Repeating the experiment exponentially decreases the probability of a cheating prover successfully guessing the swaps by chance. A single round provides only weak evidence because a color-blind impostor has a 50% chance of guessing correctly.
Conditions: The prover must possess a secret capability (e.g., distinguishing colors).; The verifier controls the randomization (e.g., swapping pens behind their back).; The protocol is repeated multiple times to reduce the soundness error.
Repeating the experiment exponentially decreases the probability of a cheating prover successfully guessing the swaps by chance. A single round provides only weak evidence because a color-blind impostor has a 50% chance of guessing correctly.
Conditions: The prover must possess a secret capability (e.g., distinguishing colors).; The verifier controls the randomization (e.g., swapping pens behind their back).; The protocol is repeated multiple times to reduce the soundness error.