So, how does a Key Derivation Function differ from other studied families of secure hash functions (like the SHA family of algorithms)? Include as much detail as possible to ensure your message is understood.

The first step of most signature schemes consists in hashing the message to be signed. Discuss which security property a suitable hash function must have, and briefly show an attack that is possible if the hash function does not have this property.

Digital signatures have a potential weakness due to lazy users. In e-commerce transactions, a contract might be drawn up and the user asked to sign its SHA-1 hash. If the user does not actually verify that the contract and hash correspond, the user may inadvertently sign a different contract. Suppose that the Mafia try to exploit this weakness to make some money. They set up a pay Web site (e.g., pornography, gambling, etc.) and ask new customers for a credit card number. Then they send over a contract saying that the customer wishes to use their service and pay by credit card and ask the customer to sign it, knowing that most of them will just sign without verifying that the contract and hash agree. Show how the Mafia can buy diamonds from a legitimate Internet jeweler and charge them to unsuspecting customers.

We know that a digital signature is for the purpose of ensuring data integrity and authenticity. a) Checksum adds all the bits of the message (or blocks), is checksum a good way to construct a digital signature scheme? How about a hash function, i.e, Sign(M)= h(M)?b) If we use a hash to generate a signature in a more complicated way as follows Sign(k,m) = σ = h(k) XOR m XOR h(m), and m, σ will be sent along. Would this be a secure signature? Briefly explain. please do not use chegg or ai tool like chat gpt please