[Cryptography] Attacking Elliptic Curve Crypto on the infinity symbol

covariant covariant at i2pmail.org
Sat Oct 24 05:16:04 EDT 2015


On 10/23/2015 03:03 AM, Bill Cox wrote:If we can compute the
> following integral, mod p, we can break ECC in this case (-1 is not a
> square mod p, or a different p would have been used), and likely gain
> insight into how to crack the general ECC case:
> 
>     arcLength(x) = integrate 1/sqrt(1  - t^4) dt from 0 to x
> 
It does not make a lot of sense to define integration modulo p, and if
you did you would not get the same properties that you would get from
integration over a continuous space.
Generalizations (such as
http://homepages.math.uic.edu/~kauffman/DCalc.pdf) have been proposed,
and further generalizations might make sense.

More fundamentally, you use concepts such as "closest" and "length"
freely, even in the absence of a well-defined distance metric.

> All we have to do is compute that simple arc-length integral.  If we can
> do that, we can reveal m.  However, no one knows how to do this, SFAIK. 

That's because it's not clear what you actually want to compute. You say
you want an integral or a length, without actually defining what you
mean by any of those two concepts.
-------------- next part --------------
A non-text attachment was scrubbed...
Name: 0x5566188E.asc
Type: application/pgp-keys
Size: 3104 bytes
Desc: not available
URL: <http://www.metzdowd.com/pipermail/cryptography/attachments/20151024/6ca44ed5/attachment.key>
-------------- next part --------------
A non-text attachment was scrubbed...
Name: signature.asc
Type: application/pgp-signature
Size: 819 bytes
Desc: OpenPGP digital signature
URL: <http://www.metzdowd.com/pipermail/cryptography/attachments/20151024/6ca44ed5/attachment.sig>


More information about the cryptography mailing list