Cryptology ePrint Archive: Report 2014/657

On the cycle decomposition of the WG-NLFSR

YUjuan Li and Wnehua Shen and Huaifu Wang and Peipei Zhou

Abstract: Recently, Kalikinkar Mandal and Guang Gong presented a family of nonlinear pseudorandom number generators using Welch-Gong Transformations in their paper [6]. They also performed the cycle decomposition of the WG-NLFSR recurrence relations over different finite fields by computer simulations where the nonlinear recurrence relation is composed of a characteristic polynomial and a WG permutation. In this paper, we mainly prove that the state transition transformation of the WG-NLFSR is an even permutation. We also prove that the number of the cycles in the cycle decomposition of WG-NLFSR is even. And we apply our results to the filtering WG7-NLFSR to prove that the period of the sequences generated by WG7-NLFSR can not be maximum.

Category / Keywords: secret-key cryptography /

Date: received 23 Aug 2014

Contact author: liyj at amss ac cn

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Version: 20140827:074338 (All versions of this report)

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