Suppose bob receives a message signed using a digital


1. Consider a group of 30 people who wish to establish pair-wise secure communications using symmetric-key cryptography. How many keys need to be exchanged in total?

2. Suppose Bob receives a message signed using a digital signa­ture scheme with Alice's secret signing key. Does this prove that Alice saw the message in question and chose to sign it?

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Mechanical Engineering: Suppose bob receives a message signed using a digital
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