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Comment by tromp | Hacker News Reader

Does the gridbach server trust all submitted results to be correct, or can it somehow verify them (much faster than the outsourced computation) ? I managed to contribute 2B verifications in a few minutes.

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I had a brief look at the network traffic and code. The network communication is very simple:

To request a new batch:

  POST https://jqarehgzwnyelidzmhrn.supabase.co/rest/v1/rpc/get_job
  apikey: ...
  authorization: Bearer ...

  {"_client_hash":"..."}

returns something like

  {
    "jobId": 755344,
    "message": "get_job() succeeded, got jobId: 755344 as a new one"
  }

which means the client should check 4000075534400000000-4000075534500000000.

Once done:

  POST https://jqarehgzwnyelidzmhrn.supabase.co/rest/v1/rpc/put_job
  apiKey: ...
  authorization: Bearer ...

  {"_client_hash": "...","_job_id": 755344,"_status": 1,"_elapsed_time": 19.54,"_p": 3463,"_q": "4000075534448687929"}

Here, _client_hash is generated by wasmHash(`{"method":"Hash"}`) in /js/worker.js (yes, the payload is a fixed string), and while I didn't try to disassemble the wasm, one can pause execution and repeatedly call wasmHash() to observe it's basically a TOTP that changes every 10s, so it doesn't carry any mathematical information.

Therefore, all the info that can be used for verification on the server is a single pair of _p and _q adding up to one number in the entire range. That's the extent of the verification.

One can of course patch the code to check a single number before reporting that the entire range has been checked. Pretty sure it's impossible for the server to detect that.

Correct me if I made a mistake somewhere.

Edit: On second thought, maybe the specific number reported back is deterministically chosen in a way that relies on finishing all the checks in the range, and thus can be compared with other reported results for the same range?

Even in that case, the server can't verify the work without repeating it. mersenne.org hands out a double checking job about 8 years later presumably to thwart determined attackers.[1]

[1] https://www.mersenne.org/various/math.php

Yeah, I mean what OP doing is statistically searching for counterexample at worst, but without verification about the completeness of the range. Only if we assign jobs randomly and multiple times, we may believe in the truth about the whole range, at least under the assumption, that there is enough people and no big enough attacker.

Thanks for giving it a try. The Gridbach server only accepts computed result sent from my component.

But how do you make sure the user actually runs your component without any modification?

All I can tell here is that I do certain level of valication on server side. As one of the goals of this project is to popularize the fun of mathematics among the general public, I think I would need to avoid a open network configuration to strictly conduct academic verification. The algorithm itself is publicly opened, so anyone can verify the computation step is correct or not. https://github.com/nakatahr/gridbach-core

zk-SNARKS maybe?

For demonstrating verification of a conjecture, surely you can do much simpler things than a zero-knowledge proof: Send one of the primes.

It would still take a nontrivial amount of computation to do all the verification afterwards. Back of the envelope calculations suggest it should less than 100x longer to find the two primes than to verify them.

It'd be neat to do the verification in the same manner by redistributing one client's results to another, therefore obtaining a proof modulo client collusion.

I am curious about alternatives or solutions in such a setting / context.

Say smaller prime is less then 10,000. Then this one or two Byte per Nummer. E.g. 100 Mio number is already 100mb or

Never trust the client. You must do a full verification. IIUC from another comment, you only ask the client to return the interval they tested and some token to ensure the server send them that interval.

You must ask for each number in the interval the two primes and a Primality certificate for each prime. https://en.wikipedia.org/wiki/Primality_certificate

The idea is that it's very hard to find the two primes and it's very hard to prove that they are actually primes. But if the client send you both primes and send you each primality certificate, then the verification is very fast. Also, you can store that info so people can see it.

Thanks. Your advice is really helpful.

That sounds interesting. How does that verification work?

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