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

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 (0)

by finally

Venue:

GCD(#,# # ) # B; from

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ECC: Do We Need to Count?

by Jean-Sebastien Coron, Helena Handschuh, David Naccache, École Normale Supérieure, Gemplus Card International, École Normale Supérieure Des Télécommunications , 1999

"... 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. ..."

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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.

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 (0)

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ECC: Do We Need to Count?