Quote from: DannyHamilton on Today at 02:49:46 PM

EDIT: I say too much and take too long to type. o_e_i_e_o has responded with mostly thee same response, only faster. I'll leave this here just in case anyone finds that it adds any interest.

Quote from: cajancharles on Today at 10:24:56 AM

why every bitcoin public address have 2^96 private key

Because with a version 1 P2PKH address there are approximately 2²⁵⁶ unique private-public key pairs. An address is based on a RIPEMD160 HASH of the public key (actually a RIPEMD160 HASH of a SHA256 HASH of a public key) resulting in 2¹⁶⁰ unique version 1 P2PKH addresses.

2²⁵⁶ keys divided by 2¹⁶⁰ addresses equals an average of about 2⁹⁶ private keys PER address.

Quote from: cajancharles on Today at 10:24:56 AM

and how can i find my (2^96- 1) private key for my bitcoin public address?

To find just 1 of those private keys...

Acquire access to enough computing power to calculate addresses from 10¹⁰ private keys per second.
Run that computing power continuously for (on average) 2.3 * 10³⁰ years

To find ALL of those private keys...

Acquire access to enough computing power to calculate addresses from 10¹⁰ private keys per second.
Run that computing power continuously for (on average) 1.8 * 10⁵⁹ years

Alternatively...

Study advanced mathematics
Become the top expert in the entire world in the mathematics related to ECDSA, SHA256, and RIPEMD160
Discover a mathematical weakness that nobody else in the world has ever discovered related to those algorithms
Use that mathematical weakness to calculate your private keys

Quote from: cajancharles on Today at 10:24:56 AM

since Elliptical curve private key and public key has 1:1 ratio, and that public key is encoded & hashed with some operation to get bitcoin public address.

Correct.

Quote from: cajancharles on Today at 10:24:56 AM

also is it possible to encrypt message with bitcoin public address and then decrypt with private key which is generated by ECC.

Don't bother. It's not worth the effort. There are better systems to encrypt and decrypt messages. I believe that some have created some software to do it (with the public key, it can't be done with the address), but I wouldn't use any of it.

You already know that its software that find keys with the public key

https://bitcointalk.org/index.php?topic=5244940.0
https://bitcointalk.org/index.php?topic=5304368.0
https://github.com/JeanLucPons/Kangaroo
https://github.com/JeanLucPons/BSGS
https://github.com/WanderingPhilosopher/BSGS