我们可以通过表示打败𝔽p2上ECDLP的平方根界限吗?

IF 0.5 Q4 COMPUTER SCIENCE, THEORY & METHODS Journal of Mathematical Cryptology Pub Date : 2020-01-01 DOI:10.1515/jmc-2019-0025

Claire Delaplace, Alexander May

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引用次数: 0

摘要

摘要给出了求解某二次域上椭圆曲线离散对数(ECDLP)的一种4-列表算法𝔽p2。利用表示技术，我们将ECDLP简化为一个多元多项式零检验问题。我们使用二元多项式多重求值解决了这个问题，为ECDLP提供了一个p1.314算法。虽然这不如Pollard的Rho算法的平方根(字段大小)复杂度为 (p)，但它仍然有可能为ECDLP打开一条通往0 (p)算法的路径，因为所有涉及的列表的大小都小到p34, $\begin{array}{} p^{\frac 3 4}, \end{array}$只是它们的计算成本太高。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Can we Beat the Square Root Bound for ECDLP over 𝔽p2 via Representation?

Abstract We give a 4-list algorithm for solving the Elliptic Curve Discrete Logarithm (ECDLP) over some quadratic field 𝔽p2. Using the representation technique, we reduce ECDLP to a multivariate polynomial zero testing problem. Our solution of this problem using bivariate polynomial multi-evaluation yields a p1.314-algorithm for ECDLP. While this is inferior to Pollard’s Rho algorithm with square root (in the field size) complexity 𝓞(p), it still has the potential to open a path to an o(p)-algorithm for ECDLP, since all involved lists are of size as small as p34, $\begin{array}{} p^{\frac 3 4}, \end{array}$ only their computation is yet too costly.

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