How does bitcoin work? (mathematical prespective)

[RogeRsIII]

Hey I am kindy new to all of this about bitcoins, cryptology and programming but I´m researching how bitcoins work through more of a math view about all the mathematical algorithims and equations used. I know about ECDSA in digital signatures and have some idea of how bitcoin mining works, so can somebody help me know about what is used for bitcoins and how.

[DannyHamilton]

Hey I am kindy new to all of this about bitcoins, cryptology and programming but I´m researching how bitcoins work through more of a math view about all the mathematical algorithims and equations used. I know about ECDSA in digital signatures and have some idea of how bitcoin mining works, so can somebody help me know about what is used for bitcoins and how.

• Elliptical Curve point multiplication: To generate a public key from a private key
• ECDSA digital signature: To prove authorization to transfer control of funds
• RIPEMD160 and SHA256: To generate a public key hash from a public key
• base10 to base58 conversion: To generate a bitcoin address from a public key hash
• SHA256(SHA256(blockheader)): To mine a bitcoin block
• Algebraic addition, subtraction, multiplication, division, and comparison: To calculate balances from the list of unspent transaction outputs, increment nonce, calculate block reward, etc.

and I'm not sure, but I think...

• AES256: To encrypt private keys in the Bitcoin Core wallet

That's about it from a high level.  Obviously this is all just a computer program, which means that almost everything is a set of machine code telling the computer which binary values to compare, copy, increment, decrement, or any of the other instructions available in the processor, but I doubt that's what you're talking about. I think there are also some checksums and parity calculations in the network communications protocol, but I doubt you're asking about that either.

[RogeRsIII]

Hey I am kindy new to all of this about bitcoins, cryptology and programming but I´m researching how bitcoins work through more of a math view about all the mathematical algorithims and equations used. I know about ECDSA in digital signatures and have some idea of how bitcoin mining works, so can somebody help me know about what is used for bitcoins and how.

• Elliptical Curve point multiplication: To generate a public key from a private key
• ECDSA digital signature: To prove authorization to transfer control of funds
• RIPEMD160 and SHA256: To generate a public key hash from a public key
• base10 to base58 conversion: To generate a bitcoin address from a public key hash
• SHA256(SHA256(blockheader)): To mine a bitcoin block
• Algebraic addition, subtraction, multiplication, division, and comparison: To calculate balances from the list of unspent transaction outputs, increment nonce, calculate block reward, etc.

and I'm not sure, but I think...

• AES256: To encrypt private keys in the Bitcoin Core wallet

That's about it from a high level.  Obviously this is all just a computer program, which means that almost everything is a set of machine code telling the computer which binary values to compare, copy, increment, decrement, or any of the other instructions available in the processor, but I doubt that's what you're talking about. I think there are also some checksums and parity calculations in the network communications protocol, but I doubt you're asking about that either.

Thanks man this actually helped me.

[YarkoL]

SHA256(SHA256(blockheader)): To mine a bitcoin block

Sha256d is also used in constructing merkle tree of transactions.

hashA = SHA256(SHA256(transactionA))
hashB = SHA256(SHA256(transactionB))
hashAB = SHA256(SHA256(hashA,hashB))

These equations describe individual nut and bolts in the system so to speak..
But is there any formalism that can describe how the network
arrives at consensus?

[belcher]

This is an excellent resource for developers / programmers. https://bitcoin.org/en/developer-guide

[kn_b_y]

I would add - familiarise yourself with Adam Back's proof of work scheme, hashcash.

I still find it incredible that someone can produce a small block of data and a number and then by using that information alone they can prove to you that they had access to a year's supply of supercomputing resources.

[vincentvincent]

I read this book and I found it incredible interesting to read and learn how bitcoin works:

https://freedom-to-tinker.com/blog/randomwalker/the-princeton-bitcoin-textbook-is-now-freely-available/

[Karartma1]

interesting thread, welcome roger. I'm no math expert but I found Andreas Antonopoulos' book Mastering Bitcoin - Unlockin Digital Cryptocurrencies very helpful.
https://www.bitcoinbook.info/