20200611, 21:37  #89 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2192_{16} Posts 
What about having known folks, like select forumites, mods, or other well trusted users do some of that as part of their routine work? If one of my machines gets 1 hour of work to verify once a week with a 1 week max turnaround (24 hours nominal), that would be no burden. It would have to jump to the top of the worktodo.

20200611, 22:39  #90 
"Mike"
Aug 2002
1111000001011_{2} Posts 

20200611, 23:33  #91  
"Mihai Preda"
Apr 2015
29·41 Posts 
Quote:
The verification effort with power==10 is (a bit more than) 1/1024 of one PRP test. So to verify 500 PRP tests per day, the load would be about halfaPRPtest per day. This is a bit too much for a single CPU. I think this is doable by either two good CPUs, or by a single GPU. Last fiddled with by preda on 20200611 at 23:36 

20200612, 20:00  #92  
P90 years forever!
Aug 2002
Yeehaw, FL
7·1,021 Posts 
Quote:
I was about to comment "how do we know the verifier did his work?", but I see that you've already come up with a plan for this. On the save file format, my only comment is a dislike "Endian" formats. Can we make the residues E/8+1 bytes from MSB to LSB? 

20200613, 00:05  #93 
"Mihai Preda"
Apr 2015
29·41 Posts 
I'm not against using bytes, but to me it seems more natural to order LSBtoMSB. And the res64 is nicely aligned at 0. And the "LSBtoMSB bytes" just so happens to convert very simply to/from the internal format on a LE arch, which is pretty much all of them now. Is there a reason for the reverse order?

20200613, 01:41  #94 
P90 years forever!
Aug 2002
Yeehaw, FL
7·1,021 Posts 

20200613, 03:40  #95 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
5^{2}·229 Posts 
If it was a vote then I'd vote for LSB at the lowest address.
It just makes sense that way. 
20200613, 17:00  #96  
P90 years forever!
Aug 2002
Yeehaw, FL
7·1,021 Posts 
Quote:
Examples: M1234567, M4321/8768767, 653*3^12345615 We need a file naming scheme. I've not done any research, but suggest a .proof or .vdf extension. So for a Mersenne number, Mexponent.proof. For a Mersenne cofactor, maybe Mexponent_cofactor.proof or Mexponent_number_known_factors.proof. I'll come up with something for the more general (k,b,n,c) case. 

20200613, 17:57  #97  
P90 years forever!
Aug 2002
Yeehaw, FL
7·1,021 Posts 
Quote:
I believe we can reduce the space cost considerably. We are saving 2^power residues because we cannot know the values of h0, h1, h2, h3 ... until the PRP completes. In the academic paper, this is because the author and the prover cannot communicate in advance. We can! I propose the h values be predetermined by the some formula agreement. The author still has no ability to select the h values, thus the proof is still safe from fakery. Here's one proposal: h0 = sha256("We love PRP proofs"  exponent). h1 = sha256(h0  exponent), etc. knowing the hvalues in advance reduces temp space requirement from 2^power residues to power residues. Last fiddled with by Prime95 on 20200613 at 23:24 

20200613, 22:27  #98  
"Robert Gerbicz"
Oct 2005
Hungary
571_{16} Posts 
Quote:
The setup, fix the base=3, and let r[i]==3^(2^(i*topK/2^e)) mod N store the residue with space=topK/2^e for i=0,1,2,..,2^e (ofcourse r[0]=3). What would be the proof check say for e=2 ? Easy it is checking: Code:
( r[0]^(h0*h1)*r[1]^h0*r[2]^h1*r[3] )^(2^(topk/4)) == r[1]^(h0*h1)*r[2]^h0*r[3]^h1*r[4] mod N then the right side is easy, because just write r[d+1] for r[d]) You can rewrite the left side in a more compact form, using much less computation: Code:
(r[0]^h0*r[2])^h1*r[1]^h0*r[3] and you can write the right side similarly. Big gain over your trivial way, now counting everything in powering to a 64 bits number: (e/2)*t exponentations and (t1) multiplications. And that makes sense for e=10. And in these costs you can double everything, because you'll do the same in the right side of the equation. ps. e=2 is still small example but you see the idea (r[0]=3 the only small base in the left side) 

20200614, 03:00  #99  
P90 years forever!
Aug 2002
Yeehaw, FL
7×1,021 Posts 
Quote:
Quote:
Now a question. Are we gaining anything by using a 64bit h value? Why not 32 or 16 bits reducing cost to 24,300 or 12,000 PRP iterations. 

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