Some relations between Semaev's summation polynomials and Stange's elliptic nets

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MI: Global COE Program Education-and-Research Hub for Mathematics-for-IndustryグローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」There are two decision methods for the decomposition of multiple points on an elliptic curve, one based on Semaev's summation polynomials and the other based on Stange's elliptic nets. This paper presents some relations between these two methods. Using these relations, we show that an index calculus attack for the elliptic curve discrete logarithm problem (ECDLP) over extension fields via an elliptic net is equivalent to such an attack via Semaev's summation polynomials.
2011-04-04