A next big thing

jasonp · 2012-07-23, 10:10

So what number is everyone going to complain about being unfactored after this one? We'll need a candidate that can support at least five years of complaining, and preferably much more.

henryzz · 2012-07-23, 10:43

Quote:

Originally Posted by jasonp

So what number is everyone going to complain about being unfactored after this one? We'll need a candidate that can support at least five years of complaining, and preferably much more.

How about M1277? After M1061 is factored it will be the smallest exponent without any factor. It is 385 digits which is hopefully large enough.
When do you guess this will be factored?

Raman · 2012-07-23, 10:43

Quote:

Originally Posted by jasonp

So what number is everyone going to claim about being unfactored after this one? We'll need a candidate that can support at least five years of sieving, and preferably much more.

What complain? It should be replaced by "be curious". Then, I will go after 2,1123+ c338 please! -> For supporting atleast five years of sieving

Not that curious like such as for 2,1061-c320
which going underwent sieving for one year, linear algebra for two months to be precise enough
I listed It since you asked for an opinion / a suggestion only actually
^{[SUP][SUP][SUP][SUP][SUP]Much easier candidates being listed below as follows

L1277 L1279 13,269- 2,1193- 7,379± 2,929- 2,947± 2,991± 2,1117- [STRIKE]6,299- 6,298+

[/STRIKE]}[/SUP][/SUP][/SUP][/SUP][/SUP]^{[SUP][SUP][SUP][SUP][SUP][STRIKE][COLOR=White] 2,1123+ L1249 3, 607+[/COLOR][/STRIKE]}[/SUP][/SUP][/SUP][/SUP][/SUP]

xilman · 2012-07-23, 14:58

Quote:

Originally Posted by jasonp

So what number is everyone going to complain about being unfactored after this one? We'll need a candidate that can support at least five years of complaining, and preferably much more.

Surely the answer is obvious: RSA-1024

LaurV · 2012-07-23, 15:50

Quote:

Originally Posted by xilman

Surely the answer is obvious: RSA-1024

Now to show you that I have learned my lesson from the past: M1061 was a SNFS job, but I beleive RSA numbers are not SNFS-able, so that would be a GNFS job, and it may be more complex then the previous suggested by others. Am I right? (I would prefer RSA numbers too!)

retina · 2012-07-23, 16:01

Quote:

Originally Posted by LaurV

Now to show you that I have learned my lesson from the past: M1061 was a SNFS job, but I beleive RSA numbers are not SNFS-able, so that would be a GNFS job, and it may be more complex then the previous suggested by others. Am I right? (I would prefer RSA numbers too!)

Yeah, you are pretty much correct there.

But as to the suggestion for RSA-1024: It should be easy if we use LaurV's method of getting the list of all primes at around the 512-bit level. Since those RSA numbers are guaranteed to be constructed with approximately equal sized primes then half our work has already been done by eliminating all those pesky smaller primes before we even start!

Oh, and I think this hasn't been asked yet so I'll go ahead and ask on behalf of everyone else:
Are we there yet?

LaurV · 2012-07-23, 16:36

Hahaha! Ten points retina! (I didn't expect that!)

jasonp · 2012-07-23, 17:21

I thought of RSA1024, but the factorization of RSA1024 is not holding up some momentous factor table completion accomplishment or other. Of course M1061 isn't either, but its replacement needs to aspire to a higher purpose than 'all your crypto are belong to us'

xilman · 2012-07-23, 17:32

Quote:

Originally Posted by jasonp

I thought of RSA1024, but the factorization of RSA1024 is not holding up some momentous factor table completion accomplishment or other. Of course M1061 isn't either, but its replacement needs to aspire to a higher purpose than 'all your crypto are belong to us'

There's serious money riding on a factorization of RSA-1024. I've a $10 bet with RDS that the first hard kilobit factorization will be completed before the end of the decade.

Think if all the bragging rights too. Kilobit RSA protects one hell of a lot of money in the Real World. Suddenly, a lot of people are going to get seriously concerned.

Paul

chalsall · 2012-07-23, 17:44

Quote:

Originally Posted by xilman

Think if all the bragging rights too.

They have better things to do than brag.

Quote:

Originally Posted by xilman

RSA protects one hell of a lot of money in the Real World. Suddenly, a lot of people are going to get seriously concerned.

They already are.

xilman · 2012-07-23, 17:50

Quote:

Originally Posted by chalsall

They have better things to do than brag.

They already are.

And quite right too, IMAO.

RSA has passed its use-by date. There are better alternatives readily available. Unfortunately, there is also an immense retro-fitting exercise to carry out.

2012-07-23, 10:10	#1
jasonp Tribal Bullet Oct 2004 DE3₁₆ Posts	A next big thing So what number is everyone going to complain about being unfactored after this one? We'll need a candidate that can support at least five years of complaining, and preferably much more.

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jasonp Tribal Bullet Oct 2004 3²·5·79 Posts	I thought of RSA1024, but the factorization of RSA1024 is not holding up some momentous factor table completion accomplishment or other. Of course M1061 isn't either, but its replacement needs to aspire to a higher purpose than 'all your crypto are belong to us'