Who is the certification authority in Bitcoin?

Depending on what function of the certification authority you are looking for, Bitcoin doesn't need one, or the blockchain does it.

Identity in e-banking vs identity in Bitcoin network

Electronic banking relies on the communication between bank and customer being secure which is what they use encrypted protocols for. They don't use either hashing, nor private and public keys in any similar fashion as Bitcoin. Actually, when you order a payment through e-banking, you have to reveal all the secrets to the bank to authenticate yourself: E.g. you put in your user name, your password, and then a specific one-time code as requested by the bank, or when using a credit-card, you give name, credit card number and security code. As these pieces of information would be sufficient to hijack the payment in a man in the middle attack, communication needs to be secure and encrypted. To that end, a certification authority gives out "passports" that allow you to make sure you're talking to the right entity.

On the other hand, communication in Bitcoin is authenticated by the content of the message itself. When you order a payment, it includes a signature that could only have been created by the owner of the address that held the money previously. Nobody can change the message, because the signature would be invalid for any other message, and they cannot produce another valid signature without having access to the private key. The secret is not revealed to order the payment. Therefore, it is not necessary to encrypt communication within the network, and also there is no need to certify the identity of network participants. One can tell directly from the message whether it is valid or not, making the identity of the source of the message irrelevant.

Authenticity of payments in e-banking vs Bitcoin network

In e-banking only the bank and you know your balance. Therefore, when you order a payment, the bank will check their ledger and confirm the payment.

In Bitcoin, everyone can check whether a balance is available to be spent. As explained above the transaction order itself can be checked for validity by every participant, so it is impossible to spend money that isn't yours. The blockchain keeps track of the balances, therefore becoming the ledger everyone referring to when checking payments. Yet, the blockchain is extended in a decentral process, so while the blockchain is central to the network, it is maintained decentrally.

Where e-banking and Bitcoin are similar

The one thing that still can be attacked in the same way in Bitcoin as in e-banking is the other side of the payment: People can try to fool you into paying something that you didn't intend to pay for. You still need to figure out where to send money. That's where Banking and Bitcoin have the same vulnerability to phishing sites. In fact, Bitcoin is a bit at a loss there, because once you've sent the money it's gone, while you may have a recourse through your bank by having them reverse the payment.