How can transactions be verified without the private key? Trying to get my head around her royal Bitcoin here...

I understand that blocks of transactions are broadcast to the network, and that miners verify that the BC is 'spendable' by trawling the blockchain and following the wallet address's transaction history (or at least I assume that's how it works).

But how does one actually verify that the BC transaction has been signed by it's owner when the miners don't have access to the private key? To put it simpler, how can verification take place without processing both the public and private keys?

I'm probably misunderstanding PKI encryption, but (say) with SSH, the private key would be on a trusted server and verification would take place on that server. How can that possibly work in a distributed network?
Bitcoin transactions are not encrypted, they are cryptographically signed.

You can use a public/private keypair 2 ways:
(massive simplification warning)


Encrypt a message using a public key and then decrypt it with a private key
Sign a message using a private key and validate the signature with the public key


The second method is the one that is used by Bitcoin. A message is placed in the distributed ledger that bitcoins have been sent from X to Y (and typically Z), and signed by the private key of X. X is the source bitcoin address, Y is the destination, and Z is the change address.