Anyone have an ETA for M1061? - Page 3

Stargate38 · 2012-04-06, 23:11

I figured out that it has about the same difficulty as a GNFS 250-270. That's almost 27 times as hard as RSA-768. Is that correct or did I miscalculate?

R.D. Silverman · 2012-04-06, 23:36

Quote:

Originally Posted by Stargate38

I figured out that it has about the same difficulty as a GNFS 250-270. That's almost 27 times as hard as RSA-768. Is that correct or did I miscalculate?

The latter.

Stargate38 · 2012-04-07, 00:00

Oh! Where did I mess up?

science_man_88 · 2012-04-07, 01:03

Quote:

Originally Posted by Stargate38

Oh! Where did I mess up?

I think it's the fact that if PARI lead me correctly it has 320 digits not 270.

Stargate38 · 2012-04-07, 01:12

I was saying how easy a SNFS320 is compared to a GNFS232 like RSA-768. They differ by 88 digits, yet the difficulty ratio is only about 81. I hope that is correct. I don't know how to calculate the SNFS factoring time, given only the difficulty in digits. I do know that there is a factor of about 3 for a 10-digit increase when using GNFS.

science_man_88 · 2012-04-07, 01:22

Quote:

Originally Posted by Stargate38

I was saying how easy a SNFS320 is compared to a GNFS232 like RSA-768. They differ by 88 digits, yet the difficulty ratio is only about 81. I hope that is correct. I don't know how to calculate the SNFS factoring time, given only the difficulty in digits. I do know that there is a factor of about 3 for a 10-digit increase when using GNFS.

yeah that means being off by 50 digits = 3^5 = 81*3 = 243 times as hard as you thought.

Stargate38 · 2012-04-07, 01:28

I know with GNFS the factoring time is 3 times bigger with every 10 digits, but what is the rate for SNFS? Is it the same?

science_man_88 · 2012-04-07, 01:29

Quote:

Originally Posted by Stargate38

I know with GNFS the factoring time is 3 times bigger with every 10 digits, but what is the rate for SNFS? Is it the same?

that I don't know because I only know what the letters mean.

Stargate38 · 2012-04-07, 01:54

I hope I got this right. I used the factor of 3 per 10-digit increase rule for GNFS:

Using GNFS, RSA-1024 would take 3^{((308-100)/10)}*5 hours on a dual core and RSA-2048 would take 3^{((617-100)/10)}*5 hours, which is ~1229277376184679090360 years. I hope quantum computers come quick or we may be waiting for 1.2 sextillion years for the factors of RSA-2048. In comparison, RSA 1024 would take ~1990173 years. That means a lot when you compare it with RSA-768. I read that 232 digits take about 3000 CPU years, but I ended up with 1820 CPU years.

bdodson · 2012-04-07, 02:11

Quote:

Originally Posted by Stargate38

I know with GNFS the factoring time is 3 times bigger with every 10 digits, but what is the rate for SNFS? Is it the same?

Does the term "sub-exponential growth" mean anything to you? -bdodson

CRGreathouse · 2012-04-07, 05:33

Quote:

Originally Posted by bdodson

Does the term "sub-exponential growth" mean anything to you? -bdodson

Oh, be nice. It's useful to approximate the time needed for factoring by piecewise exponentials.

Quote:

Originally Posted by Stargate38

I know with GNFS the factoring time is 3 times bigger with every 10 digits, but what is the rate for SNFS? Is it the same?

GNFS has that behavior around 195-205 digits by the standard formula (setting o(1) = 0, which is a bit generous); using the same in the SNFS formula gives a factor of 2.4 rather than 3. SNFS is, in general, somewhat less sensitive to the size of the number than GNFS (though obviously both depend on it).

2012-04-07, 01:12	#27
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2³×83 Posts	I was saying how easy a SNFS320 is compared to a GNFS232 like RSA-768. They differ by 88 digits, yet the difficulty ratio is only about 81. I hope that is correct. I don't know how to calculate the SNFS factoring time, given only the difficulty in digits. I do know that there is a factor of about 3 for a 10-digit increase when using GNFS. Last fiddled with by Stargate38 on 2012-04-07 at 01:14

2012-04-07, 01:54	#31
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2³×83 Posts	Just comparing some other hard numbers. I hope I got this right. I used the factor of 3 per 10-digit increase rule for GNFS: Using GNFS, RSA-1024 would take 3^{((308-100)/10)}5 hours on a dual core and RSA-2048 would take 3^{((617-100)/10)}5 hours, which is ~1229277376184679090360 years. I hope quantum computers come quick or we may be waiting for 1.2 sextillion years for the factors of RSA-2048. In comparison, RSA 1024 would take ~1990173 years. That means a lot when you compare it with RSA-768. I read that 232 digits take about 3000 CPU years, but I ended up with 1820 CPU years. Last fiddled with by Stargate38 on 2012-04-07 at 01:58

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2012-04-06, 23:11	#23
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2³×83 Posts	I figured out that it has about the same difficulty as a GNFS 250-270. That's almost 27 times as hard as RSA-768. Is that correct or did I miscalculate?

2012-04-07, 00:00	#25
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 2³×83 Posts	Oh! Where did I mess up?

2012-04-07, 01:28	#29
Stargate38 "Daniel Jackson" May 2011 14285714285714285714 298₁₆ Posts	I know with GNFS the factoring time is 3 times bigger with every 10 digits, but what is the rate for SNFS? Is it the same?