11.04.2018 | Ausgabe 2/2019
A lower bound on the 2-adic complexity of the modified Jacobi sequence
- Zeitschrift:
- Cryptography and Communications > Ausgabe 2/2019
Wichtige Hinweise
The work is supported by Shandong Provincial Natural Science Foundation of China (No. ZR2017MA001, No. ZR2016FL01, No. ZR2014FQ005), the Open Research Fund from Shandong provincial Key Laboratory of Computer Network, Grant No. SDKLCN-2017-03, NSERC of Canada (No. RGPIN-2017-06410), Qingdao application research on special independent innovation plan project (No. 16-5-1-5-jch), Key Laboratory of Applied Mathematics of Fujian Province University (Putian University) (No.SX201702), and the Fundamental Research Funds for the Central Universities (No. 17CX02030A).
Abstract
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).
