RE: Mersenne: Re: 2^4-1 Factored!

[Aaron Blosser]

It’s when they start producing near instant factors of 1024 to 4096 bit numbers that we’ll have to really think about our current encryption measures…   Even if they reduced the time it took to factor such numbers from millions of years to millions of seconds, the impact on cryptography will be huge.   But I reckon that by then, someone will have thought of some new encryption that would remove the advantage that QC has… something unrelated to factoring large numbers, I’m guessing?  Dunno what that method might be; if I did know, I’d market it and get rich. J   Aaron   -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED]] On Behalf Of [EMAIL PROTECTED] Sent: Thursday, December 20, 2001 2:50 PM To: [EMAIL PROTECTED] Subject: Mersenne: Re: 2^4-1 Factored!   Luke Welsh wrote: >http://www.research.ibm.com/resources/news/20011219_quantum.shtml Interesting...but the QC folks apprently seem to think classical factoring work is frozen in time, viz. their comment about the supposed unfactorizability of 200-digit composites. M727 is larger than 200 digits, and has a smallest prime factor of 98 digits. Of course when QC comes into its own, 200-digit numbers will be factored almost instantly. But we aren't there yet. -Ernst