Abstract:
The linear complexity of a periodic sequence over {\hbox{GF}}(p^m) plays an important role in cryptography and comm...Show MoreMetadata
Abstract:
The linear complexity of a periodic sequence over <formula formulatype="inline"> <tex>{\hbox{GF}}(p^m)</tex></formula> plays an important role in cryptography and communication (see Menezes, van Oorschort, and Vanstone, <emphasis>Handbook of Applied Cryptography. Boca Raton, FL: CRC, 1997</emphasis>). In this correspondence, we prove a result which reduces the computation of the linear complexity and minimal connection polynomial of a period un sequence over <formula formulatype="inline"> <tex>{\hbox{GF}}(p^m)</tex></formula> to the computation of the linear complexities and minimal connection polynomials of <formula formulatype="inline"><tex>u</tex> </formula> period <formula formulatype="inline"><tex>n</tex></formula> sequences. The conditions <formula formulatype="inline"><tex>u\,\vert\,p^m-1</tex> </formula> and <formula formulatype="inline"><tex>{\rm gcd}(n,p^m-1)=1</tex> </formula> are required for the result to hold. Some applications of this reduction in fast algorithms to determine the linear complexities and minimal connection polynomials of sequences over <formula formulatype="inline"><tex>{\hbox{GF}}(p^m)</tex> </formula> are presented.
Published in: IEEE Transactions on Information Theory ( Volume: 52, Issue: 12, December 2006)
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