Consider a version of the division method in which h(k) = k mod m, where m = 2P-1 and k is a character string interpreted in radix 2P. Show that if we can derive string x from string y by permuting its characters, then x and y hash to the same value. Give an example of an application in which this property would be undesirable in a hash function. CHAINED-HASH-INSERT (T, x) 1 insert x at the head of list T[h(x.key)] CHAINED-HASH-SEARCH (T, k) 1 search for an element with key k in list T[h(k)] CHAINED-HASH-DELETE (T, x) 1 delete x from the list T[h(x.key)]

Consider a version of the division method in which h(k) = k mod m, where m = 2P-1 and k is a character string interpreted in radix 2P. Show that if we can derive string x from string y by permuting its characters, then x and y hash to the same value. Give an example of an application in which this property would be undesirable in a hash function. CHAINED-HASH-INSERT (T, x) 1 insert x at the head of list T[h(x.key)] CHAINED-HASH-SEARCH (T, k) 1 search for an element with key k in list T[h(k)] CHAINED-HASH-DELETE (T, x) 1 delete x from the list T[h(x.key)]