20200624, 03:49  #188 
"Pavel Atnashev"
Mar 2020
37_{10} Posts 
It's a model to calibrate your hashes against.
Last fiddled with by patnashev on 20200624 at 04:27 
20200624, 19:48  #189 
P90 years forever!
Aug 2002
Yeehaw, FL
1101101100101_{2} Posts 
Some data (now using the attached sliding window exponentiation routine)
Proof level 8: Proof generator does 15489 or 20632 squarings (48bit vs 64bit hash) Server does 1080 or 1414 squarings Proof verifier does 390625 squarings (assuming 100,000,000 exponent) Proof level 9: Proof generator does 31485 or 41925 squarings (48bit vs 64bit hash) Server does 1207 or 1577 squarings Proof verifier does 195312 squarings (assuming 100,000,000 exponent) From a total system point of view, we can see that proof level 10 is currently optimal. Compared to level 9, generator does 42K more squarings to save the verifier 97K squarings. If 800 PRP tests a day are reported to the server, I think it can handle 1.2M squarings a day. My quad core Haswells can generate 10 million squarings a day. For me, at proof level 9, the 10500 squarings saved for 48bit vs. 64bit hash represents 1/2 PRP test a year. 
20200624, 20:02  #190  
P90 years forever!
Aug 2002
Yeehaw, FL
7,013 Posts 
Quote:
If the future weakness is a reduction in brute force effort, then a longer hash key is our safe guard. So let's rule out 32bit hash values. If the future weakness revolves around a small hash value, let's thwart them by making all hash values >= 2^32. If the future weakness results from some rootofunity issue, lets rule out multiples of the PRP base 3. I'd remove multiples of two just for good measure. Removing hashes with more small primes is also possible. In total, this does not greatly reduce the search space for the brute force attacker. I'm happy with 48bit or 64bit (or anything inbetween!). When eliminating 0 mod 3 hashes, the scheme should not be a simple "add 2" as that would favor 2 mod 3 hashes. Further comments? Time to come up with the concrete algorithm? Last fiddled with by Prime95 on 20200624 at 20:09 

20200624, 20:39  #191  
"Will Edgington"
Nov 2010
Utah, USA
2^{3}·3 Posts 
Avoiding multiples or 2 or 3 in hash values
If you just want to eliminate values that are multiples of 2 or 3:
Code:
int add[2*3] = { 1, 0, 3, 2, 1, 0 }; value += add[value % 6]; To avoid possibly exceeding 2^64, the array value could be subtracted instead, sometimes leading to a final value < 2^32. If you also want to eliminate multiples of 5, expand the array to 2*3*5 appropriately.  Will Quote:


20200624, 21:25  #192  
Just call me Henry
"David"
Sep 2007
Cambridge (GMT)
2×3×13×73 Posts 
Quote:


20200624, 22:54  #193  
"Mihai Preda"
Apr 2015
2^{7}×3^{2} Posts 
Quote:
I propose we use simply SHA3256 truncated to 64bits for the "h" exponents. The chaining of the hash OTOH is done using the full SHA3256. Maybe we should also present our "simple" hash scheme to the larger crypto community and ask them for an attack? 

20200625, 14:14  #194 
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
4209_{10} Posts 

20200628, 05:48  #195 
"Pavel Atnashev"
Mar 2020
37 Posts 
We've started searching for GFN15 Mega (b^32768+1, 1M digits). b is a hundredbit number, but Pietrzak VDF works just fine with such numbers.

20200713, 15:27  #196  
"TF79LL86GIMPS96gpu17"
Mar 2017
US midwest
1000001110001_{2} Posts 
Quote:
The LL test goes as before, but sqrt(p) residues are saved along the way? What is Z? Notation of a ring? What is the process by which those sqrt(p) saved residues are processed to produce a verification of correctness? if it works, this seems to me to offer a more convincing proof of correctly finding a Mersenne prime, than matching zero residues in multiple runs. At the cost of more programming effort to adopt it. Last fiddled with by kriesel on 20200713 at 15:42 

20200715, 08:34  #197 
"Oliver"
Sep 2017
Porta Westfalica, DE
3^{5} Posts 
Hi, I have activated the proof feature on my run of M215856353, are you interested in the data? If yes, I'd upload it. It was done using v6.11325g7c09e38 with proof 10.

20200715, 12:14  #198  
"Mihai Preda"
Apr 2015
2200_{8} Posts 
Quote:
./gpuowl prp 215856353 proof 10 which should restart the exponent 215856353 from the last checkpoint which is very near 100%, run the few last iterations, and regenerate the proof in the new format. The proof can't be uploaded yet, so you'd still need to keep it around for a bit. 

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