On the Deterministic Complexity of Factoring Polynomials
On the Deterministic Complexity of Factoring Polynomials
复制标题
关于因式分解多项式的确定性复杂性
DOI：
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发表时间：
2001
影响因子：
0.7
通讯作者：
Shuhong Gao
中科院分区：
文献类型：
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作者：
Shuhong Gao
该论文的重点是假设扩展的Riemann假设（ERH），分解多项式的分解多项式的确定性复杂性。通过Berlekamp（1967，1970）和Zassenbaus（1969）的作品，一般问题在多项式时间内决定性地减少了在素数FP上找到任何无方形和完全分裂多项式的适当因素。算法旨在拆分此类多项式。事实证明，如果其根部不满足某种严格的条件（称为超平衡），则可以在多项式时间内确定性地找到多项式的适当因素。猜想超级平衡的多项式不存在。
The paper focuses on the deterministic complexity of factoring polynomials over finite fields assuming the extended Riemann hypothesis (ERH). By the works of Berlekamp (1967, 1970) and Zassenbaus (1969), the general problem reduces deterministically in polynomial time to finding a proper factor of any squarefree and completely splitting polynomial over a prime field Fp. Algorithms are designed to split such polynomials. It is proved that a proper factor of a polynomial can be found deterministically in polynomial time, under ERH, if its roots do not satisfy some stringent condition, called super square balanced. It is conjectured that super square balanced polynomials do not exist.