Context concerning the ECDSA nonce: Questions on producing a random quantity for ECDSA

Are these nonce values public or personal? I perceive that they’re generated to be totally different each transaction and by no means reused, however until I am mistaken I can not discover any reference to them being a public a part of a bitcoin transaction. Due to this, I do not perceive how a transaction may very well be verified if a secret nonce was used, would this not obscure a big a part of the message being signed and create un-verifiable information from somebody who would not personal the personal key? Or is it that the worth is actually public, if public the place are they in a transaction? Whether it is personal how are verifications completed?