Binary Threshold Sequences Derived from Carmichael Quotients with Even Numbers Modulus

Chenhuang WU; Zhixiong CHEN; Xiaoni DU

doi:10.1587/transfun.E95.A.1197

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Binary Threshold Sequences Derived from Carmichael Quotients with Even Numbers Modulus

Chenhuang WU, Zhixiong CHEN, Xiaoni DU

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Keywords: Fermat quotients, Carmichael quotients, finite fields, binary threshold sequences, linear complexity

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2012 Volume E95.A Issue 7 Pages 1197-1199

DOI https://doi.org/10.1587/transfun.E95.A.1197

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Abstract

We define a family of 2^e+1-periodic binary threshold sequences and a family of p²-periodic binary threshold sequences by using Carmichael quotients modulo 2^e(e>2) and 2p (p is an odd prime), respectively. These are extensions of the construction derived from Fermat quotients modulo an odd prime in our earlier work. We determine exact values of the linear complexity, which are larger than half of the period. For cryptographic purpose, the linear complexities of the sequences in this letter are of desired values.

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