2009 Reports : Cryptology ePrint Archive Forum

Discussion forum for Cryptology ePrint Archive reports posted in 2009.
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2009/638

Posted by: **addyme** (IP Logged)

Date: 02 January 2010 10:33

title: Reducing Elliptic Curve Logarithm to Logarithm in a Finite Field $\mathbb{F}_q$ for Some Orders

The authors are proposing an ingenious method to transform ECDLP to DLP. I was attracted and excited. Anyhow, it seems too good to believe.

Suppose large prime integer $N$ and $#E(F_q)=q+1-t=mN$. ECDLP in $N$-torsion subgroup is considered.

Notice that $q-1|q^2-(t-1)^2$ implies $q-1|mNt$.

Two cases follow:

(1) $N |q-1$, then Tate pairing works for such transformation.

(2) $N \nmid q-1$, then $q-1|mt$, which disables newly proposed algorithm in eprint2009/638.

Unfortunately, it gives no new information than available pairings.

The authors are proposing an ingenious method to transform ECDLP to DLP. I was attracted and excited. Anyhow, it seems too good to believe.

Suppose large prime integer $N$ and $#E(F_q)=q+1-t=mN$. ECDLP in $N$-torsion subgroup is considered.

Notice that $q-1|q^2-(t-1)^2$ implies $q-1|mNt$.

Two cases follow:

(1) $N |q-1$, then Tate pairing works for such transformation.

(2) $N \nmid q-1$, then $q-1|mt$, which disables newly proposed algorithm in eprint2009/638.

Unfortunately, it gives no new information than available pairings.

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