Any new cryptographic functions?

[Impossible27]

It has been 5 months since I started a project of "a better coin". I studied blockchains, DAG, PoW, PoS (and other variations), DHT, ZK-Proofs and other things. until I reached a local minimum deadlock: a fee-less Bitcoin with no PoW for blockchain and some other things (but that is not what im trying to explaing, after all, my network won't be what you guys are thinking).

the question is: are there any new cryptographic functions?

if someone knows something (like some new functions) that I probably should know, i would really appreciate that 

[pooya87]

a fee-less Bitcoin with no PoW for blockchain

That sounds like something the fake "better bitcoin" shitcoins say to be honest.
A bitcoin-like network with 0 fee means the spam becomes free. Not cheap, but free.
Bitcoin has already suffered multiple prolonged spam attacks and that's despite having a fee market that goes up as the spam intensifies and makes sustaining the attack that much more expensive.

So I'm very curious to know how you plan to prevent flooding a network with 0 fee with spam transactions.

the question is: are there any new cryptographic functions?

A cryptographic function for which part?
For hashing transactions (txid, sighash, etc.)?
For mining? You said it won't have PoW so what's the point of it?
For digital signatures (ie. asymmetric cryptography)?
Something else?

[Impossible27]

So I'm very curious to know how you plan to prevent flooding a network with 0 fee with spam transactions.

PoW. PoW instead of fees. if you know why most of decentralized coins use fees instead of PoW (PoW in bitcoin makes every block appears in around 10 minutes. why not ~10 seconds for transactions?)

A cryptographic function for which part?

I wasn’t curious about any specific function, anything different from blockchains, new ways to validate data (other than Merkle trees), etc. they are all valid responses.

and some other things that I think would be important:

I was trying (and am still trying) to make a decentralized coin surviving with 90% of nodes offline and still be fast, dividing the network into something I called "entities" (a small group of K nodes).  without any type of blockchain (history) and many small merkle-trees (state).
when I started this project, I was like "damn, why everyone makes copys of bitcoin? I will try to make something different"

english isn’t my first language, so I may not always be clear

[RGBTC]

PoW. PoW instead of fees. if you know why most of decentralized coins use fees instead of PoW

I don't quite understand the point of this statement; do you mean I have to include my own transaction in a block to send Bitcoin?

(PoW in bitcoin makes every block appears in around 10 minutes. why not ~10 seconds for transactions?)

This has already been answered above.

I was trying (and am still trying) to make a decentralized coin surviving with 90% of nodes offline and still be fast, dividing the network into something I called "entities" (a small group of K nodes).  without any type of blockchain (history) and many small merkle-trees (state).

Interesting. So, what is the settlement process logically?
(From my limited understanding) when those nodes come back online with a different state, how do you validate within ~10 secs that the node's state wasn't corrupted while it was offline. For instance, by a double-spend?

[pooya87]

So I'm very curious to know how you plan to prevent flooding a network with 0 fee with spam transactions.

PoW. PoW instead of fees. if you know why most of decentralized coins use fees instead of PoW (PoW in bitcoin makes every block appears in around 10 minutes. why not ~10 seconds for transactions?)

That is an interesting idea. After all the idea behind PoW (originating in Hashcash) was to limit spam and DoS attacks. The "user" would perform a "work" before submitting a request.

But here is one issue I can think of if implemented: You would need to keep the work simple so that any user on any device can perform it in a short amount of time. So for example someone wanting to send a tx using their phone can do it with a click and doesn't have to overheat their phone and wait minutes to compute the hash.
But at the same time keeping it simple means anybody with a large computing power (eg. a parallelized setup using GPU(s)) can compute orders of magnitude more work and flood the network with spam transactions.

If you dynamically change the difficulty, then it still degrades user experience during high traffic times (eg. price goes up and people want to move their coins around) or during spam attacks. So what would be the difference between this and fee market?
Any other approach to prevent?

when I started this project, I was like "damn, why everyone makes copys of bitcoin? I will try to make something different"

Based on this alone I can say that you project is already so much better than a large number of altcoins out there.
Keep it up.

[athanred]

PoW instead of fees.

It can be done on top of Bitcoin. For example: https://bitcointalk.org/index.php?topic=5551080.0

If you dynamically change the difficulty, then it still degrades user experience during high traffic times

Of course. By using OP_SIZE, you can make it more or less difficult to transact, by restricting allowed signature sizes. And by connecting it with OP_CHECKSEQUENCEVERIFY or OP_CHECKLOCKTIMEVERIFY, a smaller signature can be confirmed faster, than a bigger one.

So what would be the difference between this and fee market?

Instead of fee market, there would simply be a Proof of Work market. And then, you will have "miner-only" coin, because making transactions will be possible only by miners. Regular users will be always left behind, if your coin will be successful. And then, it will be just like having a decentralized mining pool, where the strongest shares are always published on-chain, and transactions between miners is the only traffic, because regular users will have too weak hardware to actually transact.