11.04.2018
A lower bound on the 2-adic complexity of the modified Jacobi sequence
Erschienen in: Cryptography and Communications | Ausgabe 2/2019
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Let p, q be distinct primes satisfying gcd(p − 1, q − 1) = d and let Di, i = 0, 1, · · · ,d − 1, be Whiteman’s generalized cyclotomic classes with \(\mathbb {Z}_{pq}^{\ast }=\cup _{i = 0}^{d-1}D_{i}\). In this paper, we give the values of Gauss periods based on the generalized cyclotomic sets \(D_{0}^{\ast }=\cup _{i = 0}^{\frac {d}{2}-1}D_{2i}\) and \(D_{1}^{\ast }=\cup _{i = 0}^{\frac {d}{2}-1}D_{2i + 1}\). As an application, we determine a lower bound on the 2-adic complexity of the modified Jacobi sequence. Our result shows that the 2-adic complexity of the modified Jacobi sequence is at least pq − p − q − 1 with period N = pq. This indicates that the 2-adic complexity of the 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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