise, alice proposes that they use cipher a, but theyencrypt each message twice, using two independent 64-bit keys. assumethat no shortcut attack is available for either cipher. is alice's approachas secure as bob's?

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