On the judgement of full-period sequences and a novel congruential map with double modulus on Z(p n )

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This paper studies the judgement problem of full-period maps on Z(pn) and proposes a novel congruential map with double modulus on Z(pn). The full-period properties of the sequences generated by the novel map are studied completely. We prove some theorems including full-period judgement theorem on Z(pn) and validate them by some numerical experiments. In the experiments, full-period sequences are generated by a full-period map on Z(pn). By the binarization, full-period sequences are transformed into binary sequences. Then, we test the binary sequences with the NIST SP 800-22 software package and make the poker test. The passing rates of the statistical tests are high in NIST test and the sequences pass the poker test. So the randomness and statistic characteristics of the binary sequences are good. The analysis and experiments show that these full-period maps can be applied in the pseudo-random number generation (PRNG), cryptography, spread spectrum communications and so on.

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