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Trace Representation of Primitive σ-LFSR Sequences and Its Application |
Zhang Meng; Zeng Guang; Han Wen-bao; He Kai-cheng |
Department of Information Research, Information Engineering University, Zhengzhou 450002, China |
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Abstract σ-LFSR is a kind of word-oriented LFSR with high efficiency and good cryptographic properties, especially suitable for modern processors. It can be used in stream cipher for fast software implementation. But in practicality, primitive σ-LFSR sequences are of the most importance. Firstly, by the iterative relationship of the primitive σ-LFSR sequences and the trace function in finite fields, the explicit expression of primitive σ-LFSR sequences is presented. Therefore the trace representation is gotten; then a sufficient and necessary condition is obtained due to the trace representation. It can be used to check whether a σ-LFSR sequence is primitive or not. They provide the new tool for further research of primitive σ-LFSR sequences.
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Received: 10 January 2008
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