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Digital signature is typically put on the one-way hash of the message, instead of on the message directly. One of the reasons is the cost because signing a short hash value is more efficient than signing a message that can be very long. Bob says that his message is always short, so he decides to directly sign the message, rather than signing its hash. (1) Without knowing Bob’s private key, we want to generate a pair (m, s), where s is Bob’s signature on m, and m can be anything? Assume s is a random number, and describe how you calculate m. (2) If Bob signs the one-way hash of the message, can you still generate a pair (m, s)?

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