ECC: Do We Need to Count?

ECC: Do We Need to Count? (1999)

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by Jean-Sebastien Coron , Helena Handschuh , David Naccache , École Normale Supérieure , Gemplus Card International , École Normale Supérieure Des Télécommunications

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@MISC{Coron99ecc:do,
    author = {Jean-Sebastien Coron and Helena Handschuh and David Naccache and École Normale Supérieure and Gemplus Card International and École Normale Supérieure Des Télécommunications},
    title = {ECC: Do We Need to Count?},
    year = {1999}
}

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Abstract

A prohibitive barrier faced by elliptic curve users is the difficulty of computing the curves' cardinalities. Despite recent theoretical breakthroughs, point counting still remains very cumbersome and intensively time consuming.

Citations

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1	using L and a number-theoretic algorithm due to Miller - factor
1	use the 3-fork variant of the forking lemma to yield a couple of relations involving the unknown key s: #s + # = 0 mod #(n) and # # s + # # = 0 mod #(n) such that for some polynomial B, which only depends on the machine which presumably performs the exist - finally
1	we show that an algorithm which computes a substitute of s and a multiple of r with significant probability can be turned into an algorithm which computes the proper value of s: Lemma 1. An algorithm A which computes with significant probability a fixedsi - Finally