Nostr signs events with BIP-340 Schnorr over the secp256k1 curve. Each signature is 64 bytes. Verifying one is cheap enough that every client can verify every event it receives, which is the property that makes the whole "relays cannot fake events" story work.
Schnorr is interchangeable with ECDSA for this purpose, but has two nice properties: signatures are deterministic given a nonce scheme, and signatures are additive, which opens the door to more elaborate constructions later (multi-sig events, adaptor signatures) without changing the event format.