Can private keys change once the public key (address) is created?
No, you cannot. Once a public key is created, there's no way to change its private key. However, you can create a new account for the funds you own.
Ethereum, like Bitcoin, uses elliptic curves(ECs) to generate private/ public keys pairs. This might sound really complex, but, at the core, ECs are just functions which look like this:
Like the Lululemon logo turned horizontally!
Q are arbitrarily chosen points.
R is generated by playing "billiard" on the function: you draw a line between
Q, it hits
-R and then you flip the point on the x-axis. You do this many many times in a row and, lo and behold, given only a final point
S there's no way to go back to
Q (at least with the hardware we have today).
Two important properties make this possible:
- Points are mirrored on the x-axis
- Any line can intercept the function's graph at exactly 3 points*
As different point sets lead to different lines, hence different "bounced" points on the function's graph, there is no way to create more than one private key for a public key.** For a deeper understanding of the concept, I'd strongly recommend reading this article.
* Perpendicular lines on the x-axis intercept the function's graph at two points, but there is an extra point
O, ubiquitously called "the point at infinity"
** Note that this is an area of research though, and collisions are being discovered all the time, as mathematical research continues indefinitely.