Topic: Bitcoin is existentially unforgeable (Read 135 times)

This is one "algorithm" called elliptic curve cryptography. The 3 you mentioned are the components.

Secp256k1 is the name of the curve that bitcoin uses not the algorithm.
Bitcoin also uses ECSDSA (Schnorr signatures) after Taproot activation.

It has nothing to do with hash function and the algorithm is referred to as asymmetric cryptography not symmetric and also the security is calculated based on the solutions for ECDLP.

Not being able to reverse the private key to public key operation has nothing to do with ECDSA which is the digital signature algorithm.

That's a weird sentence. The "message" can have arbitrary length, the hash used in signing is 256 bit.

Digital signatures has been able to prove the authenticity to digital documents and it's true ownership. In digital signatures only the real signatory can make a signature but anyone who sees the signature can attest that it is valid. This signature are tied to a specific document which makes it unique in that no one else can take this signatures and attach it to a random document.

The Idea of Bitcoin and digital signature using cryptography has made transactions trusted using three major algorithms (Private keys, Public Keys and a signature). The private and public key pairs uses a cryptographic method to generate keys that takes  a key size to generate this pairs.

The signature takes a message usually a transaction for Bitcoin and the private key as input and then outputs a signature for the transaction using the Private key of the address. This gets verified using the public key, the signature and the message making it hard to forge.

Bitcoin specifically uses Elliptic Curve Digital Signature  (ECDSA) more specifically "secp256k1" estimated to provide 128 bits of security what this means in essence is that it is difficult to break this algorithm by performing 2¹²⁸ symmetric-key cryptographic operations such as invoking a hash function. This curve is so unique to Bitcoin that after Satoshi chose it in the early specification of how individuals funds get managed it became difficult to change.

ECDSA is a good tool for randomness because it makes guessing the private key from it's corresponding public key difficult and impossible. It can take a message of 256 bits long and this doesn't limit the amount of messages it takes has input because messages get hashed before they get signed which means any size of message can be efficiently signed.

This has made Bitcoin tied to a private key secure and personal as long has it remains on that address and if the private key gets missing along the line the coin remain lost forever.