The future international nuclear disarmament may involve the dismantlement of nuclear warheads. After the dismantlement of a nuclear warhead, the separated explosive needs authentication that it comes from the dismantled nuclear warhead. In this paper, the Monte Carlo numerical simulation method was used to study the feasibility and result of determining the source of the explosive by analyzing the nuclide abundances of the explosive and determining the age of the explosive (calculated since the explosive was placed in the nuclear warhead). First, the JMCT software was used to analyze the nuclei produced by the neutron reactions in the explosive of the nuclear warhead. As a result, it was found that C is the most promising to be used to determine the source of the explosive. Second, the relationships between the average abundance of C and the age of the explosive, the spatial distribution of the C abundance in the explosive were calculated by using the JMCT software. Finally, it is found that, compared to the WgPu warheads (nuclear warheads with weapons-grade plutonium cores), the C abundances of the explosives of the WgU warheads (nuclear warheads with weapons-grade uranium cores) are much lower (the ages of the explosives are the same), and it is more difficult to measure the latter; for the WgPu warheads with the structures based on Model 3 and Model 4 (the warhead models employed were proposed by Steve Fetter), it can be determined that whether the separated explosives come from the dismantled nuclear warheads or are common ones (or the fake ones prepared by the verified party) after the dismantlement of the nuclear warheads by measuring the C abundances in the explosives (including the average abundances and the spatial distributions of the abundances) and determining the ages of the explosives, which realizes the source authentication of the explosives.