Reducing the Computation of Linear Complexities of Periodic Sequences over $GF(p^m)$

Details Reducing the Computation of Linear Complexities of Periodic Sequences over $GF(p^m)$ Reducing the Computation of Linear Complexities of Periodic Sequences over $GF(p^m)$

2006-07-24

arxiv.org/abs/cs/0607104v2

Computer Science

Cryptography and Security

10 pages. To appear in IEEE Transactions on Innformation Theory

Scientific paper

The linear complexity of a periodic sequence over $GF(p^m)$ plays an important role in cryptography and communication [12]. 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 $GF(p^m)$ to the computation of the linear complexities and minimal connection polynomials of $u$ period $n$ sequences. The conditions $u|p^m-1$ and $\gcd(n,p^m-1)=1$ 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 $GF(p^m)$ are presented.

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