Abstract
We introduce a fast algorithm for determining the linear complexity and the minimal polynomial of a sequence with period p n over GF(q) , where p is an odd prime, q is a prime and a primitive root modulo p 2; and its two generalized algorithms. One is the algorithm for determining the linear complexity and the minimal polynomial of a sequence with period p mqn over GF(q), the other is the algorithm for determining the k-error linear complexity of a sequence with period p n over GF(q), where p is an odd prime, q is a prime and a primitive root modulo p 2. The algorithm for determining the linear complexity and the minimal polynomial of a sequence with period 2p n over GF(q) is also introduced. where p and q are odd prime, and q is a primitive root (mod p 2). These algorithms uses the fact that in these case the factorization of x Nā1 is especially simple for N= p n, 2p n, p nqm.
The work was supported in part by 973 Project(G1999035804) and the Natural Science Foundation of China under Grant 60172015 and 60073051.
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Xiao, G., Wei, S. (2002). Fast Algorithms for Determining the Linear Complexity of Period Sequences. In: Menezes, A., Sarkar, P. (eds) Progress in Cryptology ā INDOCRYPT 2002. INDOCRYPT 2002. Lecture Notes in Computer Science, vol 2551. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36231-2_2
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DOI: https://doi.org/10.1007/3-540-36231-2_2
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