Entanglement distillation protocols are generalized for qudits of arbitrary dimension by studying the group of unitary local permutations. We introduce the concept of joint performance parameter η that allows us the comparison of distillation protocols with different values of fidelity, probability of success and number of Bell pairs used altogether.We analyze several distillation protocols assisted with twirling operations as the dimension D of qudits vary. We find that the best performance according to η is not achieved for qubits (D=2), but for qutrits (D=3) and n=3 input pairs of Bell states. We propose and study an extension of the Quantum Privacy Amplification protocols that work for arbitrary dimension D, being more efficient when D is a prime number.