Integer Factorization as PoW in a Blockchain

[a1call]

So you are proposing that there is a central source who creates semiprimes by multiplying 2 known primes. Wouldn’t such a central entity defeat the purpose of blockchains which as I vaguely understand is a decentralizing concept?
Again asking because I don’t know.
Thank you for your patient.

[VBCurtis]

Originally Posted by factorn

@a1call
....Just find two large primes and multiply them together......

..... Also, semiprimes are composites without known factors in the FACT0RN PoW design.

How, in your design, are you going to know you're using "strong semiprimes" unless you factor them first? Your system is designed to use numbers without known factors, but you don't have any other way to be sure they're semiprimes.

Good planning. You really have this designed well. You can't even make a feature wishlist without contradicting yourself.

[factorn]

@a1call, I strongly suggest you read the whitepaper. You will learn a lot. Who knows? You might even have to drop the "I don't know" on every post you make of how much you will learn. Save yourself a few dozen questions by reading the whitepaper.


@VBCurtis,

How, in your design, are you going to know you're using "strong semiprimes" unless you factor them first?

You are correct. They must be factored first to know they are "strong semiprimes".

Your system is designed to use numbers without known factors, but you don't have any other way to be sure they're semiprimes.

The design is: hash the current block data and the last block data to generate a random number W, allow users to submit any number N = |W+wOffset| -- Where |wOffset| < 16* (number of binary digits of W). You must submit N, wOffset and the smallest factor of N. The system checks if N is a strong semiprime from this, if not reject your submission. Note that the W is generated from a known algorithm, so it need not be submitted, the blockchain will know how to generate it.


See appendix A for a full example.



No one could make such a list when statements are taken out of context, not even Kurt Gödel. I would suggest reading more carefully perhaps?

[a1call]

What is the advantage of:

* Having a source that creates semiprimes from known primes and is subject to hacking, insider-leaks/cheats and otherwise accessing the same known source primes via figuring its generating algorithm/s

Over:

* Using any of the following !PRP's which have remained !factored for centuries and yet are regularly factored by folks around here with gradual progress:

https://www.mersenne.ca/prp.php?show...=1000&max=4000

?

[factorn]

@a1call
It is good to see you move from "I don't know nor have I read the FACT0RN Blockchain whitepaper, but let me ask basic questions" to "I still haven't read your whitepaper nor can I be bothered to, but let me still ask basic questions". Progress? I guess?

* Having a source that creates semiprimes from known primes and is subject to hacking and otherwise accessing the same known source primes via figuring its generating algorithm

Speaking from ignorance is so wonderful, isn't it? If only there were a whitepaper that talked about this stuff? Nonetheless, here we go:
1. known by whom?
2.Technically, what isn't subject to hacking?
3. Try reversing sha3-512, Whirpool, shake2b and Scrypt simultaneously...see how that goes.
4. An attack using hashing is described in the paper along with its cost...its cheaper to factor. Who knows? Reading the whitepaper might help. Just saying.


You have clearly not read this thread in its entirety. That point was addressed previously. Just to name a few: it has a several technical loopholes, security holes, missing properties and impractical impediments. But, who am I? I am just some uneducated idiot on the internet, apparently.

[Batalov]

Originally Posted by factorn

I am just some uneducated idiot on the internet, apparently.

Passive-aggressiveness is a great way to influence people and win new friends
...not.

[a1call]

Well I did try to read the PDF, but 12 pages of the complex subject is too much for my resources.
I am asking genuine questions so please do not take my posts personally.
I did some thinking and what I can figure that may or may not be what you are intending is that:
You have block chains that take random numbers of specific size and test them to be PRP’s. This is done in a distributed network and not a centralized server. Upon finding two such PRP’s per node a/many semiprime/s is/are generated and then are mined/factored by miners. So in effect you are replacing the SHA-256-hash encryption by “encrypting” 2 random PRP’s into a semiprime. That’s what I can figure with my limited knowledge.
Regardless, thank you for your posts.

ETA: I assume the advantage of constructed semiprimes over using existing composites without known factors would be that you can adjust the difficulty level at will.

[factorn]

Originally Posted by Batalov

Passive-aggressiveness is a great way to influence people and win new friends
...not.

If you read this thread and never read past the second page of posts you will walk away with the impression that indeed I am an uneducated idiot. If you add the private messages I receive its get even worse faster than you can say "passive aggressiveness". So, that was an observation.


@a1call
There is no testing of any kind by the blockchain when generating the number around which miners will look for primes. It literally generates a pseudo random number using hashing. That's it. No testing whatsoever. It is the job of the miner to find a strong semiprime around that pseudo-random number generated within the very limited range around it that is allowed. If nothing is found in around the number, generate another pseudo-random number and try again until you do.There is no coordination either for generating the pseurandom number. There is a way in which after you submit all the work, everyone else can confirm that what you have submitted is valid and that you did not defraud the system.

The testing is done after you submit a solution to make sure that your submission is within the limited range you were allowed to search for, that your prime actually divides the generated random number plus the offset you submitted, and that both factors are reasonably prime (50 rounds Miller-Rabin plus Baillie-PSW Primality Test).

The reason it must be this way is that, if anything changes in the block being submitted then the random number generated will change, which means that the solution will change, which means that the block will be rejected, which means people cannot steal rewards, or maliciously change anything unless they mine the block properly....that's why the security of the block is tied to the this process...also why the work must be the same at every difficulty level for long as the computational power of the blockchain remains at that level.

[a1call]

Are you saying that, the “puzzle” to solve by miners, is to find semiprimes within some given set parameters (size, range, factors-separation/offset) by performing factoring and subsequent primality tests, rather than factoring some given semiprimes?

[factorn]

Originally Posted by a1call

Are you saying that, the “puzzle” to solve by miners, is to find semiprimes within some given set parameters (size, range, factors-separation/offset) by performing factoring and subsequent primality tests, rather than factoring some given semiprimes?

Correct. The miner's job is to find semiprimes by way of factoring/sieving within some parameters rather than factoring a given semiprime or simply generating a semiprime.

[chalsall]

Originally Posted by factorn

Correct. The miner's job is to find semiprimes by way of factoring/sieving within some parameters rather than factoring a given semiprime or simply generating a semiprime.

The more I read people's questions, and the answers you (sometimes) give, the less and less I think your idea will ever be useful. To anyone.

Also, it is not useful to get emotional when defending an idea. Particularly when more and more holes are pointed out in said idea.