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1. One class of weak data integrity mechanisms (which we did not discuss in any detail) can only detect accidental modification of data. (a) A single parity check bit consists of the XOR of all the bits in the data. What types of accidental errors will this simple integrity mechanism detect?

(b) In what ways are cyclic redundancy checks (CRCs) better data integrity mechanisms than parity check bits?

(c) Explain why a CRC is not a strong data integrity mechanism. (d) Identify two different applications that use CRCs to provide data integrity and explain why they do not need a stronger data integrity mechanism.

2. By considering the analogy of a birthday being a hash of a persons identity, explain the following terms: (a) preimage resistance;

(b) second preimage resistance;

(c) collision resistance;

(d) the birthday paradox.

4. Explain which of the practical and security properties of a hash function are most useful for the following applications:

(a) storing a passphrase;

(b) generating a short-lived key by hashing a long-term key;

(c) HMAC;

(d) digital signature schemes with appendix;

(e) computer virus detection.