A lower bound on the 2-adic complexity of modified Jacobi sequence

2017/04/06 by Sun, Yuhua, Wang, Qiang, Yan, Tongjiang
#FOS: Computer and information sciences #Information Theory (cs.IT)

paper · doi:10.48550/arxiv.1704.01685

Abstract

Let p,q be distinct primes satisfying gcd(p-1,q-1)=d and let D_i, i=0,1,⋯,d-1, be Whiteman's generalized cyclotomic classes with Z_pq^∗=∪_i=0^d-1D_i. In this paper, we give the values of Gauss periods based on the generalized cyclotomic sets D₀^∗=∑_i=0^(d)/(2)-1D_2i and D₁^∗=∑_i=0^(d)/(2)-1D_2i+1. As an application, we determine a lower bound on the 2-adic complexity of modified Jacobi sequence. Our result shows that the 2-adic complexity of modified Jacobi sequence is at least pq-p-q-1 with period N=pq. This indicates that the 2-adic complexity of modified Jacobi sequence is large enough to resist the attack of the rational approximation algorithm (RAA) for feedback with carry shift registers (FCSRs).

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