307 digit number factored

[James A. Donald]

     --
travis+ml-cryptography at subspacefield.org wrote:
 > AFAIK, the only advantage of ECC is that the keys are
 > shorter. The disadvantage is that it isn't as well
 > studied.

On past performance, elliptic curves are safer than
integers.  From time to time, integer based asymmetric
encryption is abruptly and surprisingly weakened by
advances in discrete log algorithms.  This is just not
happening with elliptic curves.

The cost of computing power is going down faster than
the cost of communication.  The size of sufficiently
safe asymmetric encryption based on integers is growing
considerably faster than the size of sufficiently safe
asymmetric encryption based on elliptic curves.

Thus the advantage of elliptic curve encryption
continually increases, will become overwhelming in the
near future - and a large part of that continually
increasing advantage comes from unpredictable
improvements in factoring and discrete log over the
integers.

My intuition is that because elliptic curves are
considerably less orderly than the integers, there is
less scope for discovering fast discrete log methods. We
are continually discovering improvements to finding
discrete logs over the integers.  It has been a long
time since any such has been discovered for elliptic
curves, long enough to give a plausible hope that no
further such will ever be discovered.


     --digsig
          James A. Donald
      6YeGpsZR+nOTh/cGwvITnSR3TdzclVpR0+pr3YYQdkG
      ibAQXQ+Yoy5neOvRwKJwdxVLDGSPwTxKobkv566h
      4khPsLmyqlil/F6sx2n1q9mtb65W8RMcWyqxregOo

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