Contract cheating occurs when a student outsources their assessment to a third party, regardless of the third party's relationship with the student, or whether money is exchanged. In higher education, there is a widespread belief that assessment design is a solution to the problem of contract cheating and that authentic assessment tasks are particularly effective. This research analysed two datasets -- 221 assignment orders placed on academic custom writing websites and 198 assessment tasks in which contract cheating was detected -- to investigate if authentic assessment can assure academic integrity. The authenticity of assessments was determined using five factors derived from the literature: frequency, fidelity, complexity, real-world impact and feed forward. Our analysis found that assessment tasks with no, some, or all of the five authenticity factors are routinely outsourced by students.