If P sends {v_1, v_2, v_3} and and y_1 in the same session, the result will always be T. Shouldn’t V keep {v_1, v_2, v_3} from P instead at secrets registration phase without exposing {s_1, s_2, s_3}? And the challenge-response phase would only include sessional x and {a_1, a_2, a_3}, and y_1 ? There should be 2 situations (secrets registration and challenge-response) describe by the phases right?