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- Title
Linear complexity of Legendre‐polynomial quotients.
- Authors
Chen, Zhixiong
- Abstract
Let p be an odd prime and w<p be a positive integer. The authors[AQ ID=Q1]continue to investigate the binary sequence (fu) over {0,1} defined from polynomial quotients by (uw−uwp)/p modulo p. The (fu) is generated in terms of (−1)fu which equals to the Legendre symbol of (uw−uwp)/p(modp) for u ≥ 0. In an earlier work, the linear complexity of (fu) was determined for w=p−1 (i.e. the case of Fermat quotients) under the assumption of 2p−1⧸≡1(modp2). In this work, they develop a naive trick to calculate all possible values on the linear complexity of (fu) for all 1≤w<p−1 under the same assumption. They also state that the case of larger w(≥p) can be reduced to that of 0≤w≤p−1. So far, the linear complexity is almost determined for all kinds of Legendre‐polynomial quotients.
- Publication
IET Information Security (Wiley-Blackwell), 2018, Vol 12, Issue 5, p414
- ISSN
1751-8709
- Publication type
Article
- DOI
10.1049/iet-ifs.2017.0307