## 307-Digit Number Factored

We have a new factoring record: 307 digits. It's a special number -- 2^1039 - 1 -- but the techniques can be generalized:

Is the writing on the wall for 1024-bit encryption" "The answer to that question is an unqualified yes," says Lenstra. For the moment the standard is still secure, because it is much more difficult to factor a number made up of two huge prime numbers, such as an RSA number, than it is to factor a number like this one that has a special mathematical form. But the clock is definitely ticking. "Last time, it took nine years for us to generalize from a special to a non-special hard-to factor number (155 digits). I won't make predictions, but let's just say it might be a good idea to stay tuned."

I hope RSA applications would have moved away from 1024-bit security years ago, but for those who haven't yet: wake up.

EDITED TO ADD (5/21): That's 1023 bits. (I should have said that.)

Posted on May 21, 2007 at 10:26 AM • 51 Comments

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