摘要翻译:
我们构造了两个新的有限域扩张基族。第一族中的基,即所谓的椭圆基,不是很正规的基,但它们允许快速的Frobenius幂运算,同时保留稀疏的乘法公式。在第二族基中,所谓正规椭圆基是正规基,允许快速(准线性)算术。我们证明了所有的扩展都承认这类模型。
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英文标题:
《Elliptic periods for finite fields》
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作者:
Jean-Marc Couveignes and Reynald Lercier
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最新提交年份:
2008
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分类信息:
一级分类:Mathematics 数学
二级分类:Number Theory 数论
分类描述:Prime numbers, diophantine equations, analytic number theory, algebraic number theory, arithmetic geometry, Galois theory
素数,丢番图方程,解析数论,代数数论,算术几何,伽罗瓦理论
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一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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英文摘要:
We construct two new families of basis for finite field extensions. Basis in the first family, the so-called elliptic basis, are not quite normal basis, but they allow very fast Frobenius exponentiation while preserving sparse multiplication formulas. Basis in the second family, the so-called normal elliptic basis are normal basis and allow fast (quasi linear) arithmetic. We prove that all extensions admit models of this kind.
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PDF链接:
https://arxiv.org/pdf/0802.0165