Bitcoin public key — why do we now have a compressed and uncompressed model?


My understanding is that the general public key can begin with 04 if it is uncompressed, or 02(x-coor) or 03(y-coor) if it is compressed.

What is the function of this?

Larger entropy as we are able to have a bigger public key if it is uncompressed?

And if that is certainly the case, why would you desire a compressed public key?

Would not or not it’s safer to make use of the bigger one?

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