有限域上多项式乘法的乘法复杂度

28th Annual Symposium on Foundations of Computer Science (sfcs 1987) Pub Date : 1987-10-12 DOI:10.1145/58562.59306

M. Kaminski, N. Bshouty

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引用次数: 30

摘要

设Mq(n)表示用双线性算法在q元域上计算两个n次多项式乘积的系数所需的乘法次数。结果表明，Mq(n)≥3n - o(n)。特别是，如果q/2≪n≤q + 1，我们建立紧密界Mq(n) = 3n + 1 -⌊q/2⌋。我们使用的技术也可以应用于分析多项式的乘法和模多项式的算法。

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Multiplicative complexity of polynomial multiplication over finite fields

Let Mq(n) denote the number of multiplications required to compute the coefficients of the product of two polynomials of degree n over a q-element field by means of bilinear algorithms. It is shown that Mq(n) ≥ 3n - o(n). In particular, if q/2 ≪ n ≤ q + 1, we establish the tight bound Mq(n) = 3n + 1 - ⌊q/2⌋. The technique we use can be applied to analysis of algorithms for multiplication of polynomials modulo a polynomial as well.

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28th Annual Symposium on Foundations of Computer Science (sfcs 1987)

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