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From: "Gordon Mohr" <gojomo@usa.net>
To: <fork@spamassassin.taint.org>
References: <20020816204431.ADEF4C44E@argote.ch>
Subject: Re: Elliptic Curve Point Counting, made easy
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Date: Fri, 16 Aug 2002 15:20:48 -0700

Robert Harley writes:
> Here are some numbers with the new algorithm for counting points on
> elliptic curves (over fields of characteristic 2).
> 
> In 1998, Reynald Lercier set a record at 1663 bits in 330 days of CPU
> on 266 MHz Alphas.  In 1999, Frederik Vercauteren set a record at 1999
> bits in 65 days of CPU on 400 MHz PCs.
> 
> I've been working on the problem since then.  These were measured just
> now on Rajit's 750 MHz Alpha:
> 
>   1009 bits:
>     Lift:  4.8 s + 0.64 s precomputation.
>     Norm:  2.6 s + 0.31 s precomputation.
> 
>   1663 bits:
>     Lift: 18.5 s + 2.1 s precomputation.
>     Norm:  7.0 s + 1.9 s precomputation.
> 
>   1999 bits:
>     Lift: 29.4 s + 3.6 s precomputation.
>     Norm: 16.6 s + 3.4 s precomputation.
> 
>   15013 bits:
>     Lift: 1 h 39 m + 13 m precomputation
>     Norm: 39 m + 1 h 41 m precomputation

Not knowing one whit about elliptic curve math, can you provide 
some expert interpretation of these results?

It looks like the old record for, say, 199 bits, has been
blown out of the water by a factor of ~100,000.

Does this mean that Eliptic Curve encryption is
now easily breakable? Or faster than before with
no loss in strength? Or stronger?

Raw bits are OK, cooked bits are better.

- Gordon


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