20220906, 14:58  #1 
Feb 2022
31_{16} Posts 
Integer Factorization as a Service Fair Market Price
I am curious to know, what would be the fair market price to request folks factor integers for you? Earlier this year someone started a thread where they needed help to factor a 512bit RSA key to prove a point to their employer to use bigger size RSA keys for some particular application. An observation that was made multiple times by folks who had the knowhow and computational power to do this task relatively quickly was that there was no incentive for folks to just factor a random integer someone requested. This got me wondering, at what price point would folks feel incentivized to factor integers at various bitsizes.
Say for the following bit sizes: 350bits 400bits 450bits 500bits 512bits 550bts 600bits 
20220906, 15:17  #2  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
37·313 Posts 
Quote:
I haven't done the arithmetic yet but a WAG suggests that I may do them for 50100 EUR/GBP/USD each. 

20220906, 18:19  #3 
"Curtis"
Feb 2005
Riverside, CA
7×13×61 Posts 
The purpose of the factorizations plays a larger role than the cash offered. If client refused to state the purpose for the factorizations, I would personally be rather expensive to hire. If the purpose was clearly legal and somewhat interesting, I might charge 34x the power cost, in the vicinity of $10/machineday.
500 bits is just over a machineday for me (16core machine), around 10kwh of power. 512 bits is about two machinedays, 1820 kwh. 550 bits is just over four times harder than 512, 8090kwh and 810 days. 600 is around 8 times harder than 550, ~700 kwh and 10 weeks. Anything under 500 can be done by anyone smart enough to install linux, copy/paste a git download command from CADO website, and run "make". Hardware requirements are small, like 8 or 12GB memory is the most stringent. A client not smart enough to do those things makes me question why they want factors at all. Last fiddled with by VBCurtis on 20220906 at 18:22 
20220907, 05:40  #4 
Romulan Interpreter
"name field"
Jun 2011
Thailand
3·5·683 Posts 
That would be the costs in electricity and computer parts deprecation, considering the juice prices in my area, dollartobaht exchange rate, the hardware I have, and the stateofthefart* factoring tools I use.
Code:
350 bits  105.4 digits  0.10 USD  less than 15 minutes 400 bits  120.5 digits  0.63 USD  less than 1 hour 450 bits  135.5 digits  4.13 USD  less than 8 hours 500 bits  150.6 digits  31.75 USD  less than 3 days 512 bits  154.2 digits  57.14 USD  less than a week 550 bits  165.6 digits  269.84 USD  less than a month 600 bits  180.7 digits  2174.20 USD  less than 6 months This doesn't include my work, which could cost everything from zero to hero, according to the goal of the factorization. Mostly, I factored for free here around, as the most people on this forum did, when the goal was clear and not smelly. Say, add one or few hundred bucks if it smells, depending on the odor  *stateofthefart means with my favorite tools, which are not necessarily the newest statestateoftheart like CADO (which, by the way, I never used, and I don't know how to use), but the things I know, like Yafu, which is "set and forget", so my work involvement is minimal, or resumes to babysitting, like Paul said. However, larger factorization may need more work, tweaking msieve, use GPU for getting a better poly, whatever fancy things, and may cost higher. Last fiddled with by LaurV on 20220907 at 06:08 Reason: added the number of digits to that table, for clarity, and the time, to be in line with Curtis 
20220907, 07:31  #5 
Dec 2021
29 Posts 
To throw another opinion into the hat, if I decided to offer this there would likely be a rather steep increase in price around 512 bit cofactors...

20220907, 23:36  #7  
"Curtis"
Feb 2005
Riverside, CA
7·13·61 Posts 
Quote:
RSA250 was factored in under 3000 CPUyears. Converting to my previous reply's units, that's around 100 machine years (using a 4+ghz Ryzen rather than 2.1 ghz Xeon used by the team that factored RSA240 and RSA250). Each ten digits is roughly 4x more computation, so RSA260 might take 400 machineyears, RSA270 1600 machineyears, RSA280 6400 myr, RSA290 26000 myr, RSA300 100k machine years, RSA1024 350k machine years. All of those cycles require 192GB ram per sieve process, so let's triple the hourly cost to account for the workstationgrade hardware that takes. About 20% of those cycles (filtering and matrix solving) require bigbig memory, let's again double the hourly cost for those cycles. My personal machineyear costs $3000 or so. Let's say $10k per machineyear for the sieving, at 300k years: That's around $3B. Another 50k years of postprocessing at $20k per machineyear is $1B. So, let's say $4 billion or so at the high end. However, my machineyear costs were only about 1/3 electricity. If we're talking millions or billions, my time is now a salary rather than an hourly rate and relatively negligible cost, and hardware rent is close to zero (AWS rental rates are close to my personal cost of power, including the power use). So, we can cut the cost estimate by 2/3rds, to $1.3B if we can rent machines with sufficient RAM. A more optimistic estimate for difficulty scaling is 3x per ten digits, let's say 10x per 20 digits: Now RSA270 is 1000 machineyears, RSA290 is 10000, and RSA308 is a bit under 100k machineyears. That puts the optimistic estimate around $400M, a sum feasible for a government to spend in the unlikely case a useful foreign gvmt secret was "protected" by RSA1024. tl;dr: $400M to $4B. 

20220908, 01:15  #8 
Aug 2002
8535_{10} Posts 
Just have them pay ยฝ up front!

20220908, 01:46  #9 
"6800 descendent"
Feb 2005
Colorado
2·5·73 Posts 

20220908, 03:21  #10 
6809 > 6502
"""""""""""""""""""
Aug 2003
101ร103 Posts
2A32_{16} Posts 

20220908, 04:24  #11 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
2^{4}×5×83 Posts 

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