Question 3: (34 marks) a. What do you mean by "pre-image" in hashing? Explain the two conditions for pre-image with suitable diagrams: when the number of inputs is equal and higher

than number of hashes. Calculate the total number of inputs, hashes and pre-images for each hash, when input size is 20-bit and hash size is 16-bit. (9 marks) b. What is an Avalanche Effect in cryptographic hash function? Provide an example of it using any hashing algorithm. (5 marks) c. What are the four Core Properties of Cryptography? Explain each with a suitable example and diagram. d. Calculate the output of a 64-bit matrix in the figure given below after applying the Permuted Choice 1 (PC1) operation in Data Encryption Standard (DES) algorithm. (8 marks) (7 marks) e. 1 1 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 1 01 1 0 1 1 1 1 0 0 1 0 1 1 0 1 0 0 1 1 1 0 1 1 1 1 1 0 1 0 0 0 1 0 0 1 1 0 1 00 0 1 0 1 Figure: Given 64-bit input matrix for performing PC1 Operation in DES Algorithm f. What is the "Substitution Word" process of "g()" function for the expansion of key in Advanced Encryption Standard (AES) algorithm? Explain it with a suitable diagram and perform this operation on the word xy-10101000 using the given S-Box in AES algorithm. (5 marks)