Question about Digital Signatures in the White Paper

Hey devs and Bitcoin pros! So, in the Bitcoin White Paper, it starts off by saying "We define an electronic coin as a chain of digital signatures" and explains how each owner signs the hash of the previous transaction along with the public key of the next owner. I'm curious if there are any other methods to achieve this without relying on digital signatures? Personally, I feel like it’s pretty much impossible, but I’d love to hear your thoughts. Thanks for taking the time to share your advice! - Tyler

It’s not possible to move any coin without proofing you own that coin and thats what the digital signature does it is the digital signature that actually show that you approved of the transaction and it is link to your private and the public key as well. The digital signature help proofing that you actually own the coin without revealing your private key to the network

If you mean creating address, where Bitcoin on it can be spend without digital signature, it's theoretically possible. You'll need to use P2SH, P2WSH or P2TR and specify how to use. Check REWARD offered for hash collisions for SHA1, SHA256, RIPEMD160 and other for real example.

At the moment, there is no other technology which effortlessly proves the ownership of a coin without using a digital signature, especially in case of bitcoin. Using the digital signature we can publicly prove that we are the owner of a public key without having to give away our private key. Others can verify that we are the owner publicly and hence the bitcoin whitepaper mentions it as a chain of digital signatures since we keep transferring the coin from one owner to other.

In practice, once you remove digital signatures, you automatically lose the cryptographic proof of ownership. The signature is what actually allows the network to verify that the current owner truly authorized the transfer without trusting a third party. So  yeah, it's impossible to move coin without digital signatures.

Is this related to your project about creating a "trustless credit" that can decentralize collaterals? Anyways, if you can come up with a script that utilizes standard Bitcoin "OP_Codes" that doesn't use OP_CHECKSIG/OP_CHECKMULTISIG, then you might be able to implement something that doesn't require a digital signature to spend. However, you'll most likely come up with a non-standard script that will not be relayed by the majority of the nodes. One reference to start your research: developer.bitcoin.org/reference/transactions.html#opcodes In case it's related to the project but you can consider signatures; Check OP_CLTV or OP_CSV instead (BIP-0065 / BIP-0112).

It is not from my trustless credit idea, as I was figuring out if there would be a way of doing transactions without digital signatures, so attackers using Shor's algorithm through quantum computers can't derive a private key from an on-chain public key and then produce a valid signature for a competing spend. My ideas have changed. I am currently looking into building an Offline e-cash system allowing payment transactions to happen digitally, anywhere from peer to peer, without the use of the internet. Because Bitcoin fundamentally relies on the internet for its daily operation. Imagine this scenario: with everything going digital. The fear of the Internet ever shutting down increases, and everyone gradually loses control over their money because everything is online and everything relies on the Internet. Having an Electronic/digital coin acting as the common medium of exchange, allowing peer-to-peer transactions to happen offline without the use of the internet or any financial institution.

To spend a coin, you need somehow to provide a proof of ownership, without revealing the private key. This is what a digital signature is. I'm not aware of any other cryptographic scheme that can be used to prove that you own the public key, or the pre-image of a hash, without revealing the pre-image or the private key of the public key. Why are you asking this question? Perhaps you have another question and you're a victim of XY Problem.

If it's for a new coin, it shouldn't be constrained by Bitcoin's consensus rules and policy (unless it's a Bitcoin fork) So the question should be specific so people wont take Bitcoin in consideration when posting their replies. And it should be posted in the correct board. But if it's for Bitcoin, proving ownership without the use of signature wont work, as mentioned by multiple users here. If you want to see some of the Dev's approach to counter the theoretical future QC with high enough qubits; You may consider following the Bitcoin mailing list or other bitcoin-dev discussions, there are links to those here: bitcoin.org/en/development