The product of PRF and PRP is approximately:

• A. One
• B. Zero
• C. Two
• D. Infinite

Answer: (A)

The main idea here is how two ideal, random-looking primitives behave when their outputs are multiplied. A PRF and a PRP are modeled as independent, uniformly random objects. If you map their outputs to numbers in a multiplicative group where the identity element is 1, each output is effectively centered around 1 on average. Because they are independent, the expected value of their product is the product of their expectations, which is 1 × 1 = 1. So, on average (or in an indistinguishability sense), the product stays around the neutral element, making approximately one the best description.

In other words, combining two such ideal primitives multiplicatively does not drift the result away from the identity on average, hence the answer is one. The other options would imply a bias or unbounded growth that doesn’t align with the normalized, random-looking nature of PRF and PRP.