-
[show abstract]
[hide abstract]
ABSTRACT: In this paper, the autocorrelations of l-sequences with prime connection integer are discussed. Let a\underline{a} be an l-sequence with connection integer p and period T = p − 1, we show that the autocorrelation Ca(t)C_{\underline{a}}(\tau ) of a\underline{a} with shift τ satisfies:
| Ca(t)-\fracp-1p2\undersetc=1\oversetp-1åtan( \fracpc2-tp) tan( \fracpcp) | = O(ln2p). \left\vert C_{\underline{a}}(\tau )-\frac{p-1}{p^{2}}\cdot \underset{c=1}{ \overset{p-1}{\sum }}\tan \left( \frac{\pi c2^{-\tau }}{p}\right) \tan \left( \frac{\pi c}{p}\right) \right\vert =O(\ln ^{2}p).
Thus by calculating this triangular sum, an estimate of Ca (t)C_{\underline{a} }(\tau ) can be obtained. Particularly, for any shift τ with 2-t(modp)=(p-3)/2 2^{-\tau }(\mbox{mod}\ p)=(p-3)/2 or (p+3)/2 (p+3)/2, the autocorrelation C a(t)C_{ \underline{a}}(\tau ) of a\underline{a} with shift τ satisfies C a(t)=O(ln2p)C_{ \underline{a}}(\tau )=O(\ln ^{2}p), thus when p is sufficiently large, the autocorrelation is low. Such result also holds for the decimations of l-sequences.
Cryptography and Communications 04/2012; 1(2):207-223.
-
Des. Codes Cryptography. 01/2012; 62:313-321.
-
Cryptography and Communications. 01/2009; 1:207-223.
-
[show abstract]
[hide abstract]
ABSTRACT: For an odd prime number p and positive integer e, let a{\underline{a}} be an l-sequence with connection integer p
e
. Goresky and Klapper conjectured that when p
e
∉{5,9,11,13}, all decimations of a{\underline{a}} are cyclically distinct. For any primitive sequence u{\underline{u}} of order n over ℤ/(p
e
), call u(mod;2){\underline{u}}(\rm mod;2) a generalized l-sequence. In this article, we show that almost all decimations of any generalized l-sequence are also cyclically distinct.
KeywordsFeedback-with-carry shift registers (FCSRs)-
l-sequences-generalized l-sequences-2-adic numbers-integer residue ring-primitive sequences
09/2006: pages 313-322;
-
[show abstract]
[hide abstract]
ABSTRACT: Let alowbar be an l-sequence generated by a feedback-with-carry shift register with connection integer p<sup>e</sup>, where p is an odd prime and eges1. Goresky and Klapper conjectured that when p<sup>e </sup>notin{5,9,11,13}, all decimations of alowbar are cyclically distinct. When e=1 and p>13, they showed that the set of distinct decimations is large and, in some cases, all decimations are distinct. In this article, we further show that when eges2 and p<sup>e</sup>ne9, all decimations of alowbar are also cyclically distinct
IEEE Transactions on Information Theory 09/2006; · 3.01 Impact Factor
-
SIAM J. Discrete Math. 01/2006; 20:568-577.
-
Sequences and Their Applications - SETA 2006, 4th International Conference, Beijing, China, September 24-28, 2006, Proceedings; 01/2006
