Building a secure block ciper on small and non-binary domain

We design a practical and provably-secure block ciper over small domain and non-binary inputs, which is also can be considered as a pseudorandom permutation on N elements. Our work is based on a relation we found between the small domain ciper and the negative hypergeometric probability (NHG) distribution. We prove that our block ciper achieves ideal security, that is, it is indistinguishable from a random permutation even if the adversary had already observed N plaintext-cipertext pairs. In particular, we initiate an efficient and sufficiently precise sampling algorithm for negative hypergeometric distribution.