[Cryptography] Why is ECC secure?

Tony Arcieri bascule at gmail.com
Fri May 29 20:21:24 EDT 2015

On Fri, May 29, 2015 at 12:26 PM, Bill Cox <waywardgeek at gmail.com> wrote:

> Why do we believe this is secure, other than the fact that in EEC's short
> life, no one has cracked it?  Compared to DLP and integer factorization, I
> doubt many people have tried.

For what it's worth, you can say the same thing about factorization. The
only reason RSA is secure is because factoring large numbers is generally
considered a hard problem.

Index calculus attacks aside, integer factorization and DLP have some
interesting "isomorphisms" (for lack of a better term). For example,
Pollard's rho is the best algorithm (in different forms) for solving both


My understanding is that both problems can be reduced to the Hidden
Subgroup Problem:


There's been a decent amount of research into solving DLP. Certainly it's a
problem that humanity has spent less time working on than factorization,
but so far there hasn't been any particularly interesting breakthroughs.

Tony Arcieri
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