What about a chip-and-pin card prevents a skimmer from either monitoring or emulating the radio conversation between the card and the terminal (and thus capturing the card number) and another keypad skimmer from capturing the PIN?
It seems to me that the problem is that everything required to conduct a transaction is handed to every merchant and/or untrusted machine of the merchant. (Compare to public key cryptography, where I remain in possession of a private key.) What about chip-and-pin changes that situation?
They also require the pin code to start the process, so you would have to skim that as well.
In addition to this, in the online scenario it can interact with the payment provider's servers to provide security.
The combination of these methods make rapid stealing of EMV cards difficult.
More info here: http://www.emvco.com/download_agreement.aspx?id=653
Because of backward compatibility, the transaction signature generated by the card has to fit into 8 BCD digits, which essentially precludes use of any kind of public key cryptography. Actual algorithm for how signatures are generated and verified is issuer defined and only card issuer can actually verify signatures (terminal just blindly trusts whatever was returned by card).
Public key cryptography (ie. RSA) is used in EMV to verify that card was really issued by claimed issuer (card contains data structure that is signed by issuer's key) and to optionally encrypt PIN sent to card for offline verification (PIN is somehow regarded as super-sensitive by banking industry)
One can certainly imagine better design than EMV (eg. without various implicit trust relationships), but in all, it is pretty reasonable mechanism nonetheless.
Even if these keys was relevant, the important part is that they are public keys, not private keys. You cannot get card's private key from the chip by normal means (ie. without doing something that is classified as attack, be it side-channel, physical inspection or exploiting some firmware bug/backdoor).
Apart from that, making a skimmer that sits between the chip of the card and the contacts of the machine would be much harder to make than the current skimmers. So even if the chip would not sign the transaction but just provide static data if given the right PIN, the situation would be significantly improved.
http://www.cl.cam.ac.uk/~sjm217/papers/oakland14chipandskim....
Chip and Skim: cloning EMV cards with the pre-play attack Mike Bond, Omar Choudary, Steven J. Murdoch, Sergei Skorobogatov, Ross Anderson Computer Laboratory, University of Cambridge, UK
Wireless payment by NFC is also a possibility, but at least with my card, no payments bigger than 25€ can be done through NFC.
I do agree that skimming exists over here as well, a friend of mine got his card cloned once. He'd used it with an ATM located in a very central and visible place, famous for night-time entertainment -- thiefs must have thought drunk people don't pay too much attention to this sort of thing, especially when they've been queuing for a while (which they typically have to, at this location).
Same in Italy and France, last I heard; places where banks are extremely fraud/security-conscious and continuously maintain their infrastructure to guard from these threats.