Question: 1. Consider a hash function Hash 11 that starts with an 32-bit initial value of c09db506 and repeatedly XORs it with 32-bit blocks of the

1. Consider a hash function Hash 11 that starts with an

1. Consider a hash function Hash 11 that starts with an 32-bit initial value of c09db506 and repeatedly XORs it with 32-bit blocks of the input to produce a 32-bit output. Hash1(de0fc223)=c09db506de0fc223=1e927725 and the input cd1aa915 f08d7db7 would generate the following output: Hash 1(cd1aa915f08d7db7)=c09db506cd1aa915f08d7db7=fd0a61a4 (a) Approximately how many steps would be required to perform a brute force attack to find a preimage for a given output of this hash function? (2 pts) (b) Approximately how many steps would be required to perform a brute force birthday attack to find a collision for this hash function? ( 2 pts) (c) Use the properties of the XOR operation to find a 32-bit preimage for the output 666cdce9. (3 pts) (d) Find a 32-bit second preimage for the output fd0a61a4 calculated above. (3 pts) (e) Find a collision other than the one demonstrated by your answer to (d). (hint: pick a 32-bit input, then find a 64-bit input that generates the same output using the properties of XOR.) (3 pts)

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