A digitally signed document tells the reader that the contents in the document have not been modified since the author signed it. This is achieved using a hash function f. The digital signature contains the hash value of the document, f(d). The reader can compute the hash value of their document using the hash function f and compare it to the value stored in the signature. If they match, the reader can be sure that the document has not been modified.
Consider a malicious attacker who would like to replace the document d with a modified version d'. To avoid detection, they have to ensure that f(d) = f(d'). The attacker tries to find a possible pair (d, d') by trying many possibilities until f(d) = f(d'). Suppose f is a hash function that maps an input d to a 32-bit string, such that each possible hash value is equally likely to have been assigned to the input d. How many pairs must the attacker try before they obtain a possible collision pair (d, d') with a 70% probability?