Name
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). |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s12095-018-0300-y | Cryptography and Communications |
Keywords | Field | DocType |
Gauss period, Generalized cyclotomic class, Modified Jacobi sequence, 2-adic complexity, 11B50, 94A55, 94A60 | Discrete mathematics,Gauss,Combinatorics,Feedback with Carry Shift Registers,Upper and lower bounds,Mathematics | Journal |
Volume | Issue | ISSN |
abs/1704.01685 | 2 | 1936-2447 |
Citations | PageRank | References |
1 | 0.36 | 14 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yuhua Sun | 1 | 2 | 3.81 |
| Qiang Wang | 2 | 237 | 37.93 |
| Tongjiang Yan | 3 | 87 | 19.48 |