ECDSA question for profs?

[RentGPU]

I am a big fan of cryptocurrency and bitcoin specially , so i am trying to read about the way it works and how secure it is , as i see the way of generating keys in btc is so simple and hard at same time , how comes i can generat alot of keys a even a key for every transaction and no one will collide with other ppls keys , i read about ECDSA curve , but i have a question to ask , as i understand that the publickey=privtkey*G , and we know the G and the publickey how come this equation can't be solved for the privtkey , and how it's only one way (one-way equations can't be in mathematics)....any good information will help me to understand more.....thanks in advance

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[DannyHamilton]

The quick answer is that there is a set of formula that can be used for point multiplication so that a computer can quickly compute privateKey*G.  However, there is no known set of formula yet for point division to quickly compute publicKey/G. It is not even known in mathematics if it will be possible to find such a set of formula for point division.

I don't have time right now to go into much more detail than that. Hopefully someone else will stop by to demonstrate why it is difficult with currently known maths.

[AGD]

The quick answer is that there is a set of formula that can be used for point multiplication so that a computer can quickly compute privateKey*G.  However, there is no known set of formula yet for point division to quickly compute publicKey/G. It is not even known in mathematics if it will be possible to find such a set of formula for point division.

I don't have time right now to go into much more detail than that. Hopefully someone else will stop by to demonstrate why it is difficult with currently known maths.

This one is quick and easy: https://www.youtube.com/watch?v=ZloHVKk7DHk&t=3s

edit: The difficulty to compute publicKey/G is a little bit like root calculation. It is easy to find out the numer in one direction, but a lot more difficult to calculate it in the other direction. calculating 3.8² is pretty easy (3.8*3.8=14.44), but to find out the root of 14.44 you'll need a lot more computation.

[Prodeskhp]

If you reverse ECDSA you are awarded with 1 million dollars

https://en.wikipedia.org/wiki/Millennium_Prize_Problems

P vs. NP is mathematical problem for which you are guarented one million dollar.