Public keys in public key cryptography are used to encrypt messages or verify digital signatures. Typically, public keys are represented as a pair of coordinates on an elliptic curve. There are two common representations of elliptic curve public keys: compressed and uncompressed.

An uncompressed public key consists of two coordinates (x,y) that describe a point on the elliptic curve. This representation is called “uncompressed” because it includes the full coordinates of the point, which requires more storage and transmission space. On the other hand, a compressed public key only includes the x-coordinate and a single bit that indicates whether the y-coordinate is even or odd.

This representation is called “compressed” because it takes up less storage and transmission space. Although a compressed public key is more space-efficient, generating it requires additional computation, which may result in slightly slower key generation than an uncompressed public key.

However, both compressed and uncompressed public keys are equally secure, and the choice between them depends on the specific context and the tradeoff between space and computational efficiency.