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For anonymous communication, the most popular method is to use pseudonyms instead of original identities. We previously demonstrated the possibility of a collision-free pseudonym system by uniquely assigning a permutation element to each network entity. We extend this idea by assigning k permutation elements to each entity for k ≥ 1. We analyse the randomness of the pseudonyms used in the proposed system to show the effect of k by varying k from 1 to 50. Our experimental results show that our pseudonym system can provide practical anonymity with k.