If this occurs, then Particular person B will be capable of spend individual A’s bitcoins. Nonetheless, there are solely two methods this could occur:
a) Particular person B generates the identical keypair (non-public key) as individual A
or b) Particular person B generates a special keypair, which (public key) hashes to individual A’s deal with (a hash collision)
Check out the specification for at bitcoin deal with: https://en.bitcoin.it/wiki/Technical_background_of_Bitcoin_addresses
A Bitcoin deal with is a 160-bit hash of the general public portion of a
public/non-public ECDSA keypair
For “a” to occur, individual B would wish to interrupt “secp256k1”.
I’m no professional on this area, however from what I can discover on bitcointalk.org, then the “power” of that is 2^128 bits. And in the event you’re questioning how robust that’s, then search for the video “Exhaustive search assaults” from Dan Boneh. 11 minutes within the video he says “something that is greater than 2^90 is taken into account sufficiently safe” (its about attacking 3DES, which is a symmetric block cipher so I am undecided it truly apply to secp256k1, however I actually don’t have any higher argument for why 2^128 is “so safe that you simply will not by no means, ever, ever generate the identical key as another person“
And for “b” to occur, you would wish to discover a collision on RIPEMD-160(SHA-256(pk)). So far as I do know, then neither RIPEMD-160 nor SHA-256 is thought to have any vulnerabilities to hash collision assaults. So by some means breaking each or randomly technology a key which hashes is strictly the identical as one other bitcoin deal with, is extremely unlikely.
There’s additionally an opportunity for you pc to catch on fireplace, and a number of the supplies to soften collectively right into a lotto coupon with profitable numbers on (and a sound barcode), but it surely simply will not occur due to the prospect is so unbelievably small (it is the identical with the “click on and generate one other individuals bitcoin deal with“).
EDIT Woops, one essential factor: This all assumes that every one bitcoin addresses are correctly generated utilizing “true random”. All brain-addresses and addresses generated utilizing a nasty PRG, may be straightforward to search out by both utilizing a flaw within the PRG or exploit the (flaws within the) human mind.