i'm studying both Bitcoin and Ethereum from how it is implemented and how it's used because I'm gonna be making a thesis project out of this. Would you please explain to me the difference of these two or are they even related? I know that digital signatures are a way to know that the transaction is legit using the private key in Bitcoin. How does that happen in Ethereum? Thank you in advance!
Bitcoin and Ethereum both use a blockchain, which provides a chain of transactions that are usually validated using digital signatures.
In Bitcoin, a transaction essentially consists of a reassignment of funds. You say that funds that were previously controlled by public key X can now be instead controlled by public key Y, as proved by a valid digital signature using the private key Y. It is also possible to specify other conditions; For example, you may require signatures from multiple keys, or specify a minimum date before which the funds cannot be spent.
This chain of transactions forms a shared database, or
"state"; In Bitcoin, it is a database of which funds are assigned to which keys (or more precisely, which sets of conditions, since not all the conditions involve keys.) Each transaction alters the
state, which can affect whether the next transaction will be valid or not.
Ethereum does the same, but it allows you to write arbitrary data to the
state. You can assign funds based on complex sets of conditions, and you can use it to manage data other than what keys or sets of conditions control which funds. As in Bitcoin, it is usual to use a digital signature as one of the conditions for moving funds or writing to the database.
A smart contract consists of one of these sets of conditions according to which funds or data are controlled. In Ethereum, and to a lesser extent in Bitcoin, these conditions can be arbitrarily complex computer programs, as well as simple digital signature requirements.